Department of Mechanical July 1970 AN APPROXIMATE ......Department of Mechanical and Industrial Engineering ME TR JPL 952593 July 1970 AN APPROXIMATE THEORY OF IMPERFECT MODELING WITH

Department of Mechanical and Industrial Engineering

ME TR JPL 952593 July 1970

AN APPROXIMATE THEORY OF IMPERFECT MODELING

WITH APPLICATION TO

THE THERMAL MODELING OF SPACECRAFTS

by

B T Chao and M N Huang

FINAL REPORT (

to

VJET PROPULSION LABORATORY

California Institute of Technology -

Contract No 952595

University of Illinois at Urbana-Champaign

Urbana Illinois 61801

Y [CES20NU)TIHR

O (PAGES) (ODE)

(NASA CR OR TMX OR AD NUMBER) (CATEGORY) (

N70-20517 -20548

SPACE PROCESSING AND MANUFACTURING

George C Marshall Space Flight Center Marshall Space Flight Center Alabama

5 February 1970

0

g 0

00-0- 001 0

Distributed to foster serve and promote the nations economic developmentand technological advancement

NATIONAL TECHNICAL INFORMATION SERVICE

US DEPARTMENT OF COMMERCE

0

This document has been approved for public release and sale

2N TECHNICAL REPORT STANOARD TITLE PAGE

O GN ZAT N t0-53993

RPRT 1y9N AS A TE CHN IC A L TLTE AND SUBTITLE ME O A D M4 PROCESSING AND MANUFACTURING February 5 1970MEMORANDUM SPACE ORGANIZATION6 PERFORMING C(DE

ORGANIZATION aNASA TM X-53993 7 AUTHOR(S) S PERFORMING REPoRr

9 PERFORMINGOROANIZATIONSAME AND ADDRESS I0 WORK UNIT NO

Manufacturing Engineering Laboratory 11 OR GRANT CONTRACT NO George C Marshall Space Flight Center

DMarshall Space Flight Center Alabama 35812 i TYPE OF REPORI amp PERIO COVERED

12 SPONSORINGAGENCYNlAMEAND ADDRESS Technical Memorandum

14 SPONSORING AGENCY CODE

IS SUPPLEMENTARY NOTES

I ABSTRACT

This publication contains the presentations from the Space Processing and ManufacturingSPACE PROCESSING AND MANUFACTURING necNg held at MISFC Huntsville Alabama October 21 and 22 1969

Contatas consist of the opening keynote address by Dr von Braun Director Marshall Manufactaring Engineering Laboratory Space Flight Center thirty-one presentations and the closing remarks by Dr M P Sebel

Manufacturing Engineering Laboratory MSFC In addition there is a complete listingFebruary 5 1970 of the speakers showing their affiliation mailing addresses phone numbers biographical

N70 51 ktles and alist of attendees

I O o~ 0t

NASA

George C Marshall Space Flight Center nama I7 K WORDS IDoOISTRIBUTION STATEMENTM atsball Space tlght

NA1IONatTECHN- IC 1I SECURITYCLASSIF(2I021 120 SECURITYCLASSIF0R1 1N F PAGES 22 PRICE

INIORMATION SERVICE ___________________________ _________

Department of Mechanical N7(-3q4 A and Industrial Engineering



WITH APPLICATION TO


by

BT Chao and M N Huang

FINAL REPORT

to

JET PROPULSION LABORATORY

Contract No 952593

This work was performed for the Jet Propulsion Laboratory Califorshynia Institute of Technology as sponsored by the National Aeronautics and Space Administration under Contract NAS7-100



REPRODUCEDBYNATIONAL TECHNICAL INFORMATION SERVICE

US DEPARTMENT -

OF COMMERCE_WRINGFIELD_VA22161

NOTICE

THIS DOCUMENT HAS BEEN REPRODUCED

FROM THE BEST COPY FURNISHED US BY

THE SPONSORING AGENCY ALTHOUGH IT

IS RECOGNIZED THAT CERTAIN PORTIONS

ARE ILLEGIBLE IT IS BEING RELEASED

IN THE INTEREST OF MAKING AVAILABLE

AS MUCH INFORMATION AS POSSIBLE

TECHNICAL CONTENT STATEMENT

This report contains information prepared by the Department of

Mechanical and Industrial Engineering University of Illinois at Urbana-

Champaign under JPL subcontract Its-content is not necessarily enshy

dorsed by the Jet Propulsion Laboratory California Institute of Techshy

nology or the National Aeronautics and Space Administration

NEW TECHNOLOGY

No reportable items of new technology are identified

ii

ACKNOWLEDGMENTS

During the course of the investigation Mr W A Hagemeyer

JPL Technical Representative provided property data and assistance

in many ways without which this work would not have been possible

Professor J S de Paiva Netto of Instituto Tecnologico de Aeronaushy

tica Brazil and formerly of the Heat Transfer Laboratory of the

Department conducted preliminary studies of the theory To both

we offer our sincere thanks

The assistance of Miss Dianne Merridith in typing and Mr Don

Anderson in preparing the figures and of Mr George Morris and Mrs

June Kempka in supervising the overall preparation of this report

is greatly appreciated

iii

ABSTRACT

A theory has been proposed for conducring model experimentation

which permits the use of imperfect models or test conditions that

do not conform strictly to similitude requirements It is based on

a new concept of representing the error states in a multi-dimensional

Euclidean space when errors in the modeling parameters are small

A consideration of the error path in the hyperspace leads to expresshy

sions from which the global effect of these errors may be evaluated

approximately Conditions under which these expressions would yield

satisfactory results are given

To test the usefulness of the theory a computer experiment has

been carried out for the prediction of the transient and steady state

thermal behavior of a hypothetical spacecraft using perfect as well

as imperfect models The hypothetical spacecraft has major radiashy

tive and conductive heat flow paths that crudely simulate those of

the 64 Mariner family of space vehicles Errors in the conductance

and capacitance parameters of up to 25 percent and in surface emitshy

tances of up to 20 percent existed in the imperfect models Extenshy

sive temperature data were obtained for the various components of

the spacecraft when it was subjected to a sudden heating due to its

exposure to the suns radiation and the power dissipation within the

bus followed by its attaining the steady state and the subsequent

cooling as a result of removing the suns heat Data were also acshy

quired under the condition of a cyclically varying thermal environment

iv

Generally speaking errors of up to 10 20 and 300 R originally presshy

ent in the data of the imperfect modelswere reduced to less than

31R after correction according to the proposed theory

V

NOMENCLATURE

A = area ft

-aii --shy oefficient-matrix defined in--(32-15)

B = diffuse radiosity Btuhr-ft

b = inverse ofoaj - defined in (3217)

C = volumetric heat capacity Btuft -0R

C = weighting factor for 6 defined in (215)

d = thickness ft

E = exchange factor

F = shape factor

H = irradiation Btuhr-ft2

k = thermal conductivity Btuhr-ft-degR

Q = heat flow rate Btuhr

q = heat flux Btuhr-ft2

S = solar constant Btuhr-ft2

s = are length along error path

T = absolute temperature T o = absolute reference temperature

t = time hr

a = surface absorptance

= error ratio defined in (219)


= error in modeling parameter

6 = Kronecker delta function

= surface emittance

vi

p = surface reflectance p = diffuse component of surface reflecshytance p = specular component of surface reflectance

-8 2 o4 -= 01713 X 10 Btuhr-ft - R a = Stefan-Boltzmann radiation constant

= diffuse-specular overall radiant exchange factor

Subscripts

e = refers to empty space

ij = refers to surfaces A A - I ]

m = refers to model

p = refers to prototype

Superscri pts

refers to solar spectrum B E H Q q We a p I I ~ Py and P

also refers to modification experiments P(+) P(-) s( and s(-)

(+) = refers to subspace S(+)

--) = refers to subspace S(

(Others not found in the list are defined in the text)

vii

TABLE OF CONTENTS

Page

1 MOTIVATION OF A NEW APPROACH TO THERMAL SCALE MODELING 1

2 AN APPROXIMATE THEORY OF MODELING WITH IMPERFECT MODELS 3 21 BASIC IDEAS E 3 22 GEOMETRIC REPRESENTATION OF ERROR STATES 9 23 GLOBAL EFFECT OF POSITIVE AND NEGATIVE 6S ON --

PARABOLIC ERROR PATH WORKING FORMULAE 15

3 APPLICATION OF THE THEORY TO THE THERMAL MODELING OF A HYPOTHETICAL SPACECRAFT--PRELIMINARIES 26 31 THE HYPOTHETICAL SPACECRAFT 26 32 RADIATION HEAT TRANSFER ANALYSIS AND THE DETERMINATION

OF THE OVERALL EXCHANGE FACTOR 62 28 321 Radiant Flux in the Solar Spectrum 31 322 Radiation Heat Transfer in the Infrared 37

33 NODAL HEAT BALANCE EQUATIONS 43 34 MODELING REQUIREMENTS 53

4 SOLAR FLUXES DIFFUSE-SPECULAR OVERALL EXCHANGE FACTORS AND CONDUCTANCES OF HEAT FLOW PATHS ASSOCIATED WITH THE HYPOTHETICAL SPACECRAFT 55

5 NUMERICAL SOLUTION OF NODAL HEAT BALANCE EQUATIONS 65 51 A RECAPITULATION 65 52 NODAL HEAT BALANCE EQUATIONS IN FINITE DIFFERENCE FORM

AND THE METHOD OF SOLUTION 67 53 DETERMINATION OF OPTIMUM y AND a 71

6 RESULTS DISCUSSIONS AND CONCLUSIONS 76 61 SPACECRAFT SUBJECTED TO SIMPLE HEATING AND COOLING 76 62 SPACECRAFT SUBJECTED TO CYCLIC HEATING AND COOLING 96 63 SOME RELEVANT OBSERVATIONS 125

631 Influence of Decreasing and Increasing Model Errors on Prediction Reliability 125

632 Proper Control of Model Errors and Selection of Experimental Condition 126

64 CONCLUSIONS AND RECOMMENDATION 129

REFERENCES -1

APPENDIX A THERMAL RESISTANCE OF MULTI-LAYER INSULATION 132

APPENDIX B A NUMERICAL EXAMPLE 139

viii

Chapter 1

MOTIVATION OF A NEW APPROACH TO THERMAL SCALE MODELING

Theoretical requirements for the thermal scale modeling of unshy

manned spacecrafts are understood quite well at the present time

Difficulties arise in practice when the system to be modeled consists

of components fabricated from a number of materials and they all parshy

ticipate in influencing the systems thermal performance This is

particularly true when information on both the steady state and transhy

sient behavior is sought One possible means of satisfying modeling

requirements is to modify artificially the thermal conductance of

thin struts plates shells etc by electroplating with a high conshy

ductivity metal such as copper The main objective of a previous

research contract between the University of Illinois and the Jet Proshy

pulsion Laboratory JPL No 951660 was to develop such a possibility

Test results obtained with prototypes and models of simple configushy

rations have demonstrated the technical feasibility of the concept

either with or without solar simulation With the availability of

adhesive metal foil tapest in recent years it is conceivable that

they can be applied more conveniently than electroplating In this

connectionone also sees the possibility of modifying the materials

heat capacity by using plastic (teflon) tapes However the range

tOne type of copper and several aluminum foil tapes with pressure sensitive silicone adhesive manufactured by Mystik Tape Inc of Northfield Illinois may be suitable for the present purpose

of thickness of commercially available tapes is limited Consequentlyshy

the desired thermal conductance and capacitance of the various strucshy

tural members of the system may not be mpnufactured precisely in this

manner They can only be approximated Furthermore the application

of a metal foil tape to a surface would also introduce a minor dis-shy

turibance to its heat capacity Likewise the use of a plastic tape

---would produce a minor influence on its conductance It is also posshy

sible that the desired surface radiation properties may not be duplishy

cated accurately These considerations prompted us to explore and

examine another concept of model testing in which models that do not

satisfy the similarity criteria completely are used The theory

which is presented in the following chapter contains some heuristic

but plausible arguments and in this sense it is not mathematically

rigorous It was described first in its rudimentary form in a preshy

liminary proposal Thermal Scale Modeling with Imperfect Models

prepared by the senior author and submitted to JPL for technical evaluashy

tion in January 1969 The material contained in Chapter 2 is a genshy

eralization of the theory presented in that document It includes

additional information relating to its practical implementation

To test the validity of the theory it hs been applied to a

hypothetical spacecraft having a geometric configuration that crudely

simulates the global radiative and conductive paths of the Mariner

spacecraft The results of the present study firmly established the

usefulness of the proposed new concept and one sees the welcomed flexishy

bility in the use of model testing--a flexibility heretofore imposshy

sible to attain

2

Chapter 2

AN APPROXIMATE THEORY OF MODELING WITH IMPERFECT MODELS

To begin with it should be noted that while our concern here

is the thermal modeling of unmanned spacecrafts the concept to be

expounded herein has general applicability to the immense field of

the technology of model testing As such the analysis and discusshy

sion that follow are presented with this viewpoint

21 BASIC IDEAS

Consider a physical phenomenon y which depends on a number of

independent variables x1 x2 x Symbolically we may write p

y = y(x x2 x ) (211)

If the functional relationship has general validity it must be inshy

dependent of the units of measurement Thus a consideration of the

requirement of dimensional homogeneity leads to a dimensionless form

jof the relation

44( I12 11) (212)

Methods of dimensional analysis whether based on the governing dif-N

ferential equations of the problem or on the strict algebraic formalshy

ism or on physical intuition have been well documented and need no

further deliberation here Suffice it to state that for perfect

modeling the ]ts in the model system are made indentical to the corshy

responding ffs in the prototype system

3

In the modeling of the thermal performance of spacecrafts the

dependent variables of interest are usually the temperatures of their

various components Thus the number of s with which the experishy

menter has to deal could be quite large Moreover as has been noted

previously the precise satisfaction of all modeling requirements

may not be possible in practice In fact even if it were possible

it might not be desirable from the point of view of economy This

is then the fundamental reason for using imperfect models and some

deviation in the Hs of the model system from those of the prototype

will be tolerated To facilitate further discussion we rewrite (212)

as

( i ( (213)

whete i = 1 2 bull N N being the number of different components

of the spacecraft to which a characteristic temperature is assignashy

ble The subset of all relevant variables or parameters for which

the model system is free from error is denoted by 9 Clearly for

the problem under consideration all elements of Sare passive and

can be ignored In the transient thermal modeling of unmanned spaceshy

crafts n is usually several times the value of N as will become

clear later

If we designate the errors in H by 116 and define

n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)

then $ may represent the measured entity using the imperfect model

4

eg the temperature of the component surface A of the model spaceshy1

craft which does not satisfy the modeling requirements completelyThe 0)

The quantity sought is of course () When the Ss are sufficiently

small the right-hand side of (214) can he linearized to become

n

0) + C 6 j =

in which the coefficients C are not known It may be noted that

if Taylors series is used then

(0)() (216)C 0

However (216) does not necessarily give the best estimate of the

coefficient C In fact the validity of (215) does not require

the usual restriction that needs to be imposed on the function for

the existence of the Taylor expansion

To evaluate (0) from the measured 4 one would require theoshy

retically the knowledge of the n unknown coefficients Ci This

means that n experiments will have to be conducted with n different

sets of 6s The work may become formidable even when n is only modshy

erately large say 20 or so Furthermore the accuracy required

of the experimental measurements under such circumstance could be

so high that they become impractical We therefore seek alternashy

tive solutions with some loss of accuracy

5

We begin by noting that the 6 s associated with the imperfect

model may be either positive or negative For reasons to be seen

later they are grouped separately We designate that 6 6 6 shy

are positive and that 6r+ 6 6n are negative Furthershy

more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+

+ ) Clearly and may be either positive or negative With the 1 1

foregoing (215) may be rewritten as

~ 0) (t+)+A(21)

If the imperfect model is modified or if the model test condition

is altered (in either case the extent of modification must be restricted

so as not to violate seriously the linear approximation used in the

theory) then 4 + ) and will change also A possible practical

means of effecting model modification is through the use of adhesive

metal and plastic tapes for altering the thermal conductance and heat

capacity as indicated in [lit Thus originally positive errors will

become more positive while originally negative errors will become

less negative or positive In what follows the errors following

tNumbers in brackets refer to entries in REFERENCES

6

modification will be designated with an asterisk

Let us consider that the modifications are carried out in two

steps In the first only the positive errors are altered leaving

the negative errors intact or essentially unchanged We denote the

error ratio by a Thus

6 = j = 1 2 r (219)

If Z-4+) represents the experimental data so obtained then

rn

+) + C (21) ]]] ] 21

j j = r +

Eliminating (0) from (215) and (2110) yields

Ir

j 1

If a weighted average of the error ratio is defined according to

r

6c

jl (2112)

rrthen C21ll) can be rewritten as

+)- = (a- 1) C 6( j=l

7

and consequently there is obtained from (217a)

4 - (2113)a-i

Obviously a cannot be evaluated without the prior knowledge of C

However in the event that all a s are identical say a then a =a

-and no knowledge of CI is needed While such special condition

is usually not met in practice the foregoing observation does sugshy

gest that in testing with imperfect models the experimenter shouid

seek small deviations in a s

In the second step of modification only the negative errors

are altered For clarity and for convenience of later discussion

the error ratio is to be denoted by Thus

= = j r + 1 r + 2 bull n (2114)

In this instance the measured data 4- can be written as

n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l

As in the first case if a weighted average of the error ratio is

- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)

The observation previously noted for a can likewise be made for

Thus without the knowledge of C s the precise evaluation of both

a and is not possible However they can be approximated It is

this desire of finding the appropriate mean values of the error rashy

tios that led to the creation of a new concept of model testing with

imperfect models

22 GEOMETRIC REPRESENTATION OF ERROR STATES

The central idea to be explored herein is the representation

of error states in a multidimensional Euclidean space whose elements

are 6 This will be referred to as the simple error space in con-I

trast to theweighted error space to be discussed later Such repshy

resentation is compatible with the lineal theory considered in the

present study

For j ranging from 1 to n there exist the following three points

in the n-dimensional error space

pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n

V +) There are also two subspaces and ) with their respective orishy

0( + ) gin at and J-) The elements of subspace +) are 61 62 bull

and those of ) are 6 6 If the error ratio a

0 +) is a constant the three points P and P-(+) are colinear in

$ The straight line which originates at 0( + ) and passes through

the said points will be labeled M Similarly if is a constant

d-) P and P(-) are colinear in S(- and the straight line joinshy

ing them will be labeled hen n = 3 the foregoing can be repshy

resented pictorially as is illustrated in Fig 21 No such pictoshy

rial representation is possible when n gt 3

In (+)the lengths of the line segments 0(+)P and 0+) P ( + )

are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2

If we regard + as the abscissa of a plane plot with 4t as its ordinate

10

Origin of f 8 - Space 02010)0

-1 H

)--___l -- _ SubDspaceS

p__j 2) (l c2P

Subspace S

Figure 21 Illustration of subspace S(+ ) and S in a 3-dimensional simple error space (6 6 are + 6 is -is a

plane while S(- ) is a line)

12i

L+)then a point corresponding to P and another point 4A correspondshy

ing to P-d+) may be located as shown in Fig 22(a) A conjecture

+ )in toduced is that and varies lineshyi i depends uri-uely on

arly with it It follows then

+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p

which is identical to (2113) when a = a as is the case here

An analysis based on analogous arguments can be made in subspace

S(-) Thus

= 1K 621

P 0(-shyand from the i vs -)plot as illustrated in Fig 22(b) it can

be shown readily that(- )0(-)P OPp 0shy

________ - 1 (222)

-1

which isprecisely (2118) when = B

12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0

Figure 22 Linear dependence of ti with 6 in S()and S(shy

13

3

The foregoing analysis plausible as it may seem is subject

to immediate criticism Referring to (215) one recognizes that

(0)the deviation of from 4 depends on the products C 6 instead

of 6 alone The coefficients C are in essence weighting fac-I 13

tars which prescribe the relative importance of the various errors

in influencing the dependent variable Thus a weighted error space

---whose elements--are 1C -16 -should-he used instead of the simple er-J 3

ror space and it is more logical to assume that the distance ascershy

tained in such error space from its origin is an appropriate measure

of the resultant error in i

- A-question which naturally arises is Why is it then that

for constant a and the analysis made in the simple error space

leads to correct results The reason for this may be seen easily

In S( + ) of the weighted error space the lengths of the line segments

0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =

Hence when a is a constant (+)P - =a O(+)P and the three points

P and P + ) 0 M are colinear Since only the ratio of distances

14

is involved in the expression for L it is seen that (221) reshy

mains unaltered For the same reason (222) also holds It is

significant that the linear correction formulae (221) and (222)

valid for constant aand 0 and originally deduced from a conjecture

in the simple error space are formally identical to those based on

a consideration in the weighted error space It goes without saying

that the experimenter has normally no knowledge of C and hence

the error state-points like P P(+) and P(-) cannot actually be

plotted in the weighted error space

23 GLOBAL EFFECT OF POSITIVE AND NEGATIVE 6S ON --PARABOLIC ER-ROR PATH WORKING FORMULAE

We now proceed to examine the more realistic case for which the

error ratios u and are not constants We restrict ourselves to3 3

the consideration that the range of vaiiation among the q s and among

the f s is limited The analysis which follows closely parallels

that described in [] for the evaluation of the global effect of the

errors based on a consideration made in the simple error space

Referring to Fig 23(a1) the line joining 0(+) and P(+) is

designated as the -(+)-axisSince a is not a constant but varies

with j P does not lie in this line Hence the point P and the (+shy

axis together determine a plane in S(+ ) of the weighted error space

In this plane a line 0(1)T(+) is erected normal to the (+)-axs

as shown For convenience the T+)-axis is so oriented that P lies

on -the positive side It is pertinent that EM and imply

15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d

) -Figure 23 Parabolic error paths in S( and S

and ( since the scale of the coordinates in the weighted error

spacedepends on i For simplicity the subscript i is omitted

Passing through the three points 0(+ ) P and P-+ a parabola

can be constructed Tracing the points along the parabola and toward

the origin 0( + ) may be interpreted as conducting a series of experishy

ments with controlled errors of successively diminishing magnitude

As the origin is approached all positive errors become vanishingly

small Thus the arc length along the curve measured from 0(+) is

an appropriate measure of the global effect of all positive errors

in t The choice of a parabola as the error path is to some extent

arbitrary but it is certainly reasonable Further argument in supshy

port of the choice will be given later

The equation of the parabola in the (+-7 plane is

T(+) a+) +b )2 (231)

where a gt 0 and b lt 0 The coordinates of P(+) are

r= 1142(C 6y) ]2j(a

(232b) = 0

In (232a) C implies C The coordinates of P are

r

J degO+)P (+) j=j I0 j

E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1

+4~ 2 which the overscore arrow denotes vectors It

+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)

The arc length 0( + ) P-(+) is

s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)

and the arc length 0( P is

1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _

The ratio of the two arc lengths is

2s( + )

2 (236a)(a

s(+) 1-f(aX)

where

2f(aAY = aX(l + a 2 ) + kn [(1 + a2X2) 1 2 + aX] (236b)a(l + a2 112 + Yn [(I + 2)12 + a]

and a is given by (234a) and X by (235c) In the latter two

equations we further note that

-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2

R In the foregoing the summand implies Z Consequently within

j=1 the context of the present theory the correction required for all

positive errors is

+ - (238)s(+)

19

J(4) (4+) (and the appropriate mean ais seen to be given by the ratio s s

-For the practical application of these results the followfng

observatio-ns are made

(A) WFhen the range of o is restricted (237a) and (237b)3

are weak functions of C3 They may be replaced by the following apshy

proximate expressions

-12

(239b) (23___b)

j(+)

1(6)2

Alternatively if the physical nature of the problem is such that

the dominant C s are of similar magnitude our experience indicatesI

that these approximations are also valid

Following a detailed error analysis based on the same arguments

but made for the simpZeerror space it was found that (236ab)

(234a) and (235c) remained unaltered provided that in the latter

(+) (+)two expressions the ratios p P and were calculated

according to (239a) and (239b)

(B) If the experimental conditions are so chosen that in the

(+) = 1 then = f(a)= aweighted error space 2( and00

20

s + Is = 2 which is independent of the C s This condition is

of course not generally met in practice However if a is small

say less than 05 then f(aX) becomes somewhat insensitive to variashy

tions in a Furthermore if we require that jXI be kept small say

within 01 or 02 then f(aA) is small compared to 1 Under these

conditions the error in the calculated ratio of the are lengths reshy

sulting from inaccuracies in a and X will likewise be small Thus

the use of the parabolic error path provides guidance to the proper

selection of the experimental conditions for reducing errors due to

the lack of knowledge of the weighting factors Cj

The foregoing observations (A) and (B) taken together suggest

that in the application of the linear correction formula (238)

the ratio of the arc lengths (or its equivalent W) can be evaluated

from a consideration of the simpZe error-space when the range of cz

is restricted andor when the experimental conditions are chosen as

explained

If in the modified experiments the positive errors are made

Zess positive the relative location of P and P(+) with respect to

the origin of S(+) would be as shown in Fig 23(a2) The (+)-axis

is now chosen to pass through P Following a similar analysis it

was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S

and f(aX) is given by (236b) with a and A redefined as follows

(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=

Again if the range of a is restricted andor if the experimental

condition is such that lXl is small as compared to unity the ratios

and +4 +) can be calculated from a consideration of

22

the simpZe error space namely

12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)

Clearly in (2310ef) and (2311ab) the summand implies j l

The analysis of the global effect of the negative s on 4can

likewise be treated If the negative errors are Zess negative in the

modified experiments the error path in S(-) would be as shown in

Fig 23(bl) We shall refrain from presenting the details of the

calculation and instead shall summarize the results as follows

_ s 4--I ) (2312a)

1 - shy(- )

where the ratio of the arc lengths along the error path is

( -) s - 1 - f(aX) (2312b)

2

23

and f(aA) is again given by (236b) with a and X respectively

denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n

In the above pound implies z The ratio s ( Is clearly denotes

j

the mean

The error path would be as that depjcted in Fig 23(b2) if the

negative errors become more negative after modification In this

case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)

and f(aA) is as defined earlier with a and X respectively given

by (234a) and (235c) when the superscript (+) is replaced by (-)

The ratios n -) F- and 8- ) are given by (237a) and (237b) n

with the summand r Z The discussionreinterpreted to mean j=r+l

on the validity of using approximations deducible from the simple

error space also holds

Finally the quantity sought is

25

Chapter 3

APPLICATION OF THE THEORY TO THE THERMAL MODELING OF A HYPOTHETICAL SPACECRAFT-PRELIMINARIES

31 THE HYPOTHETICAL SPACECRAFT

To ascertain the usefulness of the approximate correction theory

for imperfect modeling as expounded in the previous chapter we conshy

sider a hypothetical spacecraft shown in Fig 31 The geometric

configuration chosen is intended to simulate the global radiative

and conductive paths of the Mariner 64 spacecraft but with all secshy

ondary and minor details omitted The solar panels A1 -A2 and A-A4

are fabricated of an aggregate of aluminum sheets silicon crystals

for energy conversion and glass plate covers all mounted in an alumishy

num alloy celled structure While the local thermal properties are

of a highly anisotropic and inhomogeneous character it is quite

feasible to describe its overalZ behavior by equivalent values of

thermal conductivity and heat capacity Based on the information

transmitted to us from JPLt it appears that a reasonable value of

kd for the solar panel is 0058 Btuhr-F Also the mean specific

heat of the aggregate is reported to be 020 BtuIb-F and a typical

Mariner solar panel of 3 ft X 7 ft weighs about 30 Tbs From these

it is estimated that the Cd of the solar panel is approximately 029

2 Btuft -F

tThrough Mr William A Hagemeyer

26

---------- --

Collimated Sunlight (Either at Normal Incidence or 450)

Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4

Solar Panel A1 A2 A4 A5 -

Bus A A6 A7 A8 Aq Ao (A7 and Alo are covered wth superinsulation )

Antenna All All areas are idenlical and equal to 4 ft2

Figure 31 Hypothetical spacecraft

27

To keep the radiation geometry associated with the diffuse-specushy

lar surfaces as simple as possible the bus of the spacecraft is Taken

to be a cubical box instead of the usual polygonal configuration The

top and bottom faces of the bus are covered with multilayer superinsushy

lation The collimated suns rays are assumed to be either perpendicushy

lar to the solar panels or slanted at 450 to them but remain parallel

to the front and back faces of the bus TABLE 31 lists the materials

selected for the six component faces of the spacecraft bus The thickshy

nesses indicated afe equivaZent values they take into account the

electronic packaging subassemblies bolted to them Included is the

relevant information for the main directional antenna As will be

shown in Section 34 perfect modeling requires that the corresponding

surfaces of the model and the prototype have identical radiation propershy

ties Furthermore when the temperature fields are two-dimensional

the kd and Cd of all component surfaces of the model must bear a fixed

relationship to those of the corresponding surfaces of the prototype

TABLE 32 summarizes al pertinent surface properties and the equivashy

tlent (kd) s and (Cd)s for the hypothetical spacecraft

32 RADIATION HEAT TRANSFER ANALYSIS AND THE DETERMINATION OF THE OVERALL EXCHANGE FACTOR e9

When the surfaces of a spacecraft are under the irradiation of the

sun the absorbed and reflected radiation are in a wavelength region

totally different from that of the emitted radiation While it is posshy

sible to perform a general formulation of the problem there is neither

the need nor the justification of doing such analysis at the present

time It is well known that approximately 98 percent of suns radiation

28

TABLE 31

MATERIAL LIST FOR THE HYPOTHETICAL SPACECRAFT

(a) Solar Panel

Aggregate of silicon glass aluminum and its alloy

(b) Bus

Panel Material k C Equivalent Btuhr-ft-F Btuft -F Thickness

d in

A3 Magnesium Alloy 470 259 0125 AN-M-29

A6 Aluminum Alloy 802 371 0 1875 5086

A7 Titanium Alloy 460 350 010

A-110-AT

A Magnesium AlloyA781A(T4)

291 280 01875

A9 Magnesium Alloy 630 276 0125 ZK51-A

A1 0 Titanium Alloy 838 385 0025 -150-A(2)

(c) Antenna

Aluminum alloy 2011 (k = 823 Btuhr-ft-F and C- 393 Btuft3 -F)

Thickness - 00625 in

29

TABLE 32

SURFACE PROPERTIES AND OTHER DATA FOR THE HYPOTHETICAL SPACECRAFT

P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel

Sunlit Surfaces A1 A2 A4 As

Surface Away from Sun AiA 2A4Aw(painted with PV-100 white paint)

0

080

020

0

080

020

020

017

0

0

080

083 0058 029

A5 exterior (PV-lO0 paint)

interior (partially painted)

080 0 020

-- --

017 080

0 0

083 020

0489 0269

SA 6 exterior (PV-lO0 paint)


080

--

0

--

020

--

017

080

0

0

083-125

020

0580

exterior (superinsulation)

interior (black paint) 0

--

085 --

015 --

050 015

0 0

050 085

00383 0292

Bus A8 exterior (PV-100 paint)

interior (black paint)

080

--

0

--

020

--

017 015

0 0

083 085

0455 0437

A9 exteior (polished aluminum) interior (black paint)

0 080 020 ----

0 015

095 0

005 085

0655 0287

A1 0 exterior (superinsulation)


0

--

085

--

015

--

050

015

0

0

050

085 00175 0080

Antenna A11 sunlit face (green paint)

face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204

2 All (kd)s are in Btuhr-F (Cd)s in Btuft -F

is contained within the 0-3 pm range On the other hand less than

001 percent of the radiant energy emitted by a black surface at

530 R (room temperature) is in that wavelength range Even at 750 Rt

less than 04 percent of the emitted radiation is of wavelengths beshy

low 3 Pm The semigray or two-band analysis suggested by Bobco [2]

is based on the foregoing facts The use of such a two-band model to

account for the spectral dependence of the surface properties of spaceshy

crafts has been examined by Plamondon and Landram [3] and found to

yield very good results

A simple and often realistic description of the directional propshy

erties of the surfaces is a subdivision of the hemispherical reflecshy

tance into diffuse and specular components ie p = pd + p In

the analysis that follows we shall adopt such an idealization which

together with the semigray approximation and the assumption of diffuse

emission makes possible an analytical treatment of the problem in

a reasonably straightforward manner The essence of such approach was

used in a recent paper by Hering E41

32] Radiant Flux in the Solar Spectrum

We first present a general formulation for an enclosure

of N surfaces each of which has a uniform temperature and is uniformly

irradiated The results will then be applied to the relatively simple

configuraticn selected for the hypothetical spacecraft All propershy

ties and radiant energies associated with the solar spectrum will

be designated with an asterisk

According to the two-band model theemitted radiation in the

tThis far exceeds the ordinary operating tempeiature range of present day spacecrafts

31

solar spectrum from any surface of the system is completely negligible

Hence the radiosity of a surface A is given by

B= p (SE + H-I) (321)i d i

in which E is a type of exchange factor denoting the fraction of

the solar flux incident on A directly and by all possible specular

reflections The irradiation H is given by

N

Hi= E (322)

j=l

where the exchange factor E denotes the fraction of the diffuse

radiation in the solar spectrum leaving A which arrives at A both1 3

direbtly and by a11 possible intervening specular reflections We

note that in writing (322) the reciprocity relation AE = E- ]1I 11-3

has been used Eliminating H from (321) and (322) yields

N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1

which forms a system of N simultaneous linear algebraic equations

for the N unknown radiosities Once the Bi s are known the rate

of solar energy absorbed by Ai can be calculated from

32

+= S H)(st

A B (324)

Obviously B and consequently Ql are independent of the system

temperatures The decoupling of the solar fluxes from those of the

infrared radiation results in significant simplification of the analyshy

sis

If a surface k reflects purely specularly then pk = 0 and

accordingly B vanishes In this case

Q1 = Ad(sE + H ) (325)

We now proceed to apply the foregoing results to the hypothetishy

cal spacecraft when the suns rays are parallel to the front and rear

faces of the bus and are either inclined at 450 or normal to the

solar panels Figure 32 shows the relevant geometries involved

To evaluate Q Q and Q we need only to consider an enclosure

c6nsisting of A1 A2 A3 and an imaginary black surface A L at abshy

solute zero The latter comprises a rectangle with its long sides

shown as the dotted line in Fig 32 and two identical right triangles

both adjoining the rectangle Clearly BL 0 It is easy toeL

see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4

Designates superinsulation

A A 2I

Lw

I A5 A 4

Figure 32

Top View

Radiation geometry associated with hypothetical spacecraft

Consequently (323) becomes

B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3

When the radiosities are evaluated Q Q and Q can be determined

from (324) or (325)

When the suns rays are normal to the solar panel

bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3

To evaluate Q4 Q5 and Q we consider a similar enclosure conshy45 6

sisting of A4 A5 A6 and the associated imaginary black surface

A Rat absolute zero Again referring to Fig 32 we have

V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and

B - pI F B z S cos 450

4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6

p (F B- + F Bf) - B= -p- (U+ p )S cos 450 d 6 6-4 4 6-5 5 6 d 6 s 5

As before when the radiosities are evaluated Q- Qand Q can 4 56

be readily calculated

When the suns rays are normal to the solar panel the relevant

radiosities can be evaluated from (327b) provided that the subscripts

1 2 and 3 are replaced b y 4 5 and 6 respectively

By following the same procedure we may evaluate QP and Q

The results are

(a) For oblique solar irradiation

S cos 450sin 300 (3210a)

91 9 pw P F F

(b) For normal solar irradiation

It is only necessary to replace cos 450 in (3210ab) by unity

The top face A7 of the spacecraft bus is completely shielded from

the suns rays by a multilayer superinsulation The Appendix of this

report gives a detailed analysis of the thermal resistance of the

superinsulation and presents an expression from which the leakage

flux may be determined The rear and bottom face A8 and A10 of the

36

bus do not receive radiation in the solar spectrum either directly

or indirectly Hence Q = Q = 0- 810

322 Radiation Heat Transfer in the Infrared

Once again for generality we first consider an encloshy

sure of N surfaces each having a uniform temperature and being unishy

formly irradiated It is assumed that all emitted radiations are

diffuse and that the surface reflectances can be adequately described

by the pd-p model Our objective here is to deduce expressions

for the overall radiant exchange factor similar to Hottels diffuse

exchange factor 69 All surfaces are taken as gray within the specshy

tral range Clearly the results will be directly applicable to the

determination of similar exchange factors for internal radiation withshy

in the spacecraft bus

For any surface A of the enclosure

4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l

The system of simultaneous linear algebraic equations (3213) can

--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)

To evaluate the diffuse-specular overall exchange factor we-k

set aT = 1 and the temperatures of all remaining surfaces to zero

The heat flow rate at k is

AkakAB (3216)

where the presubscript i is a reminder of the original source of the

flux We recognize that B i(j = 1 2 N) is the solution

set of (3214) with the latters right-hand side set to zero except

for the ith equation for which it is S It is most convenient

to evaluate B by matrix inversion

38

Let [b] be the inverse of the coefficient matrix [a ] That

is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN

It can be readily demonstrated that

B -- bji (3218)

By definition i Qk = A it follows then

N Ak

-k 1gt (3219)

j=l

We now proceed to apply the foregoing general results to evalushy

ate V for the spacecrafts exterior surfaces We first consider

the enclosure formed by A1 A2 A3 and AeL the latter being black

and at absolute zero

1 A1 A2A are d- PS surfaces A A is black

A A A2 2(3) 2(3)

Figure 33 Mirror Images of Interacting Surfaces in an Enclosure Consisting of A A2 A and AL

39

In Fig 33 the surfaces under consideration are identified with

letters or numerals irediately adjacent to them Thus AI refers

to the upper surface of the solar panel and A3 the exterior surface

of the left face of the spacecraft bus The image surfaces are desshy

ignated with two numerals the one in parentheses refers to the mirror

in which a surface in question is seen For instance 2(3) is the

image of A2 as seen in the mirror A3 With the aid of Fig 33

the various exchange factors can be readily written They are

ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)

EB_ 3 = 0 ES-e = F3 -e + PsI FS( 1) -e + Ps 2 FS( 2) e

and the elements of the corresponding coefficient matrix are

a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)

a 1 = _pd 3E3-I I a32 = -Pd 3ee-2 a3 3 = 1 a = -P se shy

ae1 =0 ae2 =0 a 3 =0 aCe =1

In (3220ab) the subscript e refers to A L Using the foregoing

information the diffuse-specular overall radiant exchange factors

- 1 -9 - -s and 4- can be evaluated immedishy1-2 1-3 1 -e 2-3 2-e 3 -e

ately from (3219) Exchange factors associated with A A5 6

and Ae R can likewise be determined Surface A8 sees only the empty

space thus the relevant 19 factor becomes its surface emittance

40

Next we consider the enclosure formed by A9 A (upper surshy

face of antenna) and the associated black surrounding Ae F Figure

34 shows the two relevant mirror images 9(i1) and 11(9) associated

with the system I A

Figure 34 Mirror Images of Interacting Surfaces in an Enclosure Consisting of A 9 A II and A F

It is easy to see from Fig 34 that the exchange factors are (with

subscript e eferring to A )

Eg 9-9 0 Eg _1I Fg-_1I E9 e = Fg-e + pS I Fg9(ii) -e (3221a)

EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C

and the corresponding a Is are

ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(

a 1 1 - 9 Pd111 1 1E 1 - 9 1 a 11 -l1 l a I- = Pd I IE 1 1-e

The remaining system of the spacecrafts exterior surfaces for

which the 1 factors are neededconsists of the dark side of the solar

141

panels (A A21 A4 and A5) the outermost plastic film A1 0 of the

superinsulation covering A1 0the shaded side of the antenna A

and the associated empty space Since none of the surfaces involved

has a specular component of reflectances in the infrared region the

evaluation of a and subsequently i- requires information on

shape factors but not on exchange factors The formulation presented

in this section and the expressions (3211) to (3219) remain valid

All one needs to do is to replace pdi by p and E -j by F1 It

goes without saying that the 6 factors for interior surfaces of the

bus can be likewise evaluated

42

33 NODAL HEAT BALANCE EQUATIONS

To formulate the nodal heat balance equations we need to evalushy

ate in addition to the overall radiant exchange factors the conshy

ductances of the various heat flow paths We shall assume that there

is no conductive link between the solar panels and the spacecraft bus

nor between the bus and the antenna Further the eleven sections

(22 surfaces) which make up the spacecraft are taken to be identical

squarest as illustrated in Fig 32 Each section may have a differshy

ent thickness however Under the foregoing conditions the conducshy

tance between two adjacent areas A and A having a common edge is 2 J

(kd) (kd) -) (k )- -2 + (331)

Clearly K - If A and A are fabricated from the same ma-K~ 1

terial and are of identical thickness like A and A (or A and A )1 2 4 5

of the solar panel then (331) reduces to

= (kd) = (kd) (331a)1 -3 1 3

It is pertinent to note that the crude subdivision used in the

analysis should in no way jeopardize our present objective since

the model is to be subdivided in precisely the same manner In this

regard we may further add that solely from the viewpoint of ascershy

taining the usefulness of the proposed theory it makes no difference

tA significant simplification of the arithmetic results from this choice It is not a restriction necessarily imposed on the analyshysis

43

whether a continuum model or a discrete model is used in the analyshy

sis

The top and bottom faes of the spacecraft bus are covered with

superinsulation The exposed layer of the superinsulation for the

bottom face interacts radiatively with Al1 and thenceforth with

- Air A2 t A4 and A5 An exact analysis of the thermal transients asshy

sociated with its many layers is too involved and is not warranted

for the problem under consideration If we ignore its heat capacity

then a reasonably simple analysis can be made It is demonstrated

in APPENDIX A that the outward leakage flux (from the base plate A10

toward the outer surface of the insulation) is

4 4 - a(T1 0 T10 1) (332)

AR

where ZR = (n - 1)R + R All quantities have been defined in

APPENDIX A

We now proceed to present the heat balance equations The dishy

mensional form will first be given Set (333)

dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)

dT + q 4_(Cd)To 4T (T 4 -C (Tshy 4

A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)

d~lo 4 (Cd10d _ G (T o- T

- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4

aC 4 4T4) OF(~T T4 4D510 o 5 lot-III 10t 11

10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)

Nodal Heat Balance Equations in Dimensionless Form

To reduce the system of heat balance equations to appropriate

dimensionless forms we introduce the following nondimensional varishy

ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)

where i 1 2 3 etc and T is a suitable reference temperature0

for the problem Its choice is to some extent arbitrary For

instance T may be taken as the initial uniform temperature of the

48

spacecraft or some representative average of its steady state temperashy

tures prior to the initiation of thermal transients Since the Physishy

cal time t must necessarily be the same for all is the dimensionshy

less time T2 for the various component parisA1

must be so related

that

kI k2 k3

TIT2T3 2

By using (334abc) we obtain the following non-dimensional form

of the nodal heat balance equations set (336)

deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+

+ 5 44T411plusmn47plusmn4+47 4 7

A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A

-Rd)5sT +T4 e) ) 4 plusmn5 tTA4

5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6

+ 61091(6 (kdKS IVplusmn 6

+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9

soAa _4 44qSA4 - raaS-6+9

41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9

- [e 1_plusmn 6_plusmn4o_I 0 )(4k c(1d) 99 -8 -1 0 91 1

1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J

In numerical computations if we arbitrarily select T3 as the stanshy

dard dimensionless time then

) (k3 C1 dTl k~I C3)dT3

d642 k C 6)d2

dT etcd2

34 MODELING REQUIREMENTS

An inspection of the dimensionless heat balance equations reveals

that for perfect modeling the following scaling requirements must

be met

1 Model and prototype are geometrically similar in order that all configuration factors among corresponding surfaces are identical (Thickness distortion would have very minor or little influence on radiation exchange and is thus permitted)

2 Radiation properties of all corresponding surfaces are idenshytical

The satisfaction of (1) and (2) ensures that the model and the protoshy

type have the same e2 for all corresponding surfaces

3 The simulated solar radiation used in model testing has a spectral distribution intensity and direction the same as those of the local suns rays incident on the spacecraft

53

4 The (kd)s and (Cd)s of all corresponding surfaces must satisfy the following relationships

(kd) A L 2

(k) = - a fixed quantity (337a) P P P

(Cd) t

(Cd)p

- p

a fixed quantity (337b)

The first is associated with the geometric scale ratio and the second the time scale ratio

5 The internal power dissipation when expressed in terms of the equivalent surface flux is the same for the prototype and the model ie

S337c)

for all corresponding surfaces of the spacecraft bus

Finally we note that for complete similitude the initial

temperature field of the model and of the prototype must either be

uniform or have identical distributions The foregoing modeling

requirements have previously been stated in the literature eg

[51 and experimental verifications are available ESabcJ

54

Chapter 4

SOLAR FLUXES DIFFUSE-SPECULAR OVERALL EXCHANGE

FACTORS AND CONDUCTANCES OF HEAT FLOW PATHS

-ASSOCIATED WITH THE HYPOTHETICAL SPACECRAFT

As a prerequisite for the numerical solution of the nodal heat

balance equations the solar fluxes QA the overall radiant exchange

--- factors and the conductance of the heat flow paths K - associated

with the various surfaces of the hypothetical spacecraft must be

evaluated All relevant configuration factors can be readily detershy

mined since all surfaces or their subdivisions are chosen to be idenshy

tical squares as illustrated in-Fig 31 The results are listed

in TABLES 43 and 48 for surfaces facing the sun and in TABLE 413

for surfaces away from the sun The data were taken either directly

from an NACA Technical Note by Hamilton and Morgan [ 7] or indirectly

evaluated from the information given therein The solar exchange

factors were calculated from (326a or b) and (328) and the solar

radiosities from (327a or b) and (329) The irradiation H1 is

then given by (322) and the required Q follows from (324) or

(325) For surfaces A and ill the solar fluxes can be directly

determined from (3210a or b) In these calculations-the solar

- constant S was arbitrarily assumed to be 442 Btuhr-ft2 and the releshy

vant reflectances and absorptances were taken from TABLE 32 The

solar fluxes so calculated are listed in IABLES 41 and 42 respecshy

tively for the normal and oblique incidence of suns rays

55

The procedure used in the determination of the diffuse-specular

overall exchange factors for the spacecrafts exterior surfaces has

been explained in detail in Chapter 3 Following the evaluation

of the exchange factor E the elements of the coefficient matrix

a i were calculated according to (3215) and those of its inverse

b -j were determined by using an available subroutine in our compushy

ter laboratory For the convenience of the reader these intermedishy

ate data are listed in TABLES 44 and 49 for E_ in TABLES 45

410 and 414 for aa -j and in TABLES 46 411 and 415 for bl j

The desired diffuse-specular overall exchange factors e_- were calshy

culated from (3219) and the results are listed in TABLES 47 and

412 for surfaces facing the sun and in TABLE 416 for surfaces away

from the sun It is pertinent to note that for an enclosure of

N surfaces the overall exchange factors satisfy the following simple

relation

N

j =zs (41)

j=l

which is the consequence of the requirement of energy conservation

Equation (41) has been used to check the numerical accuracy of the

data list in the three tables last mentioned

For the interior of the spacecraft bus the radiation was asshy

sumed to be devoid of specular component and hence only the difshy

fuse overall exchange factor is involved TABLES 417 418 419

56

and 420 list respectively the data for the configuration factors

F- the elements of the coefficient matrix a the elements of

the inverted matrix b and the diffuse overall exchange factors

Finally the conductances K are listed in TABLE 421 They

were evaluated from (331) using information given in TABLE 32

It may be noted that there is no conductive link between the solar

panels and the spacecraft bus nor between the bus and the antenna

57

58

NOTE EXTERIOR OF SURFACE 10 1S DESIGNATED AS SURFACE 12

TABLE 41 SOLAR FLUX AT NORVAL INCIDENCE QA BTUHRSQFT

1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00

8 TABLE 42 SOLAR FLUX AT 45 NEINCIDENCE OAA BTUHRSOET

1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00

~~4t EXTEIOR SURFACES ct

TABLE 43 CONFIGURATION FACTORS FA(IJ)

I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040

__ - FOLOUT FRAMME -___ ____--- - IFOLDOUT FRAM

TABLE 43 CONTINUED 59

1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040

__ _ TABLE 44 EXCHANGE FACTORS E(IJ)

I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190

__ TABLE 44 CONTINUED

I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190

TABLE 45 COEFFICIENT MATRIX AA(IJ)

Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000

444 TABLE 45 CONTINUED 44

I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000

TABLE 46 INVERSE OF COEFFICIENT MATRIX BBIJ)-

I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

44 TABLE 47 DIFFUSE-SPECULAR OVER-ALL EXCHANGE FACTORS FF(lJI 4

1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534

TABLE 47 CONTINUED -

I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534

FOLDOUT FRAMEFOLDOUT FRAME 0

61 ___ TABLE 48 CONFIGURATION FACTORS FA(IJ) a

I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500

TABLE 49 EXCHANGE FACTORS E(IJ)

I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925

bull TABLE 410 COEFFICIENT MATRIX AA(IJ)

I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000

__ _ TABLE 411 INVERSE OF COEFFICIENT MATRIX BB(TJ1

J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000

TABLE 412 DIFFUSE-SPECULAR OVER-ALL EXCHANGE FACTORS FFIJ)

I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118

F__O__ _TLE4 COFGOLDOUAI FACORL =I7

FOL~D1JLEA -a -TABLE413 CONFIGURATION FACTORS FA(IJ) ___

62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600

TABLE 414 COEFFICIENT MATRIX AA IJ)

I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170

_4 TABLE 415 INVERSE OF COEFFICIENT MATRIX 58IJ) R

I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194

TABLE 416 DIFFUSE OVER-ALL EXCHANGE FACTORS F(IJ)

I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455

FOLDOUT FRAME -FOLQOLER fr

INTERIOR SURFACES OF BUS 63

TARLE 417 CONFLIGURATION FACTORS FA(IJ)I

I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973

TABLE 419 INVERSE OF COEFFICIENT MATRIX BB(IJ)

I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514

__4 TABLE 420 DIFFUSE OVER-ALL EXCHANGE FACTORS FFIJl

I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875

tt TABLE 421 DIMENSIONAL CONDUCTION LINKS AKIIJ) BTUHRDEG t _

I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00

S TABLE 421 CONTINUED

I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

FnIFODOT Mfl ERAMEamp (-FOLDOUT FRAME

CHAPTER 5

NUMERICAL SOLUTION OF NODAL HEAT BALANCE EQUATIONS

51 A RECAPITULATION

The dimensionless nodal heat balance equations for the hyposhy

thetical spacecraft presented in Chapter 3 and designated by the

set (336) are simultaneous non-linear first order ordinary

differential equations They can be compactly described by (511)

which is written for an arbitrary node i

MjT4 Q - Fgtkc _ + E s _ + 7 9Ljj

1 j1a

K K2j)-

ji ji

where

k C M __0 subscript o refers to a convenient reference

0kC1 0 surface for which the dimensionless time t

is related to the physical time t according

to T = (k C A)t One of the surfaces in 0 0

the system may suitably serve for this purshy

pose

65

Cq + q)A Q (d) Texcept Q7 which is

1 0

a S A cos 9S ( T Also Q10 = Q 01 2

ER (kd )7 T0

-C = conductance of multi-layer insulation (R) 1

The three nonvanishing conductances are C7-e

C012 and C12-1 0 bull

i- overall radiant exchange factor between A and A

The indicated summand refers to all A s which have

direct andor indirect radiant exchange with A

W-hen approriate A includes the empty space A

similar interpretation should be given toZ Xj 0

K conductance between A and A Here the indicated

summand refers only to those surfaces which have physishy

cal contact with A

All other quantities have previously been defined in Chapter 3

The introduotibn of the dimensionless parameter MI is to obtain

a Iiniform time scale for all component-surfaces in the system An

alternative is to replace the left hand side of (511) by

Ci A d4

k dt I

and the integration is to be carried out in the physical time domain

The latter is indeed adopted in our computer program for which separate

66

documents were prepared and submitted to JPL

52 NODAL HEAT BALANCE EQUATIONS IN FINITE DIFFERENCE FORM AND THE METHOD OF SOLUTION

Equation (511) may be integrated from T to T + AT AT being

deg-small indrement to give

M (T+ AT) - (T)] = Q AT- (c + (+Y4

j

+ i( fit a + _ ft dTplusmnT I

_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT

In (521) all integrals J imply f They will now be replaced by the T shy

the approximate two point integration formula namely

T+ AT

J )dt A-rf(l - a)4)Cr) + d4Kt + AT)] (522a)

T AT

f aT AT[(l - cd4f(t) + a44(T + AT)] (522b) T

in which a is the so-called integration parameter and is a pure numeral

between 0 and 1 This scheme of approximation has been used by Strong

67

and Emslie [ 8 ] in their treatment of relatively simple systems inshy

yolving combined radiation and conduction heat transport Upon

substituting (522ab) into (521) followed by some rearrangeshy

ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji

M f -Qt _t (T) +l _a-k K i (T)

Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68

4t1 ar)- i [CI 4tct + AT)

68

+ ~ _ 57(T + AT) + Zd~ Cplusmn rl(23c0j 32

Here again ) E 4x (T) and 4j (T + Ai) Ht (T + AT)

The equation set (523) was solved by a modified Gauss-Seidel

iterative procedure Current values of (T)were used as starting

approximations for (T + AT) and the Newton-Raphson method was used

for finding the physically meaningful-roots If we denote the current

root by (T + AT) then the new value of 0i (T + AT) is calculated from

Ti+ AT) e=w (T + AT) old plusmn Y T + AT) - (T plusmn AT) old] (524)

where y is the acceleration factor The next equation in the set which

is for A +I is solved in precisely the same manner using improved values

of t + AT) as soon as they are generated It has been found that in

general a and y taken together have a decisive influence on the convershy

gence rate of the iterative process

The steady state solution was obtained in a similar manner except

of course that it does not involve a By setting the left hand side

of (511) to zero and rearranging we obtain

g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j

The iteration began with a suitable set of guessed values of f For

bach node the Newton-Raphson procedure of successive approximations

was again used for determining the root of (525) The new value of

P is calculated according to

+ Y ( Snew 0i old i ol d

Thus for either the transient or steady state computations there are

two distinct iterations involved One is associated with the Newton-

Raphson method of evaluating the roots of (523) or (525) and another

is associated with the Gauss-Seidel procedure In the former when

the successive 4k is differ by less than 001 percent the result is

considered satisfactory and the calculation will proceed to the next

node The Gauss-Seidel iteration will terminate when the residual of

each nodal equation is less than a specified value This residual is

a measure of the deviation from the perfect heat balance required for

70

each node Thus we may write

g g (527a)i O i i i g4 i 4

for the steady state problem and

A t1 + f 1 4) + f4 1 4

(52 7b)

for the transient case For the hypothetical spacecraft described in

Chapter 3 go i or f0 i is of the order 102 for all sunlit surfaces and

hence we have arbitrarily set HB lt 10 as the condition to stop the

iteration This value was chosen essentially from a consideration of

the computer time on one hand and the desired accuracy of computed reshy

sults on the other hand

53 DETERMINATION OF OPTIMUM y AND a

To ascertain the optimum values of y and a for rapid convergence

of the iterative process a series of preliminary computer experishy

ments was conducted The results for the steady case with normal inshy

cidence from the sun and with a distribution of electronic package heating

similar to Mariner 64 spacecraftt are shown in TABLE 51 A redistrishy

bution of the heating source inside the bus or a change in the relative

importance of the radiative and conductive mode of heat transfer would

alter the number of iterations required to achieve the same heat balance

tThis calls for the following distribution A-29 percent A6-24 percent A8-36 percent and A9 -II percent (See Figs 31 and 32 for identifishycation)

71

TABLE 51

INFLUENCE OF ACCELERATION FACTOR ON THE CONVERGENCE RATE OF THE ITERATIVE PROCEDURE-STEADY STATE

Acceleration No of iterations factor y required to achieve

HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80

Note Normal incidence from the sun distribution of heat generation

inside the bus similar to Mariner 64 spacecraft

72

ie HBi lt10 -3I -

However these changes if kept within reasonable

limits have only a minor effect on the optimum value of ywhich is

around 13 This finding is at variance with the suggestion made by

Strong and Emslie [8]

The transient results are presented in TABLE 52 They were obshy

tained for the assumed condition that the spacecraft had initially a

uniform temperature of 400degR and at an arbitrarily chosen instant

t = 0 the internal heating over bus surfaces A3 A6 A8 and A9 was

suddenly raised to their full power and simultaneously the spaceshy

icrafts exterior surfaces were exposedto suns irradiation To a

large extent the table is self-explanatory It is seen that the

acceleration factor has a dominant influence on the convergence rate

while the integration parameter plays only a minor role The optishy

mum vAlue of the acceleration factor has been found to be 11 under

the stated conditions

The computed temperature data for the 12 nodal surfaces of the

hypothetical spacecraft at 10 100 and 300 minutes after the thershy

mal disturbance are listed in TABLE 53 Included are the data for

the steady state temperatures As one might expect the solar

panels antenna and the exterior surface of the multi-layer inshy

sulation (A1) respond very rapidly to the changing environmental

condition

73

TABLE 52

INFLUENCE OF INTEGRATION PARAMETER AND ACCELERATION FACTOR ON THE CON-VERGENCE RATE OF THE ITERATIVE PROCEDURE--TRANSIENT CASE

No of iterations required to achieve Integration Acceleration HB 10-3

parameter factor Prototype time interval Min y 0-10 90-100 290-300

02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23

Note 1 Prototype At = 10 min

2 Normal incidence from the sun distribution of heat

generation inside the bus similar to Mlariner 6i spacecraft

74

TABLE 53

THERMAL RESPONSE BEHAVIOR OF THE

HYPOTHETICAL SPACECRAFT

Uniform Initial Temperature = 4000R

Temperature OR

t = 10 min t =100 min t = 300 min Steady State

A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850

Note 1 Normal incidence from the sun solar constant taken to be 442 Btuhr-ft2

2 Cubical bus consists ofsix 4 ft2 surfaces total electronic

package dissipation 1100 Btuhr distributed over surfaces A3 (29 percent) A6 (24 percent) A8 (36 percent) and Ag (ii pershy

cent)

75

Chapter 6

RESULTS DISCUSSIONS AND CONCLUSIONS

The similitude requirements for the thermal modeling of the hyshy

pothetical spacecraft have been given in Section 34 In the present

study it was assumed that the models entail errors in the desired

values of kd Cd e and E (the prime refers to the interior of the

surfaces) There was no error arising from the requirement of geoshy

metric similarity nor was there error in the heat fluxes q and q

As has been noted previously this choice of error distribution is

based primarily on a consideration of practical model fabrication

with the present-day technology It has no bearing on the theory

itself

The general theory of imperfect modeling presented in Chapter

2 is described logically in terms of dimensionless quantities Howshy

ever in the present instance it is possible to speak of errors in

the dimensional quantities like (kd) and (Cd) since not only are they

the only quantities which may be varied in their respective dimensionshy

less groups but also they are physically apprehended more readily

by the designer

61 SPACECRAFT SUBJECTED TO SIMPLE HEATING AND COOLING

To ascertain the usefulness and limitations of the proposed theor

several sets of errors in the modeling parameters have been assigned

TABLE 61 lists the values for the first of such sets In the table

76

TABLE 61 Errors inmodeling parameters

Percentage Error in Modeling Parameters

Model MI Model MII Model MIII Surface Okd Cd 06 6E 6kd 6 Cd r GEt 6kd Cd 66 6St

K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0

6 refers to the exterior of the surface in question and 6 refers to its interior

and others which follow modei MI refers to the original imperfect

model MII refers to that for which the positive errors are modified

(in this case they become more positivp) while the negative errors

remain unaltered and MIII denotes that for which the negative errors

are modified (in this case they become more negative) while the posishy

tive errors are unchanged Thus the error state of model MI would

be represented by the point P in the multidimensional hyperspace reshy

ferred to in Chapter 2 Likewise the-error states of model MII and

- )MIII are represented respectively by Pz(+) and P

Initially the spacecraft is assumed to have a uniform temperashy

ture of 4000R At some arbitrarily selected instant t = 0 intershy

nal heating within the spacecrafts bus and of a distribution as preshy

scribed in TABLE 53 is assumed to begin instantaneously and at the

same instant its exterior surfaces are exposed to suns irradiation

Subsequent to the establishment of a steady thermal condition the

spacecraft is conceived to move into the shade of a planet thus cutshy

ting off the suns irradiation In this manner a cooling transient

is created

Using the equation set (333) and the computational procedure

explained in Chapter 5 temperature data for the heating transient

the steady state and the cooling transient are obtained for the proshy

totype (or equivalently the perfect model) and for the three models

The results are summarized in a table set 62 for normal incidence

of the solar irradiation and in table set 63 for 450 oblique incishy

dence The prototype temperatures are denoted by Tp and those of

the models by J Ji and The errors in the latter temperatures

78

TABLE 62(a) Model temperature before and after correction

Heating Transient 10 minutes after spacecraft subject to solar irradiation (normal incidence) and internal beating

Temperatures of Imperfect Models

Prototype Model Temperature or Perfect Model MI Model MIX Model MIII after Correction

Surface Model A A( A Temperature 1t

TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06

All temperatures in 0R

TABLE 62(b) Model temperatures before and after cortection

Heating Transient 30 minutes after spacecraft subject to solar irradiation (normal incidence) and internal heating

Surface

Prototype

or Perfect Model

Temperature

Temper atures of Imperfect Models

Model MI Model MII Model MIII

A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05

All temperatures in OR

TABLE 62(c) Model temperatures before and after correction



Prototype Model Temperature

Surface or Perfect

Model Model MI Model MIT Model MIII

At ) 4( A after Correction

Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06


TABLE 62(d) Model temperatures before and after correction


II

-

Surface

Prototyp= or Perfect

Model Temperature


Model 1I Model MI Model MIII

iv TbUII E1 I I A AA

t

Model Temperatureafter Correction

A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10


TABLE 62(e) Model temperatures before and after correction

HeatingTransient 500 minutes after spacecraft subject to solar irradiation (normal incidence) and internal beating


Prototype Model Temperature or Perfect Model 1I Model MIl Model MIII after Correction

Surface Model A( ( Temperature ht

A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0

A12(=A 0 ) 1850 1832 32 1879 29 1913 63 -023 470 447 1844 J06 All temperatures in OR

TABLE 62(f) Model temperatures before and after correction

Steady State


Prototype or Perfect Model MI Model MI Model MIII

Model Temperature after Correction

Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14


TABLE 62(g) Model temperatures before and after correction

Cooling Transient 30 minutes after spacecraft moving into shade


Prototype Model Temperature or Perfect Model MI Model MIX Model MIII after Corre6tion

Surface Model Temperature T Fir 1

A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0


TABLE 62(h) Model temperatures before and after correction


1 Temperatures of Imperfect Models

Prototype - M Model Temperature

or Perfect M M after Correction Surface Model

Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24

All temperatures iii OR

TABLE 63 (a) Model temperatures before and after correction

Heating Transient 10 minutes after spacecraft subject to solar irradiation (450 incidence) and internal heating

Teoeaures of imperfect Models


or Perfect Model M11I after Correction Surface Model 7 0l MI A__ A ) A[Temperature T

Tp T I TM TV1 vM 4 T

4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07


TABLE 63(b) Model temperatures before and after correction


A2

V Proottype PoPerfect

Mode Temperature

5355

3353


Model MI ModelM-ll Model MIlI

T P -- Ilz~ v L ~I I

AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153

Model Temperatur after Correction

F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08




Temoeratures of Imperfect Models

Prototyne Model Temperature or Perfect Model MI Model MI Model MIII after C6rrecLion

Surface Model A(+) A-Temperature A A

A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09



Heating Transient 300 minutes after spacecraft subject to solar irradiation (450 incidence) and internal beating Temperatures of Imperfect Models -

Model TemperaturePrtotypeor Perfect Model MI Model MIl Model MII after Correction Surface Model _ _ _ _ __t (_+ )

Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15





Prototype dModel Temperature or Perfect Model MI Model Ml Model IIl after Correction

Surface Model A+_A( ) At Temperature I j

A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18


TABLE 63(f) Model temperatures before and aftercorrection

Steady State


Prototype Model MI Model MIl Model MIll Model Temperatureafter Correction

or Perfect Surface Model

Temperature1 Ej T1 4

r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19




Prototyv T mo eatures of Imperfect Models F SPrototyp Model Temperature

or Perfect Model MI Model MI I Model MIII after Correction ModelSurface FTemperature A A At )

__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___

Al] temperatures in oR

TABLE 63(h) Model temperatures beforeand after correcti6n

Cooling Transient 200 minutes after spacecraft moving into shad6

Surface

Prototype or Perfect

Model

TemperatureTp


Model MI Model Nil Model MIII

_ _(

T ENpound ~~Eua Tv IZ ~ I i~vI )


____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


are designated by t E-ii and Irii - Equation (238) is used

to evaluate A plusmn) which is the correction for all positive errors

and A the correction for all negative errors is evaluated from

(2313) The combined correction At is simply the algebraic sum

of A and A Finally the corrected model temperatures calcushy

lated according to (2314) are denoted by 9c and their errors are

c In either set of the foregoing tables data for the heating

transients are listed in tables (a) to (e) the steady state in tashy

ble (f) and the cooling transients in tables (g) and (h)

An inspection of these tables shows that the proposed correction

theory is indeed capable of providing good results when errors in

kd and in Cd of the original model MI are up to 25 percent and ershy

rors in surface emittance up to 20 percent (corresponding errors in

models MII and MIII are much larger) As an example take the case

of heating transient at t = 100 minutes after the sudden change of

the thermal condition Uncorrected model temperatures of errors up

to approximately 10degR in MI 260R in MII and 130R in MIII are brought

to within 4OR of the prototype value after correction [see TABLE 62(c)]

For the steady state corresponding errors of up to 213 206 and

345 0R are reduced to less than 250R [see TABLE 62(f)] At a time

30 minutes after cooling begins uncorrected model temperatures exshy

hibit errors of up to 238 249 and 3930R respectively for the

three models After correction the maximum error is 250R [see TA-

BLE 62(g)] Data for the 450 solar incidence show similar results

95

To test further the performance of the theory a second set of

errors in kd Cd s and c was studied They ate listed in TABLE

64 The magnitudes of the various errors are approximately the same

as before However both positive and negative errors now occur in

kd and Cd Moreover the modifications for model MIII are carried

out in such a manner that the negative errors become less negative

The results of this study are summarized in TABLES 65(a)-(h) when

the spacecraft receives the suns radiation at normal incidence and

in TABLES 66(a)-(h) for the 450 oblique incidence The spacecrafts

initial thermal condition the manner of the initiation of the heatshy

ing and cooling transients the relative distribution of internal

power dissipation within the bus etc are identical to those conshy

sidered in the earlier study All data again lend support to the

effectiveness of the proposed correction technique The errors lc

which remain in the corrected model temperatures are in-general

smaller than those shown in TABLES 62 and 63 Our limited experishy

ence seems to indicate that the theory would yield better results

when positive and negative errors coexist in each set of the modelshy

ing parameters

62 SPACECRAFT SUBJECTED TO CYCLIC HEATING AND COOLING

For an orbiting spacecraft the temperatures of its various comshy

ponents undergo continuous cyclic changes Under such condition

there was the concern that the error in the model temperatures might

accumulate and it was not certain that the proposed correction technique

96

TABLE 64 Errors in modeling parameters

Percentage error in modeling arameters

Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0


TABLE 65(a) Model temperatures before and after correctibn

HeatingTransient 10 minutes after spacecraft subject to solar irradiation (normal incidence) and internal heating

Temperatures of Imperfect Models 1 Prototype IModel Temperature or Perfect Model MI Model MII Model MIIN after Correction

Surface Model _(+)__

TemperatureTp T E Tw Ei Iz ms I I ElI I I

A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02


TABLE 65(b) Model temperaturesbefore and after correction

Heating Transient 30 minutes after spacecraft subject to solarirradiation (noAmaln nemo) and internal heating


Protot pe Model MI Model M11 Model MIII T after Correction or PerfectI

Surface Model I _ -- A A A Temperature T E T 1ET

0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760

A (=A i) 1722 1728 06 1726 041 1725 03 -023 098 075 1721 -01A01 temperatures in OR

All temperatures in degR



Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I

Temneoatures of Imperfect Models

Model MI Model MIX Model MIII

__ _) _4 T r p ST I EplusmnIu TVU I I Ei I I

5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03


TABLE 65(d) Model temperatures before and aftercorrection



Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06



Heatinz Trim n nt 500 minutes alter spacecraft subject o solar irradiation (normal incidence) and internal heating

TemPoratures of imperfect Models

Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01

Model M11 Model MIII Pefectafter

T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008

Model Temperature Correction

T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State

SjTemperatures of Imperfect Models

Prototype Model MI Model MII Model MIII or Perfect - after Correction

Surface I Model (+) () I oeTemperaturebullT- rz t TM MUi I TFIZZI vr T

At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06



Cooling Transient 30 minutes after sp-acecraft moving into shade

Temperatures of Imerfeoct Models

Prototype odel MI Model MII Model MIII Model Temperatureafter Correction

or Perfect

Surface Model A() A1 Temperature 1 T AtT

A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09



Cooling Transient 200 minutes after spacecraft movinginto shade

Tomoeatures of Imperfect Models

Surface

Prototype or PerfectjModel

Model MI I Model Mll Model MIII A(+) K-A(-)

Model TempIrature after Correction

T e m p e r a t u r v TP

a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1


TABLE 66(a) Model temperaturesbefore and after correction



Prototype I Model MIX Model MIII ModelModel Temperature or Perfect after Correction

Surface Model _(+) -

Temperature Tix Tm 1 Tua I I

A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03



Heating Transient 10 minutes after spacecraft subjectto solar irradiation (450 incidence) and internal heating

Temperatures of Imoerfect Models y -Model Temperature

Surface Prototypeor Perfect

Model bullModel MI Model NIX Model MII

A)(-) after Correction

Temperature V E T I T I EI1 x TMC

A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03

All temperature in OR



Temperatures of Imverfect Models


Model MI Model MI I iI

Model MIII

)


Surface Model Temera tu

(I4 AA A t

Tf T I IT1 3S- T 7 I1 flvnI I

54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060

1666 -06 A12 ltemperatues-0ndeg




Temperxatures of Imperfect Models

Prototype ior Perfect

bullModel NI Model MIX Model MIII

bull bull


Surface i Model A(+) A(-) TemperatuTe i 1 TT Fi

T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09



Heating Transient 500 minutes after spacecraft subject to solar irradiation (4 50 incidence) and internal heating

Tcmeatures of Imoerfect Models

Model TemperaturePrototype I or Perfect Model MI Model MIX Model MIII after Correction

Surface Model A___ A__ I Temperature A A A

1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface

Prototype or Perfect Model

Temperature

Model

T

M Model M1 Model MIII t A(-)


M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714


TABLE 66(g) Model temperatures before and after correctioh


Surface

A1


ModelIT aure Tempert e

36

3665

Temeratures of Imperfect

Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I

Tompexatures of imperfect Models Model MI ModelMII Model M111

o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10


would still be capable of providing satisfactory results To obtain

some answers to these questions additional computer experimentation

was carried out in which the hypothetical spacecraft was subjected

to direct suns irradiation at normal incidence for 200 minutes folshy

lowed by its -ntry into the shade for 100 minutes and the cycle re-shy

peated itself thereafter The internal power dissipation was left

unaltered at all times At the very beginning the spacecraft had

a uniform temperature of 4000R throughout and the errors in the modshy

eling parameters were taken as -those listed in TABLE64 Other conshy

ditions were the same as those used in the earlierstudies Thecomshy

putation was continued for five complete cycles Because of the masshy

sive data generated only temperatures at 30 and 200 minutes from

the start of each cycle and those at the end of each cycle are preshy

sented herein In addition data for the third and fourth cycle are

omitted in the interest of conserving space This is illustrated

in Fig 61 Details of the temperature data are given in TABLES

67(a)-(i) It goes without saying that -the results are very encour-

Aging indeed A second experiment of the same kind was also conducted

in which the heating and cooling time were doubled so was the period

of-the cycle The results were equally good Details may be supplied

upon request

The foregoing studies have established beyond doubt the useshy

fulness of the proposed concept of imperfect modeling when the errors

in the modeling parameters are restricted such that the linear theory

is applicable and when they are properly controlled as pointed out in

114

700

A7 (Upper Surface of But

600f - t

o_400

H i HeaQampgIlt

Al (Solar Panel) 20o 00 mi L10in

Cooling Time m n

Pigure 61 Cyclic heating and cooling of the hypothetical spacecraft (open circle o denotes instant for which data are presented in TABLE 67)

TABLE 67(a) Model temperatures before and after correction (Spacecraft subject to cyclic heating and cooling)

30 minutes from start of the first cycle

Surface PrototypeIOr Perfect odPelfecModelA

Temzeratures of Imperfect Models

Model MI Model M11 Model M111 C-)_____A______


A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A

PrototypePrttp or PerfectMode1

Temperature

5979

Toriratures of Imperfect

Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I

Model Temperatureafe oreto after Correction

y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05


TABLE 67(c) Model temperatures before and hfter cortection

End of first cycle I

Surface


Model

Toecratures oil imperfect Models I SPrototypeI I oModel-odcl 141 Od l Tfe-Cme

Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10



30 minutes from start of the second cycle

Tcmno-ratures of Imperfect Models

Surface

PrototypeSor Perfect

Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06


TABLE 67(e) Mcdel temperatures before and after correctioh



Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A


Surface Temperature I t

A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle

Tcmopcraturcs of Imperfect Models iModel Temperature-


Model MI Model Mil _

Model MI ( A

odeafter Correction aeC ct

Surface Model Temperature T E TL

-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10



30 minutes from start of the fifth cycle 1 I

Tomperratures of Imperfect

frototype Model MI Modl MiSor Perfect Surface T~emperature WI

I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature

after Correction C Fv

A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7



200 minutes from start of the fifth cycle

Temopratures of Imoerfect Models bull II Model Temperature

Prototype odel MI Model MIX Model after ComectionM o or Perfect aeC c I

Surface Model AA A Temperature E poundUZ-00

1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06

All temperatures in CR

TABLE 67(i) Model temperatures bef6re and after correction

End of the fifth cycle

Temrocratures of I -mperfectModels

IModelI TemperaturePrototype Model MI Model MIX Model M1I after Correbtion or Perfect t A ) A-) ASur f a c e M o d e l t

Temperature r P E Tc A I 2748 2745 -03 2745 -03 -82 -036 -036 2749 01

A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir


Chapter 2 During the course of the present investigation additional

observations some of which are quite essential for the successful

application of the theory have been made They are discussed briefly

in the section which follows

63 SOME RELEVANT OBSERVATIONS

631 Influence of Decreasing and Increasing Model Errors on Prediction Reliability

The errors in the various modeling parameters as listed

in TABLES 6] and 64 are of the order of 20 to 25 percent in kd and

Cd and of 10 to 20 percent in c and e for the original model MI

It would be of interest to know how the reliability of the final corshy

rected temperature data be altered by increasing and by decreasing

such errors To this end the computations described in Section 61

were repeated first with all errors reduced to one-half of their

respective values as shown in the tables It was found that the imshy

provement in the accuracy of the corrected model temperatures of c

was totally insignificant In no case did it exceed 10R Thus if

the present theory is used for the correction of data gathered with

imperfect models there is no real need of striving for the undue

reduction of modeling errors provided that they are kept within

limits This welcoming fact allows additional flexibility in model

fabrication On the other hand when errors in the modeling parameshy

ters are doubled the reliability of the correction procedure deteshy

riorates rapidly Errors in Thc as large as 20OR have been noted

125

This points to the need of a development of a more general theory

-whichcould accommodate greater errors in the modeling parameters

632 Proper Control of Model Errors and Selection of Experishymental Conditions

-TIt-has been-demonstrated tin-Chapter 2 that the best reshy

sults obtainable from the present theory arise when the ratios

and -) are close to 12 [see Fig 23(al) and (b2)]

or 2 [see Fig 23(a2) and (bl)] depending on whether in the modishy

fication experiments the magnitude of the 6s increases or decreases

These ratios evaluated for the simple error space are respectively

0474 and 0532 for models prescribed in TABLE 61 and are 0474 and

164 for models prescribed in TABLE 64 The ranges of errors shown

in Jhese tables are in fact selected with the guidance of the said

theoretical requirements- The question which naturally arises is

In the modification experiments with models MII and MIII would it

Tnot be desirable to strive for smaller errors That is to make the

positive errors become less positive and negative errors less negashy

tivet To see if this were the case the computations described unshy

der Section 61 and pertaining to models prescribed in TABLE 64 were

repeated but with both positive errors in model MII and negative

errors in MII kept less than 5 percent The change gave rise to

rather unfavorable ratios in namely F(j42 - 031 and

4-) ) - 022 It was found that the computed data for Te showed

tSuch modification scheme may be unrealistic in practice However this is NOT the point in question here

126

little or no improvement over those given in TABLES 65 and 66

In the discussion of error paths in the multi-dimensional error

space four possibilities are considered as illustrated in Fig 23

In the first modification experiment all positive errors remain posishy

tive after modification whether they become smaller or larger Likeshy

wise in the second modification experiment all negative errors reshy

-nmainnegative -Clearly such are -not-the-only-possibilities -it-is

physically feasible to have mixed errors (positive and negative) afshy

ter modification although they should always be avoided for reasons

to be seen shortly Consider for instance the experimentation with

MIII Some of ther~piginally negative errors may become positive

after modification while others remain negative Under such circumshy

stance the parabola joining the error states P P(-) and 0-) in

-subspace S( ) would have a relatively sharp curvature thus creating

a condition that is in direct conflict with the fundamental assumpshy

tion upon which the theory is built

To provide a pictorial illustration we consider a three-dimensional

simple error space shown in Fig 62 The coordinates of the point

P which is associated with the original model MI are all negative

Suppose that after modification 6 and remain-negative but P 1 2 3

become positive Thus the point P(-) would be a8 shown in Fig 62(a)

The error path joining P P(-) and 0(-) makes a sharp bend as illusshy

trated and it would totally invalidate the linear theory developed in

[1 and in this report On the other hand if P remains negative3

as shown in Fig 62(b) the error path would have a gentle curvature

127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)

Schematic representationof error path as affected by model design

which is small everywhere along the path If all s are made posishy

tive it is again possible to have an error path which has a uniformly

small curvature This is illustrated in Fig 62(c) The three points

through which the parabola passes must now be of the sequence P

and P(-) The extension of the foregoing consideration to the design

of model MII experimentation is obvious

- Extensive numerical calculations have been carried out not only

for the hypothetical spacecraft considered in the present report

but also-for a totally different problem namely the correlation

of boiling heat transfer data and the results conclusively demonstrate

the validity of the arguments just given The nature of the error

paths has a controlling influence on the reliability of the theory

Error paths exhibiting small and sharply changing radius of curvature

such as that of Fig 62(a) should not be considered in any circumshy

stance

64 CONCLUSIONS AND RECOMMENDATION

Based on the evidence provided by a computer experimentation

of the application of the proposed new theory of imperfect modeling

to the study of the thermal performance of a hypothetical spacecraft

the following conclusions may be drawn The hypothetical spacecraft

has major radiative and conductive heat flow paths that crudely simushy

late those of the 64 Mariner family of space vehicles

(1) When errors in kd and Cd of up to 25 percent and in surface emittance of up to 20 percent exist in the model and when the spacecraft is subject to either a simple heating and

129

cooling transient with an intervening steady condition or whenit experiences a continuous cyclic transient the inshydicated model temperatures would entail errors of 10 20

and 30Rand higher These errors were reduced to less than 30R after a correction according to the theory There is no evidence of error accumulation under the cyclic conshydition investigated

(2) While the theory is deduced under the basic assumption that the errors in the modeling parameters are small and that they have independent effects on the dependent variable or variables there is no need to strive for the undue costly reduction of these errors Rather in the modifishycation experiments the model design andor the test conshyditions should be properly controlled in order that the ratios p+) 4Q) and 4p-) 4_) do not deviate excessively from 12 when the magnitudes of the 6s generally increase or 2 when they generally decrease

(3) The reliability of the theory deteriorates rapidly when errors in the modeling parameters become large At the present time it is not feasible to describe quantitativeZy what is meant by large or small error

In view of the success as well as the limitations found in connecshy

tion with the performance of the theory it is recommended that furshy

ther investigation be launched with emphasis on developing a means

of treating large errors

130

REFERENCES

[1] Chao B T A Study of Thermal Scale Modeling with Imperfect Models Proposal Gr-2-2404 submitted to Jet Propulsion LaborashytoryPasadena California May 28 19

[21 Bobco R P Radiation Heat Transfer in Semigray Enclosures with Specularly and Diffusely Reflecting Surfaces J Heat Transfer Trans ASME Series C 86 123-130 (1964)

[3] Plamondon J A and Landram C S Radiation Heat Transfer from Nongray Surfaces with External Radiation in Thermophysics and Temperature Control of Spacecraft and Entry Vehicles edited by G B Heller Progress in Astronautics and Aeronautics v 18 173-197 (1966)

[41 Hering R G Radiative Heat Exchange and Equilibrium Surface Temperature in a Space Environment J Spacecraft and Rockets 5 47-54 (1968)

[51 Chao B T and Wedekind G L Similarity Criteria for Thermal Modeling of Spacecraft J Spacecraft and Rockets 2 146-152 (1965)

[6a] Chao B T DePaiva J S and Huang M N Transient Thermal Behavior of Simple Structures in a Simulated Space Environment by Model Testing ME-TR-NGR-048 University of Illinois Urbana July 1967 78 pp

[6b] Chao B T DePaiva J S and Huang M N Results of Transhysient Thermal Modeling of Simple Structures in a Simulated Space Environment ME-TR-JPL-951660-1 University of Illinois Urbana November 1967 51 pp

[6c] Chao B T and Huang M N Transient Thermal Modeling with Simulated Solar Radiation NE-TR-JPL-951660-2 University of Illinois at Urbana-Champaign March 1969 55 pp

[7] Hamilton D C and Morgan W R Radiant-Interchange Conshyfiguration Factors NACA TN 2836 1952

[8] Strong P F and Emslie A G The Method of Zones for the Calculation of Temperature Distribution report prepared by Arthur D Little Inc to Jet Propulsion Laboratory Pasadena California No 1 July 1963

131

APPENDIX A

THERMAL RESISTANCE OF MULTI-LAYER INSULATION

The superinsulation used in todays spacecraft is a multi-layer

aggregate of aluminized mylar or teflon In the ideal condition

the layers form parallel planes and have no physical contact with

each other For the purpose of our present analysis such condition

is assumed Here again we adopt a semi-gray two-region spectral

subdivision of properties namely the solar and the infrared region

The directional properties of the surface are taken into account

by the simple diffuse-specular model ie p = pd + p All emitshy

ted radiant energies are assumed diffuse

Aluminized Surface Q-Exposed Surface (Plastic)

P T (=Txp Temp of Exposed Layer) C P

sPdbPspI T-iT

0

itrPd bPsb

yb (Temp of the Base Plate)

Fig Al A Base Plate Covered with Superinsulation

Figure A1 depicts a base plate at temperature Tb covered with

a superinsulation of n-layers The exposed surface is plastic and

132

is absorbing suns radiation at a rate

Q = S Cos 6 (A1)

where a is the solar absorptance of the plastic layer and S is the Zocal PI

solar constant (at the outer fringes of earths atmosphere S = 442

Btuhr-ft2) All properties shown in Fig A1 without an asterisk

are for the infrared range and the subscript a refers to aluminum

and p refers to plastic Appropriate values of reflectances and

absorptances of aluminized mylar or teflon currently used in spaceshy

craft applications are listed in Table Al

TABLE A1

REFLECTANCES AND ABSORPTANCES OF ALUMINIZED MYLARt

Solar Range (0251-25p) Infrared Range (gt 5p)

Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050

Consider a typical section of two adjacent layers of the supershy

insulation eg A2 and A3 of Fig A1 We assume that the temperashy

ture of each layer is uniform and that the edge effects are neglishy

gible Figure A2 shows the equivalent resistance network when steady

condition prevails in the figure Eb is the black body emissive

power B denotes the diffuse radiosity and E23 is the exchange factor

tData transmitted to the author by Mr W A Hagemeyer of JPL

133

The subscripts 2 and 3 have the usual meaning

B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P

Fig A2 Radiation Network for Infinite Parallel Planes

Since A2 = A = A the thermal resistance per unit area is

R = b - Eb 2 Pd a Pd pQA (i -P ) + Pa sxa p sp

++ Es~(P - )(1 P (A2)2 l sa)(l - P)

The exchange factor E2 3 can he easily evaluated using the image techshy

nique Recognizing that the separation distance between layers is

very small as compared with the lateral extent of the superinsulashy

tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence

Pd ad p iP P (1- ) (1- P ) (l1 s )(l - P)Sa S+p (A4)

a sa p sp sa Sp

134

If the surfaces are diffuse p = Pp = 0 and Eq (A4) simplishy

fies to

1 1 R=-plusmn+---1

a Ea p

---which is a well-known result

The resistance per unit area R I between the aluminum surface

of the last layer of the superinsulation and the protected surface

of the base plate can also be evaluated from Eq (A4) provided

That the three properties associated with the plastic namely E

pd P and p P and replaced by the corresponding properties of the

base plate Sb Pd b and Pb

The inward leakage heat flux through the superinsulation

can be determined from a consideration of the heat balance at its

outermost exposed surface It is

oT4 -aT

kt SCOS aO - T4 Tep (A5a) A p p exp

with

ER = (n - 1)R t RV C A 5 b )

n being the total number of layers in the superinsulation In pracshy

tice for the sunlit surfaces of the spacecraft

135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)

and hence a valid approximation for Eq (A5a) is

A R(EPS Scos - a1T)

b (A7)

which may be either positive or negative When the superinsulation

sees only the empty space any possible heat leak is away from the

surface A straightforward calculation leads to

Q A

-1

P

4 Tb

+ R

(A8)

where E R is again given by Eq (ASb)

While the foregoing results were obtained under the assumption

of steady heat flow they may be used for transient analysis withshy

out entailing significant errors since the heat capacity of multishy

layer insulation is usually quite small and in spacecraft applicashy

tion the transients are seldom very rapid

To ascertain the effectiveness of of superinsulation in reducshy

ing surface heat flux we consider an aluminum base plate with and

without the superinsulation when it is exposed to

a sunts irradiation of a local intensity of 300 Btuhr-ft2

and

136

b the black empty space

The plate has a temperature of 528 0R and is either highly polished

or is sprayed with PV-100 white paint By using Eq (A4) and the

relevant data in TABLE AM one finds

R = 21 for aluminized mylar or teflon plastic side out

388 when the aluminum base plate is highly polished Rt =

202 when the base plate is covered with PV-100 white paint

Then it follows from Eq (A5b) that for a five-layer superinsushy

lation R = 1228 and 1042 respectively for the highly polished

and painted base plate The corresponding valuesfor a-ten-layer

insulation are 2278 and 2092 and for a twenty-layer insulation

4378 and 4192

With the foregoing information the leakage surface flux can

be readily calculated from Eq (A7) and Eq (A8) The results

are shown in Table A2 In practice the effectiveness of insulashy

tion is somewhat less due to the unavoidable conduction leaks

137

TABLE A2

Effect of Multi-Layer Insulation on Surface Heat Flux Btuhr-ft2

of an Aluminum Base Plate at 528degR

Based Plate Highly Polished Base Plate Covered with PV-100 White Paint

Without With Superinsulation Without With Superinsulation Superinsulation Superinsulation

(number of layers) (number of layers)

5 10 20 5 10 20

Surface Exposed 533 -035 -019 -010 - 506 -041 -021 -010 to Suns Irradiation

Surface Exposed - 67 -107 -058 -030 -111 -125 -063 -032 to Empty Space at 00R

The positive value is for heat flow into the base plate all negative values are for heat flow away from the base

plate

APPENDIX B

A NUMERICAL EXAMPLE

As an example we consider the case in which errors in the modshy

eling parameters are as shown in TABLE 61 and the suns rays strike

the solar panels at normal incidence Specifically we refer to data

listed in TABLE 62(d) which is for a heating transient 300 minutes

after the spacecraft is subjected to solar radiation and internal

heating The choice of TABLE 62(d) for illustration is totally arshy

bitrary any other tabulated data given in the report may serve the

purpose equally well

First we note that the perfect model temperatures listed under

T are calculated from the equation set (336) using the theoreti-P cally correct values of the modeling parameters This is achieved

by the combined Newton-Raphson and Gauss-Seidel procedure as explained

in Chapter 5 The various temperatures of-the three imperfect models

II II and Tlll are computed from the same equation set using

the same procedure but with modeling parameters entailing errors

as listed in TABLE 61

To illustrate how the various corrections are computed-it is

sufficient to work out the details for one of the surfaces say A6

At t= 300 minutes after the start of the heating transient

TI = 542JPR TII = 5383degR and M1 II 55540 R These may be MI

compared with the theoretically correct temperature of 52440R and

hence their respective errors are 177 139 and 3100 R All

139

temperatures cited here may be read from TABLE 62(d) in entries folshy

lowing A In passing we note that the three temperatures associshy

ated with the three imperfect models correspond to the function

of Chapter 2 as follows

T~

T TLIII i

T

4 ) DETERMINATION OF CORRECTION FOR POSITIVE ERRORS A

Prom TABLE 61 it is seen that the various positive errors are

(a) for Model MI

A A A4A 5 A A A A0 A A1

kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140

The asterisk designates errors after modification In the present

instance all errors become more positive after modification Hence

the error path is as illustrated in Fig 23(a1) and (238) is the

appropriate formula for determining A + )

From the foregoing data we may readily calculate

2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740

Using (239a) we find

141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687

Also ( = 3687 192 Hence from (234ab) we determine p

1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056

Substituting the foregoing values of a and X in (236b) gives

f(aA) = 00549

and hence the ratio of arc lengths is

- 2 = 2116

I 00549S(+)

as according to (236a) Finally the required correction for all

positive errors is given by (238)

+ 5383 - 5421 21=- 340oR2116 - 1

which is listed in TABLE 62(d)

142

-DETERMINATION OF CORRECTION FOR NEGATIVE ERRORS A(

From TABLE 61 it is seen that the various negative errors are

(a) for Model MI

A7A A3 A A A A1 -A AAAIA

kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008

and 6 = -0102 for superinsulation covering A and A 0

(b) for Model MIII

A A A A A A A6 A7 A8 A Ao A1A1

kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128

and 6 = -0205 for superinsulation covering A and A0 Again the ER7

asterisk denotes errors after modification Since all errors become

more negative after modification the error path is as illustrated

in Fig 23(b2) From the data we find

+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1

which is given in TABLE 62(d) The total required correction is

At = P + - -340 + 1989 r 1649degR

and hence the corrected model temperature is

1649 = 52560Rc = 5421 -

Upon comparing with the theoretically correct value of 52441R one

sees that the error in TC is 120R

145

N70-20517 -20548

SPACE PROCESSING AND MANUFACTURING

George C Marshall Space Flight Center Marshall Space Flight Center Alabama

5 February 1970

0

g 0

00-0- 001 0

Distributed to foster serve and promote the nations economic developmentand technological advancement

NATIONAL TECHNICAL INFORMATION SERVICE

US DEPARTMENT OF COMMERCE

0

This document has been approved for public release and sale


O GN ZAT N t0-53993









I ABSTRACT





I O o~ 0t

NASA







WITH APPLICATION TO


by


FINAL REPORT

to


Contract No 952593





US DEPARTMENT -


NOTICE














NEW TECHNOLOGY


ii

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145


O GN ZAT N t0-53993









I ABSTRACT





I O o~ 0t

NASA







WITH APPLICATION TO


by


FINAL REPORT

to


Contract No 952593





US DEPARTMENT -


NOTICE














NEW TECHNOLOGY


ii

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145




WITH APPLICATION TO


by


FINAL REPORT

to


Contract No 952593





US DEPARTMENT -


NOTICE














NEW TECHNOLOGY


ii

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

NOTICE














NEW TECHNOLOGY


ii

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145







NEW TECHNOLOGY


ii

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

ACKNOWLEDGMENTS












iii

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

ABSTRACT
























iv




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145




V

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

NOMENCLATURE

A = area ft






d = thickness ft

E = exchange factor

F = shape factor








t = time hr






= surface emittance

vi




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145




Subscripts



m = refers to model


Superscri pts






vii

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

TABLE OF CONTENTS

Page














REFERENCES -1



viii

Chapter 1















































sible to attain

2

Chapter 2







21 BASIC IDEAS



y = y(x x2 x ) (211)




jof the relation

44( I12 11) (212)







3











as

( i ( (213)








clear later


n (1 + 6 ) s2 (214)= j [111 ( 1 + 61) 112(1 + 62)


4





n

0) + C 6 j =



(0)() (216)C 0













5





more we define

r

P) C (217a) j=l

n

p)3 c6 8(217b)

j =r+



~ 0) (t+)+A(21)











6






6 = j = 1 2 r (219)


rn

+) + C (21) ]]] ] 21

j j = r +


Ir

j 1


r

6c

jl (2112)


+)- = (a- 1) C 6( j=l

7


4 - (2113)a-i










= = j r + 1 r + 2 bull n (2114)


n1

)- + c06 (2115)

1j ++

It follows then

n

- C ( - 1) (2116)

j r+l


- defined namely

n

j=r+l (l7)

E Q 6 =r+l 2

then

= 1 (2118)






imperfect models







present study



pound

(6 6 6 1 6)

S 2 r r+ n

pd- ( 6 6 6 6shy(6 1) 2 r r+1 n












are

j 120T)P=LI1= 12

and

_______112 __

aL 12

0(+p(+ = (6D) = tj = a O+p1[jr-+

[j r 16)2


10


-1 H


p__j 2) (l c2P

Subspace S



12i





+ =1 1 (221)J+) 4 +) -- 1a

0( + ) p



S(-) Thus

= 1K 621



________ - 1 (222)

-1


12

--

0+ 1 p (+)

r-_l

(b)

-)p P(-) 0


13

3















0(+)P and 0 +) P (+ ) are

C ) P = (C )2 12

and

12

0($)P +) - (C 6)

j =



14
























15

(a1) (a2) A

__(b1) ) ( _ _ C+P (b2) shy

_________

A

0)0

ampige (+d















T(+) a+) +b )2 (231)


r= 1142(C 6y) ]2j(a

(232b) = 0


r


E - - j1n 2 (233a)

7+ shy+

17

in

(+) )

EVI[P)P12 - (4) I2 1~2 Ij=l1


+)

a b +-

1-shy

2(96

can be shown that

(2s33b)

(234ab)


s4 +) f 1

1 -

Ll+GV- i 2( + 12 C2i12

a( + a) + Zn [(1 + a2 + all (235a)


1 =-0-[b- a(l + a2) 12 2a)+~~Y 2 2n2(i+2 a

where

- aX(l + a 2x2 12-- n [Ci-+ a 22 ) 2 + aX] (235b)

2b (+) = 2 P (-1 lt X lt 1) (235c) a P +(+)

18

_ _ _


2s( + )

2 (236a)(a

s(+) 1-f(aX)

where




-12 12

C(2) Z 2(6) I_ __TIP I__-cent+ = p )2

(237a)

4+) Zc66 (237b)

4+ + shy2 -c2_ 2



positive errors is

+ - (238)s(+)

19







-12

(239b) (23___b)

j(+)

1(6)2











20
















explained





was found that

4(2310a)

1

(+) s

21

in which

sd + ) i - f(ax) (2310b)

f +) 2 S


(+)

a i 1 (2310c)(+) (2310)qPP

1shy

(+)

P

(+)

wherein

gt (22gt 2o 2

2W-27 C2 6I L ((2310e)

and

(2310f)4+) c22=




22


12

(1gt2) 5 - 2 J(2311a)

and

4- (23lb)







_ s 4--I ) (2312a)

1 - shy(- )


( -) s - 1 - f(aX) (2312b)

2

23


denoting

a = ------ (2312c)

---C-)

i 2 (2312d)

--wherein

12C 7Co2--v2s ) = (2312e)

and

=) (2312f)

n


j

the mean



case

24

-) _ I - - cent(2313a)

sC_ shy

where

-)_ 2 (2313b)

S-) 1 - f(aA)








25

Chapter 3




















2 Btuft -F


26

---------- --


Xii 450

A8

I 7 AG I

A7 )

i i i 5

A6 A4





27


























28

TABLE 31


(a) Solar Panel


(b) Bus


d in


A6 Aluminum Alloy 802 371 0 1875 5086


A-110-AT


291 280 01875



(c) Antenna



29

TABLE 32


P

Solar

P or Pd

Infra-red

PS a(=E)

kd (equivalent)

Cd (equivalent)

Solar Panel



0

080

020

0

080

020

020

017

0

0

080

083 0058 029



080 0 020

-- --

017 080

0 0

083 020

0489 0269



080

--

0

--

020

--

017

080

0

0

083-125

020

0580



--

085 --

015 --

050 015

0 0

050 085

00383 0292



080

--

0

--

020

--

017 015

0 0

083 085

0455 0437


0 080 020 ----

0 015

095 0

005 085

0655 0287



0

--

085

--

015

--

050

015

0

0

050

085 00175 0080


face away from sun

025

--

005

--

070 018

095

0

0

082

005 0428 0204




























31



B= p (SE + H-I) (321)i d i




N

Hi= E (322)

j=l






N

B BS= pa SE + p B (323)E 1 1 d i 1 3

j=1




32

+= S H)(st

A B (324)




sis



Q1 = Ad(sE + H ) (325)










see that

= cos 45 B = 1 1 1 -2 1-3 1-3 (326a)

E=E = E =ED = 0 E =F 2 3 2 3-3 2-3 _3

33

Ao

Front -c--

A11 A1i0A

10_

A 2iComputer

__

logram)

_ __

2

Front

__

View

flA51 A4


A A 2I

Lw

I A5 A 4

Figure 32

Top View



B1 - p 1F -B = p s cos 450

B - p 2F2 B3 = 0 (327a)d2 2-

p (F B + F3B -B = 0 d3 -1 -2 2 3


from (324) or (325)


bull 1 B 1 = 0 E- F

E= 1 E = 0 E F (326b)

EB 0 E_3 0 I

Consequently

- P F Bwd 1 --3 3 = o SI -dI

B=p (327b)F S

P- (F B + B) - B = 0d 3- 1 F3-23-1 2- 3




V cos 450 4o 4-6

E=(lp )cos 450 E =6 F1ES + P6 = B_ = F5 -6 (328Y

= ( + p ) 005 450 E- = 0 6 S5 6-6

35

and


4 4 -66 cil 4 o 5

B - p F B = p ( p )S cos 450 (329)

4

d5 5-6 6 d 5 s6








The results are


S cos 450sin 300 (3210a)

91 9 pw P F F








36















4

B = T- + P H (211)

and

S E B (3212)

j =3

37

Thus

N

B = T - P i EB (3213)

j=l


--be-rewritten as

N4

aBB i =1 2 N (3214)

jnl

where

a = 6j Pd iE (3215)




AkakAB (3216)






38


is

b1 1 - b1 2 bIN

a- [b 21 22b2

(3217)

bN bN bN


B -- bji (3218)


N Ak

-k 1gt (3219)

j=l






A A A2 2(3) 2(3)


39









ElB 1 = El_ 2 = 0 E1_ 3 = F_3 11_ = F _ p 3F1( )

E2- 2 z 0 E2_3 = F2_3 E2- = F2 -e + P 3 F2 ( 3 )-o (3220a)



a1 1 =1 a1 2 = 0 a1 3 = -Pd IB-l 3 a -d IEl e

a2 1 = O a2 2 1 a2 3 = -Pd E2 3 a = - d 2 E2 -0 (322 b)


ae1 =0 ae2 =0 a 3 =0 aCe =1







40




with the system I A





EII I 0 E1l -C = I Il e + p 9 F11( 9) _-C


ag _9 i a-19 1 -_d 9d9g-1 1 a9- = Pd99e I(




141











42











(kd) (kd) -) (k )- -2 + (331)




= (kd) = (kd) (331a)1 -3 1 3







43


sis










4 4 - a(T1 0 T10 1) (332)

AR


APPENDIX A



dT1At (Cd) d- + )a (T4 T24 _ a (T 4)

I 9T -2 9 C 4

1-1 (1 T5 )-6tl -4 (T41 T42 4a T4

T4 K1 2IV 4 If-1_ 1aTl 1 1 A (T1 T2

44

dT2 4

44

- d a(T - ) - (T T2 _1 2 - T3 2

-2-I ( r ( T4 )a T112 11

44- TII) AA r(T 2 -T 14 4shy)


A (T-T- T3 2

A (T$ - T8 ) A(T 3 6 -T T T

AT3 10T A 31- T 7 S-e 3 Y-T3 -

K 3 _1 0 A T3

2-1100AT10)

43i0

-- 5 )ar( A 3 4

A4cC 2 4- -5T 4 T5 or 4-6 ( 4 T +- 4-e4 4t-1 4 1

I4t-2

CT4

4 - T74)

2 - 27

4-101 T~4

4 T 4

10t

4 A K4 -5 14 11 4( 1)T

4~5

dT 54

A (Cd)- 4 T- - 10(T

+ S4 A (- T4 4

T q -4q( plusmn4-4(d )T -2 -(T -T)4(

6 66

6

T

o

-

4 -A

T ) 4

a

K (T-i r

T7

- T )

-~ OC(T7-T)676-8 6-7 aT 4

K6-8e

- A6-T14T

K

4-7 T

6-7

6- 4 6T 4

6-1

T

7

A-7

- -T 9)7_T

-lt76-e K7-66T 6--

A (T6 - T9 -42 OC OT (6C 10 At 6

- (

76)

(--T- 7

T

( 7 -T8

-T1 44 4 4

7-6 ( 7

45 (

Y7 --9 atr

A (-T7 467

- - 7

4 -4) - -

T K)-6

A7 - T6

8 CTT7

r(

(T

CT8

T8a 4 T

- ) 8

(T 7lc

-9 -- CT 7 T9

463

A8 (Cd) dT

- 9 - -7

4 -

(T 8

T7)7

4 4 a (sT - -

- 95 a (T8-9 8

9aC4

-

T49

4 T

-

- (T

-

-T

TI0) K8-7

)A--(T-7)

(TA

1(8-10

A (Cd)99

dT

9dt - 8-96plusmn q9

T4 T9-1 8-97K_0 - 4-

911 9 -e TIoT

9 T(T

A

Al0

(Cd)


- oC7~ -gt 9lto-3

A ((T 4- T

- 9-7 9 7

e2 GT4 T4

-10 9

(- T A (T9 - T

4 -- =( -7((T

10 10plusmn 0

41 T4 o) - - ( 1O

-9_ -b

K9o9-6

9 AC(T - T)

9-8 9 8

- 9lt93 (7T o10A 9 - T9

K- 7

A 9 7

4 4)4lT) 0 10-3 10

T4

9-_I0

A

4

3

0

- 6 10 6

4 OF8 a(T

10-8 0

K 03(T -T)-0-A 10 3

K~~ )- -T

A 10 8

10-7 10 7

CT(T - T4

10-90

(7 -T A 10

(T A 10 9

4F7

- 7 t4 )(T 4a1 41 0 o0 01 1

ZR

40-4 10 4


10

T 4

A1 1 (Cd) dtT - T UT1111 dt 111-9 11 9 11-e 11

4 _TT4

c(T4 TT44 or (CT4- 74 4 11-1 11 4111-5 11 5

- -o 1 - lot - aT4 11 1 01 c T1)




ables

T2F (334a)

0

ki tS3

(33 4b)C A

3 cT A

= (334c)

-(kd)




48





must be so related

that

kI k2 k3

TIT2T3 2



deI qA

r - + - + z5 + z 7 + V A A(kd) - [1-- - e- 1 - 1

4+ + + + -I -St_ -1 t10 1 t 5 tI 1-2 1-~L~ 2~l3

(kd)-( ) (--

A 7 2 (kd)2To 2 It 1 t 23 +22+Y 4t

4 4

2L-1 -5 amp 21-10 tO

457 1 K21 2tL1T 1J (kd)2

4~9

t

dt3

~

(q + q3 )A

( d T-~+c

[

+ +

04

S 73-10 10]9 4 4

-7+plusmn 2 4

- z- -4

4

Y3 -7K-_43 9K3_

4 d4= 4 -

(kd)4-( 4

53-2 2 -o3-_6 +63_-7

-k- 97- 2s 33 3)

qA [T- $ + (d) T 4464+


A14

4

8

3

+

3 _9

_7 9 _

1-

L1 L2

+4

A + 4)

4

4- d It]-21 2shy

-V

K4-5 ( k)4

4 10 A0

5

is2

55Aq6A


5 -6 ~6 75-llI Z5- 2t - L1tl

4

OloI

ii kd) 5 ( 4

50

+ 66-7+lt(4 t + 6-(gj ~d~~ )A

66A6

44-

-)069 +-F + 6 _8c 66 _(K6


+ -3 4

Td6

0 +

-kshy-- +

--

d c1-76~l 9 2

-d 7 -425 - 7-

A ( 7Tk70 t0 )R

_ +74987-33 +Th71 e7 7

4 y 7 - + r 7

9 (k 7 -1 1 Tkd) 7

-81 plusmn K7 -6~+ -7 plusmn+5 7 -9


41

8 7tY-ss +1S-10 5 K8 7

I K

dcent (q9 + +

A 9 7 kd 9+ (k9+09-7 - 0

K1 -6

1 (lcd)9

( 6

(K9


1 - 9 8 81 - 0

- + K(9-6 + Y1(-7 + K9 -10 )09

+ k--79 _39-R

1(9_3 + (lcd) 9

4 3

0K9 -9-7

+ (kld) 9 6 + 4(kd) 9

_ _Z7 40Y9 -0 (ld)9 10

A1 0

do 10 d1 0

i __I5103+ + 10-6 10 -7+_

o4-_ 0 -8

+ 4 2

0-

(P4

10

421

R

4

lt

4qi

10-3

44 4

4)04 0-6 10-7 7

Z42 18

A)44474 8

44

lO- 9 j

A

-(lcd)

K 10-6

(lcd) 1 0

101 ++

RL 4)4o

4 10P

R0-1 11

0 -3

1 OK0-8

6

0-

i tI

So06 + 0-8+

K 0-9

Sl (lcd)1

10

10-2 02

+ 42Z p +

Kl0 -9010

9

1 0 14 T 4)4

47O21 42

II0

+ (lcd)

1015

1 -

3

4)4

+ OW5 1O 11 0e)io _e

52

(kd)q T ii+2 AI1 64)1 = fd 1 T 118 11-e- 111-11 11-2

11111-11 e 11shy

-42 1 1 it2 Th 11-4 4 1 t5

Z11i-lot 10J




d642 k C 6)d2

dT etcd2




be met






53


(kd) A L 2


(Cd) t

(Cd)p

- p




S337c)







54

Chapter 4
























55















relation

N

j =zs (41)

j=l







56








57

58



1

3535999

2

3535999

3

00

4

3535999

5

3535999

6

00

7

00

8

00

9

02376

10

00

11

1547000

12

00


1

2500340

2

00

3

00

4

2579092

5

2980498

6

750102

7

00

8

00

9

01680

10

00

11

1093899

12

00



I

1 2 3 1(3) 2(3)

3(l) 3(2)

J 1

00 00 0032810

0 03 28 10

2

00 00 0200040

0-200040

3

0032810 0200040 00 0032810 0200040

E

0967190 0799960 0767150 0032810 0200040

0032810 0200040



1 3 4 5 6 E

4 00 00 0032810 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767150 4(6) 0032810 0032810 5(6) 0200040 0200040 6(6) 0032810 0032810 6(54 0200040 0200040


I 1 1 2 3 E

1 00 00 0032810 0967190 2 00 00 0200040 0799960 3 0032810 0200040 00 0767190


I 4 5 6 E

4 00 00 OO328lO 0967190 5 00 00 0200040 0799960 6 0032810 0200040 00 0767190


Il J 1 2 3 E

1 1000000 00 -0006562 -0193438 2 00 1000000 -0040008 -0159992 3 -0005578 -0034007 1000000 -0130422 E 00 00 00 1000000


I 4 5 6 E

4 1000000 00 -0006562 -0193438 5 00 1000000 -0040008 -0159992 amp RME2

FOLDOUT FRAME

60 6 -0005578 -0034007 1000000 -0130422

F 00 00 00 1000000


I

1 2 3

E

1

1000036 0000223 0005585

00

2

0000223 1001362 0034054 00

3

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000

TABLE 46 CONTINUED

I

4 5

6 E

I J 4

1000036 0000223 0005585 00

5

0000223 1001362 0034054 00

6

0006571 0040064 1001399 00

E

0194338 0165478 0137133 1000000


1

1 2 3

J 1

0000117 0000715 0021816

2

0000715 0004360 0133012

3

0021816 0133012 0005670

E

0777351 0661913 0669534


I

4 5 6

I 3 4

0000117 0000715 0021816

5

0000715 0004360 0133012

6

0021816 0133012 0005670

E

0777351 066113 0669534



I J 9 11 E

9 00 0021500 0978500 11 0021500 00 0978500 9(11) 0489250 0489250 00 11(9) 0021500 0021500


I I J 9 II E

9 00 0021500 0978500 11 0021500 00 0998925


I J 9 II E

9 1000000 00 00 11 -0003870 1000000 -0179806 E 00 00 1000000


J 9 11 E

9 1000000 00 00 11 0003870 1000000 0179806 E 00 00 1000000


I I J 9 11 E

9 0000000 0000881 004911811 0000881 00 0819118



62

I J 1 2 10 5 4 11 E

1 00 00 00 00 00 0002700 0997300 2 00 00 00 00 0019500 0980500 10 00 00 00 00 00 0087000 0913000 5 00 00 00 00 00 0002700 0997300 4 00 00 00 00 00 0019500 0980500 11 0002700 0019500 0087000 0002700 0019500 00 0868600


I I 2 10 5 4 Ii E

i1 1000000 00 00 00 00 -0000459 -0169541 2 00 1000000 00 00 00 -0003315 -0166685 10 00 00 1000000 00 00 -0043500 -0456500 5 00 00 00 1000000 00 -0000459 -0169541 4 00 00 00 00 1000000 -0003315 -0166685 11 -0002565 -0018525 -0082650 -0002565 -0018525 1000000 -0825170


I J 1 2 10 5 4 i1

1 1000001 0000009 0000038 0000001 0000009 0000461 0169942 2 0000009 1000061 0000275 0000009 0000062 0003327 0169580 10 0000112 0000809 1003608 0000112 0000809 0043662 0494484 51 0000001 0000009 0000038 1000001 0000009 0000461 0169942 4 0000009 0000062 0000275 0000009 1000061 0003327 0169580 II 0002575 0018594 0082959 0002575 0018594 1003734 0873194


I I J I 2 10 5 4 1I

1 0000005 0000035 0000093 0000005 0000035 0000112 0829715 2 0000035 0000250 0000671 0000035 0000250 0000812 0827947 10 0000093 0000671 0001804 0000093 0000671 0002183 0494483 5 0000005 0000035 0000093 0000005 0000035 0000112 0829715 4 0000035 0000250 0000671 0000035 0000250 0000812 0827947 11 0000112 0000812 0002183 0000112 0000812 0OOOOTO o0455




I 3 6 7 10 8

3 00 0199820 0200040 0200040 0200040 6 0199820 00 0200040 0200040 0200040 7 0200040 0200040 00 0199820 0200040 10 0200040 0200040 0199820 00 0200040 8 0200040 0200040 0200040 0200040 00 9 0200040 0200040 0200040 0200040 0199820


I 3 6 7 t0 8

3 1000000 -0159856 -0160032 -0160032 -0160032 6 -0159856 1000000 -0160032 -0160032 -0160032 7 -0030006 -0030006 -1000000 -0029973 -0030006 10 -0030006 -0030006 -0029973 1000000 -0030006 8 -003000f -0030006 -0030006 -0030006 1000000 9 -0030006 -0030006 -0030006 -0030006 -0029973


I I J 3 6 7 10 8

3 1057707 0195533 0220391 0220391 0220391 6 0195533 1057709 0220391 0220391 0220301 7 0041323 0041323 1017-411 0046514 0046545 10 0041323 0041323 0046514 1017411 0046545 8 0041323 0041323 0046545 0046545 1017412 9 0041323 0041323 0046545 0046545 0046514


I 3 6 7 10 8

3 0002885 0009777 0046833 0046833 0046833 6 0009777 0002885 0046833 0046833 0046833 7 0046833 0046833 0083875 0224043 0224193

FO-L1U I0 0046833 0046833 0224043 0083875 0224193 8 0046833 0046833 0224193 0224193 0083875

9

0200040 0200040 0200040 0200040 0199820 00

9

-0160032 -0160032 -0030006 -0030006 -0029973 1000000

9

0220391 0220391 0046545 0046545 0046514 1017412

_

9

0046833 0046833 0224193 0224193 0224043 rfltlYO

T5_ 64 9 0046833 0046833 0224193 0224193 0-224043 0083875


I 11 2 3 4 5 6

1 2 3 4 5 6 7 8 9

10 11 12

00 0058000 00 00 00 00 00 000 00 00 00 00

0058000 00 00 00 00 00 00

0 00 00 00 00

00 00 00 00 00 00 0071100 0471490 0560795 0033714 00 00

00 00 00 00 0058000 00 00

00 00 00 00

00 00 00 0058000 00 00 00

7 760 00 00 00 00

00 00 00 00 00 00 0074391 0667263 0861395 0034437 00 00


I J 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

00 00 0071100 00 00 0074391 00 0070706 0072435 00 00 00

00 00 0471490 00 00 0667263 0070706 00 00 0033626 00 00

00 00 0560795 00 00 0861395 0072435 00 00 0034012 00 00

00 00 0033714 00 00 0034437 00 0033626 0034012 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 00 00 00 00 00 00 00


CHAPTER 5


51 A RECAPITULATION







1 j1a

K K2j)-

ji ji

where






pose

65


1 0


ER (kd )7 T0











cal contact with A





Ci A d4

k dt I



66





M (T+ AT) - (T)] = Q AT- (c + (+Y4

j


_j f dT) - d) K_ dT

J ji

iK T (521)

j - TI-AT



T+ AT


T AT




67




ment one obtains

4

f4AT) + fl(T+ AT) +f ( 0

where

= (c gt+ - 7 _ )

fl (kd) K AT

ji


Ta AT (d) _12 ji

(523)

(523a)

(523b)

1-1

(lcd) 1

5

4t

-) (1cfS d(T) + (T)

+

j68


68

















g4i -i-g+i + go 0 (525)

where

(525a)4 1 -1 ++ plusmnC

69

g 1 (d) K _ (52 5b)

jjigo k )-d)( shy

go - K

j















70


g g (527a)i O i i i g4 i 4


A t1 + f 1 4) + f4 1 4

(52 7b)

















71

TABLE 51



HB 10 - 3 1

03 gt80

05 65

07 38

09 24

11 14

13 10

15 17

17 33

19 gt80



72

ie HBi lt10 -3I -






















condition

73

TABLE 52




02 09 5 5 4

04 09 5 5 5

06 09 6 6 5

08 09 6 6 5

10 09 6 7 6

02 12 5 4 3

04 11 5 4 3

06 11 5 4 3

08 11 5 4 3

10 11 5 4 3

02 13 9 7 6

04 13 9 8 6

06 13 9 8 6

08 13 9 7 6

10 1 9 7 6

02 15 16 13 10

04 15 16 12 10

06 15 16 11 9

08 15 16 1 9

10 15 16 11 9

02 17 31 24 18

04 17 31 21 17

06 17 31 26 19

08 17 31 24 18

1810 17 31 23




74

TABLE 53




Temperature OR


A1 5181 5978 5979 5980

A2 5205 6038 6047 6048

A 4294 5191 5339 5344

A 5181 5976 5979 59794

A 5202 6028 6042 6043

A 4122 4988 5244 52556

A 4015 4796 5277 5295

A8 4207 4995 5240 5250

A9 -4159 5116 5462 5475

A 0 4030 4908 5277 5290

All 4763 5680 5681 5681

A 2(= A 0) 1528 1811 1848 1850




cent)

75

Chapter 6











itself







by the designer





76




K 100 X 00 X100 X 100 X 100 lt 100 00 X 100 X 100 100 X 1OOO00

A 0 0 0 0 0 0 0 0 0 0 0 0

A2 0 0 0 0 0 0 0 0 0 0 0 0

A3 250 250 -180 100 550 525 -180 200 250 250 -288 100

A4 0 0 0 0 0 0 0 0 0 0 0 0

As 0 0 0 0 0 0 0 0 0 0 0 0

A6 250 200 -200 100 450 500 -200 200 250 200 -320 100

A 200 250 150 -80 400 550 270 -80 200 250 150 -147

A8 250 250 -180 -80 575 575 -180 -80 250 250 -259 -115

A9 250 250 250 -80 450 450 450 -60 250 250 250 -160

A10 200 250 150 -80 440 600 330 -80 200 250 150 -128

A 0 0 0 0 0 0 0 0 0 0 0

A12 (=A0 ) 0 0 150 0 0 0 330 0 0 0 150 0



















is created









78






TJ_ I I T Iv TMc

A 5181 5181 0 5180 -0i 5180 -01 -0-01 -005 006 5181 0

A2 5205 5200 -05 $200 -05 5198 -07 -005 -032 7037 5204 -01

A_ 4294 4262 -32 4219 -75 4275 -19 -389 188 -201 4282 -12

A4 5181 51810 -01 5180 -01 5180 -01 ~0 -004 -004 5181 0

A 5202 5200 -02 5199 -03 5197 -05 -02 -025 027 5202 0

6 4122 4114 -08 4092 -30 4120 -02 -195 098 -097 4123 01

A7 4015 4009 -06 4006 -09 4009 -06 -029 -011 -040 4013 -02

As 4207 4190 -17 4154 -53 4200 -07 -323 137 -186 4209 02 A9 4159 4129 -30 4109 -50 4130 -29 -176 023 -153 4144 -15

A1 0 4030 4018 -12 4010 -20 4016 -14 -066 -029 -095 4027 -03

A1 47E3 4763 0 4763 0 4763 0 -0 -0 -0 4763 0

12(=A01 )1A (-A

1528 OR

1533 05 32 04 154- 13 007 118 1n8

111

1522 1522 ~06




Surface

Prototype

or Perfect Model

Temperature



A ()

At

Model Teimperature

after Correction

A1 5907 5906 -01 5906 -01 5905 -02 -004 -007 -011 5907 0

A2 5949 5942 -07 5939 -10 5939 -10 -022 -043 -065 5948 -01

A

A4

A

A

4745

5905

5939

4403

4690 -55

5905 I 0

5935 0

4368 -35

4594

5905

5934

4303

-151

0

-01

-00

4720

5905

59341

4383

-25

0

01

20

-861

-002

-011

-583

447

-004

-020

224

-414

-006

-031

-359

4731

5905

5939

4404

-14

0

0

01

A7 4131 4093 -38 4065 -66 4091 -40 -252 -030 -282 4121 -10

A8 4506 4489 -17 4410 -96 4516 10 -7j10 409 -301 4519 13

A9 4454 4387 -67 4328 -126 4396 -58 -524 137 -387 4426 -28

A1 0 4243 4183 -60 4129 -114 4183 -60 -479 -001 -480 4231 -12

A1 1 5476 5476 0 5476 0 5476 0 001 -0 001 5476 0

A (=A1o0 ) 1722 1723 01 1719 -03 1729 07 -036 087 051 1717 -05






Surface or Perfect



Temperature A t

A1 5978 5977 -01 5976 -02 5976 -02 -006 -008 -014 5978 0

A2 6038 6031 -07 6026 -12 6027 -11 -036 -047 -083 6039 01

A3 5191 5243 52 5150 -41 5325 134 -835 -1224 389 5204 13

A4 5976 5975 -01 5974 -02 5975 -01 -006 006 -012 5976 0

A5 6028 6021 -07 6017 -11 6019 -09 -037 -033 -070 6028 0

A6 4988 4998 10 4880 -i08 5059 71 -1052 913 -139 5011 23

A7 4796 4694 -102 4541 -255 4711 -85 -1368 255 -1113 4805 09

A8 4995 5050 55 4948 -47 5123 128 -914 1081 167 5034 39

A9 5116 5069 -47 4942 -174 5119 03 - 1 1 36 751 -385 5108 -08

A 0 4908 4862 -46 4725 -183 4900 -08 -1225 579 -646 4926 18

A 5680 5681 01 5681 01 5681 01 ~0 -0 0 5680 0

A2 (=Alot1) 1811 1816 05 1802 -09 1830 19 -118 222 104 1805 -06




II

-

Surface


Model Temperature




t


A 5980 5979 -01 5979 -01 5979 -01 -003 -005 -008 5980 0

A2 6047 6044 -03 6042 -05 6042 -05 -015 -030 -045 6049 02

00 A

A4

5339

5979

5507

5978

168

-01

5476

5978

137

-01

5636

5978

297

-01

-285

003

1922

-003

1637

-006

5344

5979

05

0

A 6042 6041 -0 6039 -03 6039 -03 -017 -019 -036 6044 02

5244 5421 177 5383 139 5554 310 -340 1989 1649 5256 12

A7 5277 5406 129 5338 61 5505 228 -614 1468 854 5321 44

A3 5240 5430 190 5392 152 5553 313 -346 1832 1486 5282 42

A9

A10

11 5462

5277

5583

5412

121

135

5517

5355

55

78

5696

5513

234

236

-593

-511

1684

1504

1091

993

5474

5313

12

36

A 568 01 5682 01 5682 01 002 002 004 5681 0

A12 (=A 1 ) 1849 1877 28 1869 20 1906 57 -063 442 379 1839 -10







A1 5980 5979 -01 5979 -01 5979 -01 -001 -005 -006 5980 0

A2 6048 6045 -03 6045 -03 6044 -04 -005 -027 -032 6048 0

A3 5344 5528 184 5517 173 5663 319 -100 2011 1911 5327 -17

A 5979 5979 0 5979 0 5978 -01 -001 -003 -004 5979 0

A 6043 6042 -01 6042 -01 6041 -02 -004 -015 -019 6044 01

A6 5253 5453 200 5444 191 5595 342 -077 2123 2046 5235 J8

7 5294 5459 16 548 144 5559 275 -189 1637 1448 5301 07

A3 5250 5461 211 5449 199 5591 341 -104 1940 1836 5269 19

A 5475 5623 148 5591 116 5745 270 -293 1819 1526 5468 -07

A10 5290 5455 165 5435 145 5564 274 -178 1638 1460 5297 07 A1 5681 5632 01 5682 01 5682 01 002 002 004 5681 0



Steady State




Surface Model

Temperature

TP I

I (+)

A

A(-)

At

A1 5979 5979 0 5979 0 5979 0 -001 -005 -006 5980 01

A2 6048 6045 -03 6045 -03 6044 -04 -003 -026 -029 6048 0

A3 5344 5530 186 5522 178 5665 321 -068 2020 1952 5335 -09

A4 5979 597910 5979 0 5979 O -0 -002 -0-03 5979 0

A 6043 60421 6042 -01 6042 -01 -001 L014 -015 6044 01

A 5253 54551 202 5452 199 5598 345 -031 2136 2105 5244 -09

A 5295 5463 168 5450 155 5574 279 -115 1654 1539 5309 14

A8 5250 5463 213 5456 206 5594 344 -Ot60 1951 1891 5274 24

A9 5475 5626 151 5600 125 5749 274 -238 1833 1595 5467 -08

A10 5290 5458 168 5445 155 5568 278 -119 1652 1533 5304 14

Al 5681 5682 01 5682 01 5682 01 002 002 004 5681 0

A12(=AID)0 1850 1882 32 1880 30 1914 64 -016 473 457 1836 -14







A() A A-) jt__

A1 3765 3765 0 3765 0 3764 -01 001 -012 -011 3766 01

A2 3905 3901 -04 3902 -03 3897 -08 003 -066 -063 3908 03

A 5162 5396 234 5404 242 5547 385 078 2257 2335 5162 0

I A44 A5 j

3764

899

3763

3895

-01

-04

3764

3895

0

-04

3762

3889

-02

0

001

005

-014

-080

-013

-075

3765

3902

01

03

A6 5130 5368 238 5379 249 5523 393 094 2314 2408 5127 -03

A7 5270 5445 175 5436 166 5557 287 -081 1673 1592 5286 16

A8 5226 5445 219 5442 216 5578 352 -034 1978 1944 5251 25

A9 5434 5596 162 5574 i40 5722 288 -202 1880 1678 5428 -06

A10 5255 5432 177 5424 169 5545 290 -075 1686 1611 5271 16

All Al2 (=AI0 )

3952 1504

3953 1565

01 61

3953 1563

01 59

3953 1621

01 17

004 -018

004 837

008 819

3952 1483I

0







Temperature Tp Tt

I E

M1 TM I TDI Ic E

A( + ) A(- )

TIc

_

F _

A1 2298 2297 -01 2298 - 2295 -03 007 -036 -029 2300 02

A2 2757 2754 -03 2757 0 2745 -02 025 -133 -108 2765 08

A3 5003 5246 243- 5251 247 5409 406 045 2446 2491 4997 -06

A4 2290 2289 -01 2291 01 2285 -05 014 -058 -044 2294 04

A5 2727 2723 -04 2729 02 2709 0 050 -214 -164 2740 13

AA6 4918 5184 266 5196 278 5356 436 111 2580 2691 4914 -04

A7 5088 5286 198 5283 195 5413 325 -024 1901 1877 5098 10

A3 51041 5332 228 532-8 224 5474 370 -040 2123 2083 5124 20

A9 5256 5436 180 5416 160 5577 321 -183 2113 1930 5243 -13

A10 5083 5278 195 5272 189 5406 323 -054 1909 1855 5093 10

A11

A12 (=A10 )

2356

1348

2360 04

1427 79

2361

1426

05

78

2361

1498

05

150

016

-015

020

1051

036

1036

2356

1324

0

-24








4774 4773 4773 -01 4773 -01 -001 -007 -008 4774 0I fI -

2 3701 3695 -06 3695 -06 3693 -08 -006 -044-05 3701 0A 4257 4237 -20 4198 -59 4253 -04 -35 6 - 74249 I -

A4 4810 4810 0 4810 0 4809 -01 -001 -008 -007 4810 0

As 4993 14988 -05 4988 -05 4986 -07 -006 -033 -039 4992 -01

4304 4269 -35 4218 -86 4277 7 -457 4303 -01 A7 4017 4011 - 06 4007 -10 4010 -07 -034 -011 -045 4016 -01I

A8 4213 4195 18 4158 -55 4205 -08 -33 140 -193 4215 02

A 4169 4138 -31 4117 -52 4140 -29 -193 027 -166 4155 -14

AI 4036 4922 -14 4014 -22 4021 -15 -078 -026 -104 4033 -03

All 4476 4476 0 4476 0 4476 9 001 0 Q01 4476 0

A 1421 1429 -08 1427 -06 1439 -18 -010 160 150 1414 -07




A2


Mode Temperature

5355

3353




AI

5354 5354 -02 53541 -02 3336 -17 3331 -22 3328 -25

f

At T

-0041-01

-037 -416

I

-016

-153


F6

5356 3351 -02

A 577 459 -08 4488 -89 4614 37 -718 -679 -039 4572

A

A

A

5419

5683

4806

51-01

8 3 4732

09

-74

5417

56 4608

-02

-12

-198

5417

5671

4757

-02

-12

-49

-006

030

-1118

-009

-048

364

-015

-078

-754

5419

5682

1 6 -4808

0

-0

02

A7 4149 410 7 -42 4075 -74 4106 -43 -292 -023 -315 4139 -10

A 4535 4517 -18 4437 -102 4546 11 -757 438 -319 4549 14

A~i I 14505 4436 -69 4368 -137 4448 57 - 8 182 -426 4478 -27

A1 4276 4213 1 -63 4151 -125 4214 -62 -554 029 525 4265

A I 4980 4980 0 4980 0 80 0 001 -0 001 -4980 0

Aj(tAoI 1555 1556 01 1550 05 1566 11 -057 147 090 1547 -08







A1 5463 5461 -02 5460 -03 5460 -03 -008 -013 -021 5463 0

A2 2962 2923 -39 2903 -59 2906 -56 -173 -251 -424 2965 03

A 4981 5089 108 5002 21 5200 21-9 -781 1667 886 5000 19

A4 5534 5531 -03 5530 -04 5530 -04 -015 -013 -028 5534 0

A 5816 5802 -14 5794 -22 5798 -18 -078 -068 -146 5817 01

A6 5528 5560 32 5403 -125- 5657 129 -1410 1445 035 5557 29

A7 4906 4811 -95 4632 -274 4842 -64 -1604 455 -1149 4926 20

A8 5079 5151 72 5040 -39 5237 158 -999 1283 284 5123 44

A9 5249 5227 -22 5083 -166 5297 48 -1284 1049 -235 5250 01

A10 5026 4997 -29 4841 -185 5054 28 -1400 8L45 -555 5053 27

A 5206 5207 01 5207 01 5207 01 -0 001 001 5207 01

A (=A )0 1672 1681 09 1660 -12 1706 34 -185 369 184 1663 -09





Temperature j T At

^ 5465 5464 -01 5464 -01 5464 -01 -002 -Q08 -0 i r0

A2 2908 2898 -10 2886 -22 2887 -21 -108 9-a i 1-17

(0 A 5152 5399 247 5387 235 5564 412 -104 2472 10__2o

A4 5538 5537 -01 5536 -02 5336 -02 -007 -008 -051 5538 0

A5 5834 5829 -05 5825 -09 5826 -08 -033 -038 -071 58 02

A6 5734 59 6 202 5884 150 6102 368 -462 2485 2023 5734 0 A7 5401 5576 175 5515 114 5700 299 -542 1860 1318 5444 43

A8 5331 5556 225 5525 194 5699 368 -277 2138 1861 5370 39

AS9 U96 5763 167 570-3 107 5902 306 -534 2076 1542 5609 13

A10 5400 5580 180 5530 130 5706 306 -446 1887 1441 5436

Aia 5209 5210 01 5210 01 5210 01 002 004 006 5209 0

A1(=A) 1722 1767 45 1759 37 1812 90 073 671 598 1707 -15







A_ 5455 5465 0 5465 0 5464 -01 001 -006 -005 - 5465 0

A2 2914 12917 03 2919 05 2910 -04 019 -105 -086 2926 12

A3 5157 5417 260 5427 270 5587 430 085 2541 2626 5155 -02 A4 5538 5537 -01 5537 -01 5537 -01 -003 -007 -010 5538 0

A5 5834 15831 -03 5829 -05 5828 -06 -018 -034 -052 5836 02

TI

A___ 573 595 218 5929 1906128 389 -250 2566 2316 5725 -14

A7 5413 5618 205 5602 189 5750 333 -140 1979 1839 5434 21

A3 5337 5581 244 5575 238 5729 392 -047 2216 2169 5364 27

A9 5605 15794 189 5766 161 5939 334 -253 2169 1916 5603 -02

A1 0 5410 95613 203 5598 188 5746 336 -i33 1981 1848 5428 l-8

A11 5209 15210 01 5210 01 5210 01 003 004 007 5209 O

o723 j1772 49 1770 47 1819 96 -023 696 673 1705 -18



Steady State





r I______

T 5

) I

IMC IA A(-)

71Cz

5465 5465 0 5465 0 5464 -01 002 1-006 -004 5465 0

A2 2915 2919 04 2924 09 2913 702 045 -098 -053 2925 0

5158 5419 261 5431 273 5589 1 431 110 2546 2656 5153 j -05

A4 5538 5537 -01 5537 -01 5537 -01 -003 007 - 10 5538 0

A 5834 5831 -03 5829 -05 5828 -06 -015 -034 -o49 5836 02

A 5739 5958 219 5933 194 6130 391 -223 2572 2349 5723 -1

A 5414 5620 206 5610 196 5753 339 -088 1987 1899 5430 16

A8 5338 5582 244 5580 242 5731 393 -017- 2221 2204 5362 24

A0 5606 5796 190 5772 166 5942 336 -21Z 2175 1960 5600 -06

A1 o 5410 5615I _ 205

_ _ 5605

_ 195

_ 5748

_ 338

_ _ -092

_ 1987

_ 1895

_ 5425 15

A11 5209 5210 5210 01 5210 01 003 004 007 5209 0

A2(=f 0 1723 1773 50 1771 48 1819 96 7016 698 682 1704 -19






__ _ I - T1 N Tz 1j _ _ Tc _I_ I__ _1 A 3665 3665 0 3665 0 36 01 03 -010 -007 3665 0

A2 J 2886 2890 04 2895 10 2883 -03 -104 -056 2896 10j0248 A 5125 5391 266 5408 283 5562 437 146 255 2701 5121 -04

A4 3705 3704 -01 3705 0 3703 -02 002 -015 -013 3706 01 AS 3904 3900 04 3902 -02 3895 -09 016 03081 -065 3907

A6 5295 5577 282 5607 312 5754 459 272 2651 2923 5285 -10

A7 5367 5582 215 5581 214 5714 347 -006 1975 1981 538-5 18

A8 5290 5540 250 554-5 255 5688 398 049 2211 2260 5314 24

A0 5526 5726 200 5713 187 5872 346 -119 2175 2056 5521 -05

A 5343 5557 214 5558 215 5688 345 013 1966 1979 5359 16

A 3831 3833 02 3833 02 3833 02 005 006 011 3831 0

A1 2 (=A1)0 1497 1571 74 1571 74 1635 138 001 964 965 1474 -23 All in OR___




Surface


Model

TemperatureTp



_ _(



____t___

1T

A2

2278

2699

2279

270 0J 01

01

2281

2707

03

08

2277 1-0i

2692 -07

016

060

-033 1 -017

-131 -071

2280

2707

02

08

A 5005 5253 248 5264 259 5419 414 097 2480 2577 4996 -09 1

A4

A

2288

2734

12288

2735

0

01

2291 1

2745

03

01

2285

2722

-03

-02

026

090

-052

-190

-026

-10

2291

2745

03

11

A6

7

A

L4924

5096

5109

5197

5306

5344

273

210

235

5217

5314

5346

293

218

237

5372

5437

5488

44B

34

379

185

078

023

2626

1958

2160

2811

2036

2183

4916 f-08

5102 06

5125 16

A9

A10

5262

5090

5451

5294 i

189

204

544 0

I 5298

178

208

5596

5425

334

335

r-l06

030

2160

1955

2054

1985

5246

5096

-16

06

JA

All

(=A )i

2340

1348

2344

1431

04

83

2346

1432

06

84

2346

1502

06

154

019

006 1067

041

1073

240

1323

0

-25


























95



















ing parameters






96



Surface

A1

x 66

Ao 0

Model MI

6 6 6Cd

00O o K A o 0 0 0

6lc6d

1

0

Model MII

6Cd 6Cd

iMo

0 0

6J00X6Id lcX66d

x 0o xAOO 0 0

Model MIII

X610K6l 6Cd

x 1000o 0 0

6lti o

0

A2

As

0

-200

0

200

0

-288

0

i00

0

-200

0

420

0

-288

0 0

200 -110

0

200

0

-180

0

100

A4 0 0 0 0 0 0 0 0 0 0 0 0

A5 0 0 0 0 0 0 0 0 0 0 0 0

A6 180 -150 -320 100 396 -150 -320 200 180 -82 -200 100

A7 200 150 150 -147 420 330 270 -147 200 150 150 -80

A8 80 -150 -259 -115 192 -150 -259 -115 80 -90 -180 -80

A9 -100 -150 250 -160 -100 -150 450 -160 -65 -82 250 -80

A10 -180 150 150 -128 -180 360 330 -128 -108 150 150 -80

A11

A12(=A )

0

0

0

0

0

15 0

0

0

0 0

0

0

330

0

0

0

0

0 0

150

0

0







A Tr117 FMIC

A 5181 5180 -1 5180 -01 5181 0 -001 -009 - 010 5181 0

A2 5205 5199 -06 5198 -07 f 520 1 -04 -004 -054 -058 5204 -01

A3 4294 42927 -02 4253 -41 4277 -17 -359 378 019 4290 -04

A4 5181 5180 rOl 5180 -01 5180 -01 -0 -007 -007 5181 0

A5 5202 5198 -04 5198 -04 5199 -03 -0 -041 -041 5202 0

A6 4122 4167 45 4167 45 4147 25 -001 517 516 4116 -06

A7 4015 4015 0 4013 -02 4014 -01 -016 015 -001 4015 0

A3 4207 4278 71 4276 69 4250 43 -019 709 690 4209 02

A 4159 4183 24 4178 19 4169 10 -043 355 312 4152 -07

A)o 4030 4030 0 4025 -05 4029 -01 -044 040 -004 401 01

All 4763 4763 0 4763 0 4763 0 -0 0 0 4763 0

A(=AO) 1528 j1534 06 1534 06 1531 03 -005 090 085 1526 -02







0 F

T ~5 x ~ I0 - -01 I0 -0 0 A1 5907 5906 -01 5905 -02 1 003 -012 -015 5907 0

A 5949 5940 - 09 5938 -11 5943 -06 -017 -070 -087 5949 0

A 4745 4780 35 4702 -43 4739 -0-6 -719 1052 333 4747 02

A4 5905 5905 10 5905 01 5905 0 ~0 -004 -004 5905 0

A5939 5936 -03 5936 -03 5937 -02 0 024 -024 59391 0

A 4403 4516 113 45114 11 4464 61 -024 1327 1303 4386 -17

4131A 4134 03 4118 13 4128 -03 -149 160 011 4133 02

Aa 4506 4662 156 465-1 145 4599 93 -0-99 1588 1489 4513 07

A0 4454 4525 71 -450S6 52 4484 30 - 3 1025 852 4439 -15

AI 4243 41261 18 4228 -15 4243 0 -300 443 143 4246 03

A1 5476 5476 0 5476 0 5476 10 001 -0 001 54760





Surface

Al

Prototypeor Perfect

Model Temperature

Tp

5978

I

I




5977 -01 5976 -02 5977 -01 -003

----shy

-010 -013


__ _t

T c I

5978 0

A2 6038 6031 -0 6029 -09 6034 -04 -019 -066 -079 6039 01

A 5191 5976

5420 5976

229 0

5374 5976

183 0

5313 5976

122 0

-426 -001

2724 -004

2298 -005

5190 5976

-01

A5

A6

6028

4988

6025

5237

-03

249

6025

5216

-03

228

6026

5124

-02

136

-007

-196

023

2872

-00

2676

6028

4969

0

-19

A 4796 4901 105 4825 289 4840 44 -700 1538 838 4817 21

A3 4995 5261 266 5235 240 5154 1519 -2t45 2720 2475 5014 19

A5116 5306 200 52t8 142 5209 93 -441 2456 2015 5105

A0 4908 5076 168 5019 lli 4993 85 -521 2097 1576 4918 10

A A

(=A1 5680 1811

5681 1837

01 26

5681 1831

01 20

5681 1824

0l 13

001 -056

002 346

003 290

5680 1808

0 -03





Surface

AI

rPerfectPrototSe

Model

Temperature

I bull

5980

11

5979

I Tj I

-01

Model Nil

I TI

5979 -01

Model MIll

II iiD

5979 -01

A(+)

-001

-

A(-)

-007

Po p

I

bull -008

Model Temperature

after Correction T

7C

5g8 o 0

A047 6043 -04 6043 -04 6045 -02 -006 -043 -049 604R 0

A A

5339 5979

5659 5978

320 -01

5646 5978

307 -61

5522 5979

183 0

-113 -shy001

3462 -004

3349

-004

5

5

shy 1

0

5

A1 A5

A6

6042

8244

tI 604 0

5584

-0 2

340

604 0

5573

-02

329

604 2

5439

0

195

-005

-103

-021

3666

-0 25

13563

16043604 8

5228

0110

-16

A7 5277 5565 288 5542 265 5447 170 -217 2987 2770 5288 11

A8

A0

A0

5240

5462

5277

5585

5749

5566

345

287

289

5572

5718

5544

332

256

bull 267

5452

5622

5448

212

160

I 171

-119

-286

-198

3360

3209

3000

j 3241

2923

2802

5261

5457

5286 I

21

-05

09

All A 2(=A1o )

5681 1849

5682 1895

01 46

5682 189

01 5682 44 1874 01 25

002-026 004 553

006 527

5681 1843

0 -06





Surface

Prototypeor Perfect

Model Temperature

5980

Model MI or

z I Era

5979 -01


T1TIM I I

5979 -01 5979 -01

A(+)

-001

I

(

-007

At

-008


T

T c

5980 0

2

A3

6048

5344

6044

5669

-04

325

6043

5662

-05

318

6046

5532

-02

188

-003

-072

-042

3491

-045

3419

6049

5337

01

-07

A

A6

5979

6043

5253

5979

[6042

5599

O

-01

346

5978

6041

5592

-01

-02

339

5979

6042

5453

0

-01

200

-0

-003

-060

-004

-021

3695

-004

-024

3635

5979

6044

5248

0

-01

-05

A7 5294 5592 298 5579 285 5473 179 -120 3031 2911 5315 21

A3 5250 5600 350 5591 341 5466 216 -075 3383 3308 5277 27

A1o

All

50

5290

5681

5768

5587

5682

29

297

01

5573

5689

269

283

01

5641

5467

5682

166

177

01

-228

-128

002

3234

3029

004

3006

2901

0106

5471

5309

5681

-04

19

0

__ 0)_ __1850 1898 48 1896 46 1876 26 -018 5 544 1837 -13



Steady State




At T11c

A 5979 5979 0 5979 0 5979 0 -001 -007 -008 5980 01

6048 6044 -04 6044 -04 6046 -02 -003 -042 -045 6048 0

A_ 5344 5670 326 5662 318 5532 188 -069 3491 3422 5328 -16

A3j 5979 597940 0 5978 -01 5979 0 -0 -0044 -004O 59799 o

A5 6043 6042 -01 6041 -02 6042 -01 -003 -021 -025 6044 01

A 5253 5599 346 5593 340 5453 200 -057 3696 3639 5235 -18

A7 5295 5594 299 5581 286 5474 179 -113 3032 2919 5302 07

-A 5250 5600 350 5592 342 5467 217 -071 3383 3312 5269 19

A 5475 5769 294 5745 270 5642 167 -223 3234 3011 5468 -07

A10 5290 5588 f298 5575 285 5468 178 -122 3030 2908 5297 07

All 5681 5682 01 5682 01 5682 01 002 004 006 5681 0

A (=Ao) 1850 1898 48 1896 46 1876 26 -017 562 545 1844 06






or Perfect


A 3765 3764 -01 3764 -01 3765 0 0 -019 -019 3766 01

A 3905 3897 -08 13897 -08 1 3901 -04 -0 -104 -104 3907 02

A 5162 5544 382 5547 385 5390 22-8 033 3889 3921 15151 -09

A4 3764 3762 -02 3762 0 3763 -01 -001 -023 -024 3765 01

A I 3899 3888 -01 3888 -01 3893 -06 -005 -129 -134 3902 03

A6 5130 5504 374 5499 369 5348 218 -043 3944 3901 5114 -16

7

A

52705226 5574

5579

304

353

5563

5572

293

346

5453

5445

183

219

-095

-q69 j 3061

3411

2966

3342

5277

5245

07

19

A9 5 34 5736 302 5713 279 5606 172 -214 3292 30 78 5428 -06 A I

A0 5255 5560 305 5549 294 5438 183 -102 3074 2972 5263 08

A 3952

I__1504

3953

1 _592

01

88 3954

1589 _

02

85

3953

1553 01

4 9 -004

0249 -007

96 -011 972

3952I1 9 5 0 -0

A 24 996 972 1495 -09





Surface





a T

1 I T t TIITNII

Al 1 2298 2294 -04 2294 -04 2296 -02 -001 -057 -058 2300 02

A2 2757 2742 -15 2741 -16 2751 -06 -008 -208 -216 2764 07

A 5003 5403 400 5398 395 5237 234 -039 4184 4145 4988 15

A4 2290 2284 -06 2284 -06 2287 -03 -001 -092 -093 2293 03

A5

A6

2727

4918 2703

5345

-24

427

2703

5343

-24

425

2717

5170

-10

252

-005

-016

-338

4434

-343

4418

2738

4903

-11

l5

A 5088 5426 338 5414 326 5290 202 -101 3430 3329 5693 05

A8 5104 5478 374 5470 365 5334 230 j - 81 3653 3572 5121 17

A0 5256 5596 340 5572 316 5450 194 -215 3692 3477 5248 -08

A10 5083 5420 337 5407 324 5285 202 120 3440 3320 5088 05

A 1 2356 2361 05 2363 07 2360 04 019 034 0153 2156 0

121348 1463 15 1459 111 1412 64 -033 1290 1257 1337 i1








A j 4774 4773 -01 4773 -01 4773 -01 -001 -012 -013 4774 0

A2 3701 3693 -08 3692 -09 3696 -05 -005 -074 -079 3700 -01

A 4257 4270 13 4234 -23 4251 -06 -330 463 133 4256 -01

A4 A 4810 4809 -01 4809 -01 4810 0 -0 -009 -009 4810 0

A5 4993 4987 -06 4987 -06 4988 -05 -0 -050 -050 4992 O1

A6 4304 4381 77 4380 76 4345 41 -015 922 907 4291 -13

A7 4017 4018 01 4016 -01 4017 0 -016 023 007 4017 0

A8 4213 4287 74 4286 73 4258 45 -009 745 736 4213 0

A9 4169 4198 29 4194 25 4182 13 -036 407 371 4151 -08

A1 0 4036 4038 02 4032 -04 4035 -01 -048 061 013 4036 0

A 4476 4476 0 4476 0 4476 0 001 -0 001 4476 0

A12 (=A1 0 1) 1421 1430 09 1430 1 09 1425 04 -006 125 119 1418 -03









A 5356 5354 -02 5353 -03 5354 -02 -003 -021 -024 5356 0

A2 3353 3330 -23 3327 -26 3338 -15 -030 -190 -220 3352 -01

A5 4577 4670 93 4504 27 4612 35 -606 1468 862 4584 07

A4 5419 5418 -01 5418 -01 5419 0 -0 -01 600 549 0

As 5683 5677 -06 5677 -06 5679 -04 -002 -054 -056 5683 0

A6 4806 4992 186 4981 175- 4904 98 -098 2226 2128 4779 -27

A 4149 4160 11 4144 -05i 4151 02 -155 246 091 4151 02

A

A9

A

4535

4505

4276

471

4604

4312

176 4705 170

99 4589 84

36 4278 02 j

4641

4552

4287

106

47

11

-054

2142

-311

1794

1325

635

1740

1183

324

4537

4486

4279

02

-19

03

All 4980 4980 0 4980 0 4980 0 001 P02 4980 0 1A(=A 1555 1567 12 1563 08 1560 05 -033 17 143 1552 -03







Model MIII

)



(I4 AA A t


54 5451 I 2 541 -02 42 O-004 -017 -021 5463 0

A2 2962 2924 -38 2913 -49 2937 -25 -105 -319 -424 2967 05

A A01

41 5534

523 5533

I

8s2 -01 0

5250 269 5532 j-02 5153

5533 35534

172 -01

-388 -003 - 3

3530 -011 01

314 -014 01

4979 5534

-02 0

1

A5 5816 5809 -07 5807 -09 5811 -05 -016 -055 -073 5817 0i

A 6 552 -I8581 33 5825 297 5708 180 -331 3888 3557 5506 -22

A7 4906 5075 169 4996 90 4987 81 -729 2217 1488 4926 20 As 5079 5398 37

353 2

297 5270 191 052

f915093

14

A9 249 5508 259 546- 212 5383 134 -427 3166 2739 5234 - 5

A 5026 5251 235 5206 180 5150 124T j -505 2801 2296 5031I 05

A11 (A )[

5206 1672

5207 1718

01 46

5207 1710

j02 38

5207 1694

01 22

j002

074 004-

595 006 52060








bull bull



T 9 0 I - m1 IvtI

A 5465 5464 -01 5464 -01 5464 -01 -0Oi -012 -012 0

A2 2908 2894J -14 2890 -18 2902 -06 -037 -179 -216 2916 08

A 5152 5564 412 5561 409 53914 bull24-2 -031 4310 4279 5137 -15

A4 5538 5537 -01 5536 -02 5537 -01 -03 -OlO_ -013 5538 0

5834 5829 -05 5828 -06 5831 -03 -o13 1-050 --063 5835 01

A6 5734 6140 406 6118 384 5964 230 -2p4 4473 4269 5713 -21 A 5401 5753 352 5735 334 5610 209 -166 3608 3442 5409 08

A8 5331 5725 395 5719 388 5574 243 -069 3855 3786 5348 17

A 5596 5945 349 5918 1322 5794 198 -250 3820 3570 5588 -08

A 5400 5752 352 5735 335 5609 209 -154 3612 3458 5406 06

A 1 5209 5210 01 5211 02 5210 01 003 007 010 -5209 0

il 2 (=Ai 1722 1794 72 1791 69 1761 39 -028 844 816 1713 -09







1 5465 5464 -01 5464 -01 5464 -01 0-00 -010 5465

2 214 29 08 29 08 2912 -02 ~0 -157 -157 2921 07

A 5157 5573 416 5574 417 5402 245 009 4323 4332 5140 -17

4 58 8 53 - 1 55 7 -01 5537 -01 -002 - 0 -012 55380

ls 5834 1 5830 -04 5828 -06 5832 -02 -O1 -051 -032 5836 02

bull A579 61 409 6130 391 5971 232 T -1 7 3 4482 4309 5717 -

bullA 7 5413 5772 359 5762 349 5629 216 -087 3618 3531 5419 06

A 5337 5737 400 5733 396 5584 247 -cent32 3860 3828 5354 17

A9 $5805 5959 354 5937 332 5808 203 -202 3823 3621 5597 -08

Ao 5410 5766 356 5756 346 5624 21T 4 -097 3616 3519 5414 04

S All 5209 I52i0 01 5211 02 ]5210 01 004 007 0ii1 5209 0

IA12(=A i ) 1723 1797 74 179-S 72 17683 40 - 018 848 83 1714 -09



Steady State


Surface


Temperature

Model

T



M j A I 46 5464 546 5464 -0546001 - -009 5465 0

2 2915 2907 -08 2907 -08 2913 -02 064 -156 -152 2922 07

AA 5158 5573 415 5575 417 5403 245 011 4323 4334 5140 -18

5538 5537 101 55371 -01 10

5 53

-021 -002 010 -062 5538 p2 As 5834 5830 -04 5828 06 5832 -02 -011 -051 -062 5836 02

6 5739 6149 410 6136 391 5972 233 -171 4482 4311 5718 -21

A7 5414 5772 358 5763 349 5629 215 -083 3618 335 5419 05 A8 5338 5737 399 5734 396 5585 247 -630 3860 3830 5354 16

A 5606 5959 353 5937 331 5808 202 -199 3822 3623 5597 -09

A 5410 5767 57 5757 347 5624 214 -093 3616 3523 5415 05

A 5209 5210 01 5211 02 5210 01 004j 007 011 5209 0

-2723 1797 74 1795 72 1764 41 -017 848 1714




Surface

A1



36

3665


Model MI Model MIT

Ei v__ __

0 36

3664 -01

Models

Model Mill

E___ _ _ _

3664 -01

oeMood M

A _ _ _ _ __ _ _

~0 -016

_ _ _

1

__


_ _

36T

3665 0

A2 2886 2877 -09 2877 -09 883 -03 005 -168 -163 2893 0

2 5 5542 417 5544 419 5372 247 025 4303 4328 5109 -16

A

11 3705 3904

3702

3890

-03

-14

3702

3888

-00

16

3703

3896

-02

-08

- 03

-01 6

-030

-156

-b33

172

3706

3907

01

03

A6 5295 5687 392 5676 381 5523 228 -102 4162 4060 5281 -14

A7 5367 5718 351 5712 345 5580 213 -057 3516 3459 5372 05

A8 5290 5674 384 5668 378 5528 238 j056 3709 3653 5309 19

A

A

5526

5344

5864

5687

338

344

5841

5679

315

335

5720

15551

194

207

-212

-075

3651

3454

3439

3379

5521

5349

-05

05

A

A 2(=A-0

3831

1497

3833

1600

02

103

3834

+598

03

1101 3833

1554

02

57

006

-019

011

1148

017

1129

3831

1487

0

-10




Surface

A2


j Model Temperature

S2

1 2278

2699

5005

I


o MIafter

M I E I- TII tIIM

2274 -04 2274 -04 2277 -01

2684 -15 2683 -16 2693 -06

5407 402 5403 398 524 26

-o

-003

-029

A(-))

-057

-227

4200

-057

-230

4171

Model Temperature

Correction

_ _

ml

2280 1 02

2707 08

4989 -16

A 2288 2281 -07 2281 -07 2285 -03 -001 094 -095 2291 03

A 2734 2710 -24 2710 -24 2724 -10 -003 -836 -339 2744 10

A 4924 5352 428 5351 427- 5176 252 -008 4446 4438 4908 -16

A7 5096 5437 341 5428 332 5301 205 -082 3450 3368 5100 04

A3

A9

5109

5262

5485

560

376

342

5477

5582

368

320

5340

J5458

231

196

-073

-204

3665

3704

3592

3500

5125

5254

16

-08

A 10 5090 5429 339 5418 32 8 1 5293 20 3 -06 3454 3348 5095 5

A1 2340 2346 06 2348 08 2344 04 020 036 056 2340 0

A 1348 1465 7 1461 113 1413 65 -030 1f97 1267 1338 10






















upon request





114

700


600f - t

o_400

H i HeaQampgIlt


Cooling Time m n








A

A2

Temperature

5907

5949

rT

5906

5940

E

-01

-09

5905

5938

z I

02 5906

-11 5943

-01

-06

shy003

-017

-012

-070

-015

-087

T

5907

5949

FC

0

0

A

A4

4745

5905

4780

5905

35

0

4702

5905

-43

0

4739

5905

-016

0 -

-719

0

1052

-004

333

-004

4747

5905

02

0

A 5939 5936 -03 5936 -03 5937 -02 -0 -024 -014 5939 0

A6 4403 4516 113 4514 111 44641 61 -024 1327 1303 4386 -17

4131 4134 03 4118 -13 4128 -03 -149 160 011 4133 02

A1

A

4506

4454

4662

4525

156

71

4651

4506

145

52

4599

4484

93

30

-099

-173

1588

1025

1489

853

4513

4439

07

-5

A10 4243

Al 547 6

4261

5476

18

0

4228

547 6

-15

0

4243

547 6

0

0

-300

001

443

-0

143

001

4246

547 6

03

0

A 2(=A I 1722 1728 06 726 04 172 -024 098 07- 1721 -01




Surface

A


Temperature

5979


Model I Model M11

T I

5978 1-01 5978 -01

Models

Model MIll

I

5979 0

AAAt

-001

A

-008 1-009

I


y

5979

A 06046 6041 5604 -06 6043 -03 -01o -046 -056 6047 01

A

A

As

5313

5978

6040

5615

5978

6038

302

0

-02

5592

5978

6037

279

0

-03

5483J 170

5978 0

6039 101

-207

-Q01

-008

3331

-004

-022

3124

- 005

-030

15302

5978

1041

-1

01

A6 5203 5523 3197 5503 300 5383 180 -178 3522 3344 5188 -15

A

A

A9

5199

5198

5404

5448

5524

5668

249

326

264

5400

5502

5625

201

304

221

5340

5396

5546

141

198

14

-442

-21

I3 94

2753

3243

3077

2311

3042

2683

15217 5220

5399

18

22

-5

A10 5215 5477 262 5440 225 5365 150 -346 2847 2501 5227 12

IA

A

(=A 0 )i

5681

1842

5682

1884

01

42

5682

1879

01

37

5682

1864

01

22

002

044

003

514

005

470

5681

1837

0

-05




Surface


Model


Md MI MModl M111

_ _ _ _ _ __) i

A Temperiature

after Correction

Temperature C

A

A0

2747

3042

27747

2744

3828

-03

-14

2744

3026i

-03

-16

2745

3035

-02

-07

-003

-014

j-0381J-175

-041

-189

2748

3047

01

05

A 5033 5423 390 54171 384 5262 229 -056 4085 4029 5020 -13 A4 2744 2739 05 2738 -06 2741 -03 -004 058 -062 2745 01

A- 3026 13004 -22 3002 -24 3015 -1i -020 -2 6 8 288 3033 07

A 4964 5371 407 536 5400 5202 238 -061 4267 4206 shy 4950 -14

A7 5141 5455 1314 54f6 295 5328 187 -175 3213 3038 5151 10

A 55136 3_ __

5497 _ _

351 _ _

5484 _ _ _

1348 _ _ _

5358 _ _

222 _ _

Z118 _ _

13529 3411 5156 _ _

20

A9 5102 5621 319 5592 290 5483 181 -266 6509 3243 5297 -05

A 5130 5q46 316 5427 (297 5318 188 -173 b254 3081 5138 D8

A11 2897 2900 03 2902 04 2899 02 009 018 027 2897 0

A (=A- 1488 105 1484 101 1441 58 -045 1195 1150 1373 -10





Surface


Model Temperature

Model MI

T7 E

Model

T1

MIX Model

NtlTI

MIII A(

_ __

A(- )

00

^

04

after Correction

580c 0

A- 5806 5805 501 5 805 1 -001 -010 5806 0

-A 5905 5901 1-04 5900 -05 5903 -02 -008 -04d -048 5906 21

A 5183 5523 339 5505 32r2 5374 191 -154 3756 3602 5162 -21

A 5804 5804 0 5803 -01 5804 0 -01 -009 -010 5804 0

A

A6

A7

] 5896

5045

5135

5895

15437

545 4

-01

392

320

5895

5431

5436

-01

386

302

5896

5274

5325

0

229

190

-005

-056

-166

-030

4128

3284

-03

4072

3118

5899

5030

514 3

03

-15

08

A

A 9

A0

A

5139 a

5$11

5134

5212

5502

5633

5453

5214

1363

322

1319

02

5490

5605

5434

5214

351 I

294

300

02

5362

5493

5323

5213

22-3

182

19

01

-108

-258

-175

005

3561

3544

3301

011

3453

3286

3126

916

5157

5304

5140

5212

18

-07

06

0

A(=A) 1764 1818 54 1815 51 1793 29 -025 627 602 1758 -06





Model

Tod odel MI Mod 2

IM _

1 Model MIII[ _ A

lt - AC-P A



A 5980 2gt

5979 rt

-01 va I

5979 )V IvX TIM I

i-01 597 9 b1 -O 0 -00771-008 j C

598 0 --C

SI -01 -0 A2 6047 6044 -03 6043H -04 6045 -02 -004 -041 -045 6048 01 A 5340 15665 325 5656 316 5527 18-7 -083 35W0 34 pound7 5323 -17

A

A5

A ____ ___

A

5979

6042

5246 __28 __ 5281

__

5978

6041

5592

15581

-01 5978159 3I_ _

-01 60411 I I1

346 5585130o___ __ 5565j 300 5565i

-01 _

-01

339284 2

_I_ 5979

_

6042

5446

0 _

0

200

178

_ -001

_ _

2003

-070

-144

_ -003 -004 5979 0I _ _ __ _ 0_ _

-019 -022 6043 J01

I - - 7j3714 3644 5228 -18I_5459_ _3 ]_52I 3071 2927 5288 07

A9 I

5242

5465

5593

5760 3-51

295II

5584

5734

342

26L9

5459

5631

2i7

166

-085

-241

3405

3266

3320

3025

5261

5457I

19

-08

A0 5279 5578 299 5562 283 5457 178 -144 3063 2919 5286 07

A 568568 15682 01 5682 01 5682 1 01 00

2004 o4 6 _____ 5681 0o6

AC=Al0 1849 8 8 1895 46 1875 26 -020 563 53 1843 -06



End of second cycle




Model MI ( A



-Tj 1 E4

A A At

A1 2748 2745 -03 2745 -03 2746 -02 shy0 -036 -036 2749 01

A2 3044 3032 -12 3033 -11 3039 -05 001 -166 -165 3049 05 50 54 396 5433 394 25272 233 -011 4116 1 04105 I 0 5024 -15

A4 2745 2740 -05 2740 -05 2742 -03 -001 -057 -058 2746 01

As

A5157

3030

4973

3010

543

-20

325

3009

5384 5473

-21

4L1 316

3020

5216 5353

-10

243 196

-006

-016 -078

-262

4300 3266

-268

42184 3188

3037

4958

5163

07

[-15 06

A8 5145 5511 366I 5503 358 5371 226II

-073 3557 3484 5163 18

A 5314 5641 _1_

3271 5618 _

3041 1 5501

1 187 -207 3541 3334

_ _ II 5307

J_

-07

A0 5142 5467 325 5456 314 5337 195 -102 3290 3188 5148 05

Ai 2898 2900 02 290l[ 03 2900 02 0

010 -02

018 028 1179

2898 1^7I

0

1 1I(=A I ) 1386 1494 108 1491 105 1446 60 -028 1207 1376 -10






I

Models 1

Model MTI T Z A(

bullModel

AI At

ot Temperature


A

2

A

A

5806

5905

5186

5804

5805

5902

15530 I5804

-01

-03

344

0

580

590i

5516

D1

D4

330

0

5805

5903

5381

5804

-01

-02

195

0

-001

-004

-122

-0

-008

-038

3774

-008

-009

-042

3652

-008

5806

5906

5164

5805

0

01

-22

01

_

A

_ _

A-

_

5897 5051

5145

1 5896

5447I 5472

396

327

58g4 5444

5461

-0101 393

616

5898 5283 __ 1

5341

01 232

196

-001

-023

-09

308 4148 3 1 3315

-031

4125 2 1

5899

5034

5150

02I-17

05 I__

A

5144

518

5512

5645

368

327

5503

5622

359

304

5370

5505

226

I187 -076

3561

3577 3501

3347

5161

5311

17

-07

A 5142 5467 25 5453 311 5335 193 -123 3322 3199 5147 05

A 2 (=Ao )

5212

1765

15214

11820 1

02

55

S02

1818

5213

53 1795 30

6

-018

1

633 017j 5212

615 1758

jFo 7







1 1 5980 5979 -01 5979 -01 5979 -01 -001 -0 -008 5980 o

6047 6044 -03 604 -04 6045 -02 -004 -041 - 5 6048 j 01

A 5340 5665 325 5657 317 bull 5527 187 -079 3501 3422- 5323 -17

A4 5979 5978 -01 5978 -O1 5579 0 0 -003 -003 5979 0

A5 604 041 -01 6042 0 -019 -022 6049 01i003 A 5246 347 5586 340 5446 200 -066 3715 3649 5228 -18

5281 5582 301 5567 286 50 136 3071 2935 5288 07 30582 567 5461 18 -1360

5243 551 5585 342 5459 216 -091 3405 3324 5261 18

A 5465 5761 296 5735 270 5632 167 -235 3266 3031 5458 -07

A0 5280 5579 299 5564 284 5458 178 -138 13063 2925 5286 06

A 5631 5682 01 5682 01 5682 01 002 004 006 5681 0 (=A 0 1 1849 1897 48 1895 46 1875 26 -066 3715 3649 1843 -06







A 3044 3032 -12 3033 -11 3039 -65 001 j 01 -016 3049 05

A3 5039 5435 396 5434 395 5272 2 3 -010 4107 5024 15 I A 2745 2740 -05 2740 -05 2742

I--63 -001 -057 -058 2746 I 012 2 II - 3030 3010 -20 3009 -2-1 3020 -10 -006j -268 3037 07

A4973 5386 4 53843 85 412 5216 243 -015 4306 4285 495 -A I_o 7 i _____________366 5474 1 5353 -6 -077 j3189 5163 06__

A3 5145 5511 366 5504

A7 5157 5482 325 i535 317 526[ 3266 3189 151631 06

359 5371 226 -072 3557 3485 5163 )8

A 5314 5641 327 5618 [304 5501 187 -206 354d 3334 5307 -07

A 5142 5467 325 5456 314 5337 195 -101 3290 3189 5148 06 A1 2898 2900 02 2901 03 2900 62 0 oao 018 028 o8986

[2(1A 1494 108 1491 105 1446 60 -0 27 1207 1180 1376 10 All i [R -ir

























125
























126


























127

F-

I

I

7D

(a)

Figure 62

-83 -83

(6) (a)
















stance









129









130

REFERENCES











131

APPENDIX A













sPdbPspI T-iT

0

itrPd bPsb





132


Q = S Cos 6 (A1)








TABLE A1



Aluminized side 085 0 015 095 000 005

Plastic side 085 0 015 000 050 050








133


B2 B3

Eb 2 1 -P 1-pp Eb3

p pdo di p

E A (1-P A 1-p)

1

A2 E2 3 (l-p )(1-P




++ Es~(P - )(1 P (A2)2 l sa)(l - P)




tion one finds

+ + 2 ++ (A3) 2 l+PSa sIp s~a sp -P P

sa SIp

Hence


a sa p sp sa Sp

134


fies to

1 1 R=-plusmn+---1

a Ea p











oT4 -aT


with

ER = (n - 1)R t RV C A 5 b )



135

Sltlt A

COI S Cos e

or E aTgT

4

p exp

(A6)


A R(EPS Scos - a1T)

b (A7)




Q A

-1

P

4 Tb

+ R

(A8)











and

136












4378 and 4192





137

TABLE A2






5 10 20 5 10 20




plate

APPENDIX B

A NUMERICAL EXAMPLE






















139





T~

T TLIII i

T



(a) for Model MI


kd -- 025 025 020 025 025 020

6 025 020 025 025 025 025 Cd

6 015 -- 025 015 -- 015

6 010 010

(b) for Model MII

A A A A4 A5 A6 A7 A8 A9 A 0 A11 A12

6 - 055 045 040 0575 045 044 kd

6 0525 050 055 0575 045 060 -shycd

6 -- -- 027 -- 045 033 -- 033

6 -- 020 - 020

140






2 2 2 2 2 2 2 = 025 + 025 + 010 + 025 + 020 + 010I

+ 0202 + 025 + 0152 + 0252 + 025

2 2 2 2 2 + 025 + 025 + 020 + 0252 + 0152 + 015

= 0833

lt 052 2 2 2 5= + 0525 + 020 + 045 + 050 + 020I

+ 0552 + 0272 + 05752 + 05752 + 0452 + 0402

2 2 2 2 2 + 045 + 045 + 044 + 060 + 033 + 033

- 3687

6 6 = 025 X 055 + 025 X 0525 + 010 X 020 + 025

X-O45 + 020 X 050 + 010 X 020 + 020

X 040 + 025 X 055 + 015 X 027 + 025 X 0575

+ 025 X 0575 + 025 X 045 + 025 X 045 + 025

X 045 + 020 X 044 + 025X 060 + 015 X 033

+ 015 X 033 = 1740


141

p F0833 X 3687 11011i(174 0= 0112

5 1740 = 0472

3687


1 a = 0112 X = 02121 - 0472

0212 b = - 021 = -0110

192

and from (235c)

A = 1 - 2 X0472 0056


f(aA) = 00549


- 2 = 2116

I 00549S(+)



+ 5383 - 5421 21=- 340oR2116 - 1


142



(a) for Model MI


kd

Cd

-- 018 -020 -- -018 -- -shy

6 - -008 -008 -008 -008


(b) for Model MIII


kd

Cd

6--- -- 0288 -032 -- -0259 -

-- -0147 -0115 -016 -0128





+ (-008)2262 = (-018)2 + (-020)2 + (_008)2 + (_018)2

+ (-008)2+ (-008)2 + 2x(-0102 )2 = 01512

143

Z (602 = (-0288)2 + (-032)2 + (-0147)2 + (-0259)23

+ (-036)2 + (-D128)2+ (-0115)

2 + 2x(-0205) = 0412

661 = (-018)(-0288) + (-020)(-032)

+ (-008)(-0147) + (-018)(-0259)

+ (-008)(-0115) + (-008)(-016)

+ (-008)(-0128) + 2(-0102)(-0205) = 0247

Hence

n) _ -01512 X 0412 112 = 0158

(-) 02472

p _ 02470412- 0601

= 412= 0642

and

r1

a = 0158 1 03951 0601

0395b = 064 =0 6150 642

F 1 - 2 X 0601 = -0202

f-(aX) -0198 (from 236b)

s ( -) ( -) _ 2 s= 1+0198 = 1669 (from 2313b)

144

and

= 5554 - 5421 _ 19890R (from 2313a)1669 - 1


At = P + - -340 + 1989 r 1649degR


1649 = 52560Rc = 5421 -



145

Documents

Department of Mechanical July 1970 AN APPROXIMATE ......Department of Mechanical and Industrial Engineering ME TR JPL 952593 July 1970 AN APPROXIMATE THEORY OF IMPERFECT MODELING WITH