A STUDY OF THE THERMAL AND PHYSICAL PROPERTIESAND HEAT TRANSFER COEFFICIENTS OF SULPHATE

PAPER MILL BLACK LIQUOR

RICHARD L. HARVIN

A Dissertation Presented to the Graduate Council of

The University of Florida

In Partial Fulfilment of the Requirements for theDegree of Doctor of Philosophy

UNIVERSITY OF FLORIDAJANUARY, 1955

ACKNCWLEDGEMENT

I wish to acknowledge the helpful assistance of my supervisory

committee chairman. Dr. W. F. Brovm, and the other members of the

committee. Dr. M. Tyner, Dr. H. E. Schweyer, Dr. H. A. Meyer and Dr.

A. C. Klelnschmidt for their help and patient use of their time. The

writer is grateful to Dr. W. H. Beisler, Head of the Chemical Engineering

Departinent, for his part in making this study possible. Thanks are also

due Dr. W. J. Nolan for helpful suggestions and comments throughout the

course of this work.

ii

TABLE OF CONTENTS

Page

ACK>;aiJLEDGEKEMT ii

LIST OF ILLUSTRATICNS V

LIST OF TABLES vii

LIST OF SYMBOLS viii

Chapter

I. ITJTRODUCTION 1

II. HEAT TR.WSFER INVESTIGATIONS AND RESULTS 5

A. TheoreticalE. ApparatusC. Experireents.l ProcedureD. DataE. Sample CalculationsF. Calculated ResultsG. Analysis of Results

III. SPECIP'IC HEAT 66

A. Background3. ApparatusC. Derivation of EquationsD. Experimental ProcedureE. DataF. Sample CalculationsG. Calculated Results and Discussion

IV. THE31MAL CONDUCTIVITY INVESTIGATIONS AND RP^SULTS .8'+

A. BackgroundB 5 ApparatusC. Derivation of Eqxiations

D. Experimental ProcedureE. DataF. Sample CalculationsG. Calculated Results and Discussion

iii

Chapter Page

V. VISCOSITY 105

A. BackgroundB. Apparatus and ProcedxxreC. Calculated Results and Discussion

VI. SPECIFIC GRAVITY II3

A. Apparatus and ProcedureE. Data and Calculated Results

VII. INTERRELATION OF THERMAL j»JTD PHYSICAL PROPERTIESAND THE HEAT TRANSFER COEFFICIENTS 11?

VIII. CONCLUSIONS I35

BIBLIOGRAPHY I38

APPENDIX lZ+1

BIOGRAPHICAL ITEMS ik^

iv

LIST OF ILLUSTRATIONS

Figure Page

1. Heat Transfer Apparatus 11

2. Heat Transfer Apparatus 12

3. Diagramatlc Layout of Heat Transfer Apparatus ... 13

4. Thermocouple Installation in Heat Transfer Tube . . 15

5. Heat Transfer Tube— Inlet End l6

6. Heat Transfer Tube—Outlet End 17

7. Cross Section of Heat Transfer Tube ^3

8. Temperature Variation in Heat Transfer Tube .... ^5

9. Assembled Specific Heat Apparatus 68

10. Cross Section of Specific Heat i^paratus 69

11. Heating and Cooling Curves for Specific Heat

Determination 73

12. Specific Heat versus Per Cent Solids 79

13. Ncxtiograph for Specific Heat 83

lU. Assembled Thermal Conductivity Apparatus 88

15. Thermal Conductivity Apparatus out of Insulated

Container 89

16. Diagramatic View of the Thermal Conductivity

Apparatus 90

17. Details of Thermal Conductivity Apparatus 92

18. Thermal Conductivity versus Per Cent Solids .... 101

V

Figure Page

19. Thermal Conductivity versus Per Cent Solids . . . I03

20. Nomograph for Thennal Conductivity 104

21. Viscosity versus Temperature 110

22. Ncsnograph for Viscosity 112

23. Specific Gravity versus Per Cent Solids 116

2^^. J Factor versus Reynolds Number 123

25 • j /(^ versus Reynolds Number (Sieder and TateNatural Convection Factor) 12?

26. i /<^ versus Reynolds Number (Kern and OthmerNatural Convection Factor) 128

27. j /(p versus Rej7iolds Number (Eubank and ProctorNatural Convection Factor). 129

23. j /(|) versus Reynolds Number (Natural ConvectionFactor of Equation 50) I33

29. Thennal Conductivity of Water 142

30. Viscosity of Water 143

31. Sample Data and Work Sheet 144

yi

LIST OF TABLES

Table Page

1. General Information on Fluid Systems 28

2. Experimental Heat Transfer Data 29

3. Calculated Heat Transfer Data 53

4. Experimental Specific Keat Data 75

5. Calculated Specific Heat Data 78

6. ExjJerimental and Calculated Thermal ConductivityData 99

7. Experimental and Calculated Viscosity Data. . 109

8. Specific Gravity Data llij.

9. Heat Transfer j Factors—Reynolds Number Above3000 118

10. Heat Transfer j Factors—Reynolds Number Below3000 120

il

LIST OF SYMBOLS

A Area Sq. ft.C Weight Fraction iCp Specific Heat BTU/(Lb.)(°F.)D Diameter Ft.

d Pipe Wall Thickness Ft.G Mass Velocity Lbs./(Hr.)(Sq. ]rt.)

g Acceleration of Gravity- Ft./(Hr2) .

Hl Heat Loss BTU/Kin.h Film Heat Transfer Coefficient BTU/(Hr.)(Sa.ft .)(°F.)

k Thermal Conductivity- ETU/(Hr.)(Sa.ft .)(^./ft.)L Length Ft.

Q. q Quantity of Heat BTUr Radius Ft.

S Cross Sectional Area Sq. ft.

s Specific GravityT, t Temperature ^.U Overall Heat Transfer

Coefficient BTU/(Hr.)(Sq.ft .)(°F.)

W Mass Rate of Flow Lbs./Hr.X Thickness of Liquid Layer Ft.

Subscripts

b Bulkf Film1 Lowerm Mean •

o Outsides Surfaceu Upperw Wall

ureeK

/3 (Beta) Coefficient of Cubic Expansion % Sxpansion/^F.A (Delta) Finite Difference>t (Mu) Viscosity Lbs./(Hr.)(Ft.)/? (Rho) Density Lbs,/Ft3

(t>(Phi) Natural Convection Term

e (Theta) TL-ne Hr.

CHAPTER I

INTRGDDCTIOI^

This dissertation is concerned with the transfer of heat from a

tube wall to a stream of moving sulphate black liquor, the determination

of the physical properties pertaining thereto, the calculation of the

film heat transfer coefficients prevailing at various conditions, and

the interrelation of said physical properties and film coefficients.

The general subject of heat transmission is one that has

received considerable treatment in the literature. It vjas in 1798 that

Count Rumford (26) first gave an account of his experiments on "An

Inquiry Concerning the Source of Heat v/hicVi is Excited by Friction" and

this paper may be regarded as marking the commencement of the study of

heat as molecular kinetic energy. Yet today the problems remain so

countless and the complexities so great that heat transmission con-

tinues to capture the thought and imagination of research workers.

The study undertaken involves principally the process of heat

transfer to a fluid moving inside a tubular heat exchanger and the

mechanism is, therefore, primarily one of convection. Throughout the

long history of this subject the knowledge and vmderstanding of the

convection heat transfer mechanism has advanced steadily but has never

shown any period of phenominal growth comparable with, say, the recent

1

2

expansion of the nuclear energy field. Jakob (13) pointed out that the

study of heat transfer phenomena has never been brilliantly fashionable

due to the slow cumbersome flow of heat and the difficulty of restrain-

ing the flow along well defined channels as compared with, for example,

electricity. Consequently experimentalists in search of academic

distinction have tended to avoid this subject as unwieldy and vmprofit-

able. On the other hand the steady advance of industry and the need

by engineers of sound design methods has demanded a continued effort

toward improvement in our methods of handling heat transmission. Early

contributors such as Reynolds (25) and later Prandtl (24) and Nusselt

(21) did much toward developing the basic concepts of heat flov/ and

established powerful methods of correlation. However, it has been due

to efforts of engineers of rather recent years that through semi-

empirical methods the basic correlations have been developed into

reliable relations suitable for use with a wide variety of materials.

All such relations involve the use of dimensionless moduli making

possible correlation of data from various investigators without regard

to the units employed in the work.

The variables which by reasoning may be expected to have

influence on the transfer of heat by convection may be classified as

follows

:

A. Fixed variables (characteristics of the apparatus).

Length of heat exchange tube, L; and inside diameter of

The word "correlation" is used to mean an interrelationbetween variables, and does not have the usual statistical connotations.

3

tube, D.

B. Independent variables (operating conditions).

Mass rate of flow, W; inlet fluid tenperatiu'e , T, ; and the

temperature of the heating medium, t .. The choice of thest

fluid to be heated is another independent variable of

primary importance. However, at a particular temperature

it is characterized by its thermal and physical properties

and enters into the relationships only in this way.

C. Dependent variables.

Temperature increase of fluid (duty), AT; driving force

temperatur-e difference. At; constant pressure specific

heat, Cp; viscosity, yW ; thermal conductivity, k; coef-

ficient of cubic expansion, yS ; density, /O; and film heat

transfer coefficient, h.

Other variables and constants enter into the calculation of the above

variables but do not have a direct bearing on the convection process.

In the design of heat exchange equipment it is neces'jary to

have knowledge of all variables in order to have confidence in the

result. This presupposes that adequate thermal and physical data are

available on the system under study. Such was not found to be the case

in regard to sulphate black liquor and this was a primary reason for

its selection for study in this work. A thorough study of the litera-

ture revealed only a limited amount of data on sulphate black liquor

and some of this was in conflict.

The general problem was divided into two parts; (l) the heat

transfer study consisting of operating suitable heat transfer

apparatus usin^ liquors of various concentrations to measure the film

heat transfer coefficients, and (2) a thorough study of the physical

properties of black liquor. The final correlation of all properties

and measxirements according to the most proven methods serves a twofold

purpose. It demonstrates the reliability of the methods as well as the

consistency of the data.

CHAPTBR II

HEAT TRANSFER INVESTIGATIONS AND RESULTS

A. Theoretical

This dissertation will not attempt to review the history of the

development of the basic dimensionless groups. Neither will it treat

the early correlations which now have been superseded by improvements

made possible by an ever mounting voliime of data collected using refined

experLmental techniques. Exhaustive discussions on this subject are to

be found in all of the standard texts (5, 13, 1^^, 19).

Through the application of dimensional analysis it has been

shown that the variables are logically grouped into four dimensionless

numbers or moduli. Thus, the Reynolds number. Re = — , the Prandtl/^

number, Pr = -y . the Stanton number, St = —— , and the Grashof

number, Gr = 2^£^£A!L, The Interrelation of all the variables con-

cerned would result in mathematical relations of considerable complexity

were It not for the use of the dimensionless groups presented above.

Thus, a perfectly general equation between the variables in convection

can be written in the form:

St » F (Pr Re Gr) (l)

where F is an undetermined function. By the methods of dimensions the

general relation between all the variables has been reduced to one with

5

6

only four variables.

There is a distinct difference between the mechanism of heat

transfer for fluids flowing in turbiilent motion on one hand and

streamline motion on the other. Consequently, certain factors, notably

average velocity of the fluid past the heat-transfer surface, in general

have a more marked effect upon the rate of heat transmission for fluids

flowing in turbulent motion than in streamline motion. Other factors,

such as tube length, often have greater importance for streamline motion

than for turbulent flow. Hence, these two cases are treated separately,

first consideration being given the more common turbulent flow.

The general equation for convection heat transfer (l) may be

simplified for the case of turbulent flow by eliminating the Grashof

number, Gr, since this factor accounts only for that contribution due

to heat flow by natural convection. In most instances of forced con-

vection the "forced" current is many times more intense than the

natural circulation. Thus, the equation for heat flow becomes,

St = f (Pr Re) (2)

where the functions must be determined experimentally, Colburn (6)

determined these functions wherein all physical properties, except Cp

in the Stanton number, are evaluated at the film temperature, which is

taken as the average of the bulk mean temperature of the fluid and the

mean temperatiire of the heat transfer surface. Thus,

J » (St) (Pr)°*^^'^ . 0.023 (Re);°-^ (3)

t^ + tgwhere t^ = — and j is a dimensionless group related to the

7

Stanton and Reynolds numbers. The properties in this equation were

evaluated at the film temperature in order to effectively take into

account the conditions in the viscous layer which offers the major

resistance to heat flow.

In fluids with large temperature coefficients of viscosity a

somewhat more convenient method of including the radial variation in

viscosity due to temperature gradients was also suggested by Colbum (6)

but was later modified by Sieder and Tate (30)« This method added

another dimensionless group which was the ratio of viscosity at the

bulk stream temperature to the viscosity at the pipe wall or surface

temperature. Thus Sieder and Tate were able to correlate a wide variety

of data at Reynolds nvirabers greater than 10000, using their equation

which is presented here in a form similar to equation (3)»

i' . (St) CPr)"-^*'' {ji) "•'*= C.027 (R«)-°-' M

All properties of the fluid are detennined at the convenient

bulk stream temperature, except the viscosity at the wall surface tem-

perature. This equation was used as a basis for interrelation of the

heat transfer data in this work for Reynolds numbers in excess of 10000

where turbulent flow is well developed.

Viscous or laminar flow is usually found at Reynolds numbers

less than 21C0 but may also exist up to values of 3OOO in cases of

undisturbed flow. In such systems Graetz (lo) showed that the ratio

of the temperatiire rise produced in the liquid to the temperatttre

difference between the fluid at the entrance and the wall was partially

dependent on the ratio of tube diameter to heated length. Longer tubes,

other things being equal, are less effective at transferring heat to

laminar liquids than short ones because longer tubes permit more time

for the building up of temperature gradients vhich oppose heat transfer.

In turbulent flow, the rapid mixing prevents this build-up. Thus, the

ratio — is significant in viscous flow and must be included.

Colburn (6) derived the expression,

i ' (St) (Pr)5-*«7 , 1., (,,,-0.667 ^Sj°-333 ^^)^-333 ^^j

wherein most of the properties are determined at the film temperature,

Sieder and Tate (30) put this equation into a more convenient form by

using the bulk temperature for evaluation of the properties and their

viscosity correction term. Their equation as recomiriended by McAdams

(19) was.

y - (St) (p.)^-^^{^f-'' . i.a6 <R.)-^-«^

{^J-'"'(6)

In streams flowing in viscous notion the natural convection

currents may have a profound effect on the heat transfer coefficient.

Natural convection is favored by lov; velocities of floif, high tempera-

ture differences betveen the fluid and the wall, and large diameters.

Studies of free or natural convection have shoivn the value of the

Grashof number in correlating these data. In the case of combined

forced and free convection it is not unccwnon to find film coefficients

as much as 100^ in excess of the values predicted by correlations that

do not take free convection into account. Therefore, a number of

9

investigators have corabined a function of the Qrashof number with the

equations for forced convection in the viscous region. Sieder and Tate

(30) proposed that for values of Grashof ntsabers exceeding 25OOO a

correction for free convection may be obtained by multiplying the values

of "h" from equation (6) by the term (p = 0.8 (1 + C.OI5 Or^'^^^) where

the terras are evaluated, using, the b\ilk stream temperature. Equation

(6) becomes.

Where (p = 0.8 (1 + O.OI5 Gr*^'^^^)

(7)

Kern and Othmer (I5) found that closer agreement of data from a

wide range of pipe diameters could be obtained by defining a free con-

vection factor which was a function of the Reynolds number as well as

the Grashof number. By empirical means they arrived at a correction

factor 6 .= £'23 (1 •»• 0.010 Gr )^ Applying this factor to equation

log Re

(6) t- ere results,

J-= ^ = 1.86(Rer^'^7^£f-^^^ (8)

where <*' = 2.25 (1 ^ 0.010 Gr''^^-'^)~log Re

Eubank and Proctor (9) critically surveyed the available data for

viscous flow in horizontal tubes and arrived at a "tentative" empirical

equation of a form considerably different from those presented pre-

viously. This was,

10

(Nu)

o

hDThe term Nu is the Nusselt number and is equal to ~. The Nusseltk

number is also equal to the product of the Stanton, Reynolds and

Prandtl numbers. The term Gz is the Graetz number, which is equal to

--^. This number is also equal to the product of the Reynolds and

Prandtl ntanbers, and the ratio of £ and a constant. H.L k

This dissertation vrill utilize the equations (6), (?), (5), and

(9) as bases for correlation of the heat transfer data in the viscous

region.

B, Apparatus

The design of the heat transfer apparatus was formulated by

consideration of the designs of other investigators (5, 15, 30). The

over-all ap;->aratus is sho\m in Figures 1 and 2 by photographs and in

Figure 3 by a schematic diagram. It consisted essentially of (l) a

heat transfer section, (2) a flow-straightening section, (3) a mixing

chamber, (4) a fluid cooler, (5) a discharge measirring tank and scale,

(6) a return pump, (7) a storage and preheating tank, (8) a circulating

pump, (9) a preheating section, (lO) a steam pressure reducing and

regulating system (ll) a vacuum system, (12) a potentiometer with its

auxiliary equipment and (I3) the necessary piping, valves, fittings and

gauges. The construction and function of each of these principal com-

ponents will be discussed in detail below.

The heat transfer section was mounted horizontally and consisted

Iu

uencn)

5U

U

13

Ik

of two parts. The inner tube wai- a section of Type 30i^ stainless

seamless tubing having an inside diameter of O.5I inches and an outside

diameter of O.75 inches. This was surrounded by a steam jacket con-

sisting of nominal 3 - inch galvanized iron pipe. Eight copper-

constantan thermocouples of No. 30 gauge wire in a fiberglass duplex

cable were buried in the stainless steel wall and their leads were

brought out through four equally spaced packing glands in the steam

Jacket wall. The thermocouples were located in grooves milled longi-

tudinally along the top of the tube. The grooves were -i_ of an inch

1^^

deep and __ of an inch wide and 2 1 inches in length. The thermocouple16 2

junction was placed at the bottom of the groove at the end nearest the

fluid inlet and the insulated leads extended through the groove emerging

from the other end. The entire groove was filled by peening in a strip

of soft solder and the surface was made smooth by filing away the excess

solder followed by a fine emory cloth. The thermocouple leads were,

thus, located in the pipe wall for at least 2 inches dowm stream from

the point of measurement and another 5 or 6 inches of the leads remained

in the steam space until they finally emerged from the packing glands

in the wall of the steam jacket. Figure 4 shows an enlarged view of one'

themccouple groove with the thermocouple mounted as described above and

emerging from one of four thermocouple packing glands. Two additional

thermocoiiples passed through the packing glands into the annulus section

and were used to measure the steam temperature at the two ends*

The details of the construction of the ends of the heat exchanger

are shown in Figures 5 and 6, The heated length of the tube was 6 feet

15

Leads toPotentiometer

RubberStopper

Figure 4

Thermocouple Installation in Heat ExchangerTube

16

17

18

and the design of the end flanges was intended to prevent additional

heat transfer surface beyond the prescribed heated section. This was

acccMiiplished at the inlet end (Figure 5) by minimizing the metal to

metal contact between the tube and the flanpie. At the outlet end the

cross section of the tube was reduced by turning down the outside

diameter to O.56 inches in an effort to minimize conduction of heat

along the tube. The thermocouples were mounted at distances fron the

inlet of U.5, 13.5, 22.5, 3I.5, ^0.5, ^^9*5, 58.5. and 67.5 inches or

k,5 inches from each end and every 9.0 inches in between.

The stainless steel heat exchange tube extended beyond the

heated section at the inlet end for a distance of 18 inches and served

as a straightening section for the flowing liquid. A standard j- inch

"tee" was attached to the end of the stainless steel tube as shown in

Figure 5. A packing gland was provided at this point for the thermo-

couple tube for measuring the fluid inlet temperature. The thermocouple

tube was made of a section of — inch brass tubing fitted with small

32

spacing struts to insure a central position. This entire' assembly was

given a nickle coating to prevent corrosion by the black liquor.

At the outlet end the fluid stream passed through a mixing

chamber and thence past a short thermocouple tube which measured the

fluid outlet temperature (Figure 6). The fluid then reversed its flow

in the concentric annulus and finally left the heat exchanger via

standard piping. The flow arrangement thus prevented heat loss from

the mixing chamber prior to the temperature measurement. The entire

apparatus, straightening section, heat exchange section and mixing

19

chamber were insulated with standard thickness, 85 per cent ma;^nesia

pipe insulation.

The fluid passed from the mixing chamber at the end of the

heat exchanger into a seven-tube, single pass cooler containing: 1 —

inch tubes, 1^ feet long. The cooler was used to remove sufficient

heat from the fluid to allow for continuous recycling and to prevent

flashing of the hot fluid in the weigh tank. Fresh city water was used

as the coolant and was regulated by a one-inch globe valve to give the

desired fluid temperature in the storage tank.

The fluid discharged from the cooler into a 55 gallon steel

tank resting on an indicating dial type Toledo Scale with i pound

subdivision and a capacity of 800 pounds. Flow rates were measured

using a stop timer in conjunction with the weigh tank and scales.

Usually sufficient time was allowed for the accTomulation of 50 - I50

pounds of fluid.

The 1 — inch suction line from an open impeller centrifugal pump

manufactured by the Gould Pump Company also dipped down into the weigh

tank nearly to the bottom. The pump vjas used to return the fluid to

the top of the storage vessel either continuously or intermittently and

a convenient control was provided. A lever type quick opening valve on

the 1 77 inch discharge line was used to prevent drain back through the

pump into the weigh tank during flow measuring periods when the pump was

not operating.

The storage vessel was an 80 gallon stainless steel jacketed

reactor manufactured by the Blow-Knox Company. The temperature in the

20

storage tank was measured by a thermocouple inserted in a deep well

extending down from the top of the vessel. The discharge line from the

tank was in the center of the hemispherical bottom and lead to a posi-

tive displacement pump used for circulating the fluid through the heat

exchange apparatus. The pump was a one inch rotary gear pump manu-

factured by the Worthington Pximp Company and was driven by a five

horsepower electric motor. The pump was provided with a by-pass and

valve and this was used as partial regulation of the flow rate.

Upon leaving the pump the fluid first passed through a seven-

tube single pass preheating unit. The tubes were 1 — inches in

diameter and 1^ feet long and provided a hold up period in the flow

sufficient to insure uniformity in the fluid temperature. Low pressure

steam was used in the steam jacket in order to obtain rapid preheating

of the entire system when starting up and in operation the steam was

usually turned off and the large heat capacity of the unit was used

simply to prevent rapid fluctuation of the fluid temperature.

After passing through the preheater the fluid went directly to

the heat exchange test section or could be diverted back into the

storage vessel. A valve at the entrance to the heat exchange test

section was used in connection with the valve on the pump by-pass to

control the flow of fluid.

Valves and piping were provided in order to completely drain

the heat exchanger, preheater, cooler and piping to a low level tank.

The centrifugal return pump could be used to pximp the fluid from the

low level drain tank back into the storage tank or to the sewer.

21

All piping for transporting the fluid was standard 1 i inchk

black iron pipe and was insvdated using standard materials. The

complete piping layout is shown in Figure 3.

Steam was supplied to the system at 130 psi and was reduced to

the main header pressure, of about UO psi by a 1J inch Keckley regu-

lator, type AR . Freceeding the regulator was the main cutoff valve,

a strainer, and a continuous bleed-off valve which rid the line of

condensate as well as some entrained air. Steam for the storage tank

was further reduced to approximately 10 psi, using a one inch Keckley

regulator. Type PT. Steam for the preheating heat exchanger was

reduced using a i inch Foster regulator, Type 50G2C to approximately 5

psi. Finally the steam used in the test heat exchanger was reduced

using another _ inch Foster regulator to pressures lower than atmos-

pheric. In order to provide a method of discharging steam condensate

at pressures below atmospheric a vacuum system was connected to the

steam condensate discharge line. The vacuum was maintained using a

reciprocating vacuum pump manufactured by Worthington Pump Company and

driven by a three horsepower electric motor. The vacuum system was

connected to the condensate line through a 100 gallon accumulation tank.

In order to reduce the load on the vacuum pump the condensate from the

steam chest was passed through a cooling coil and then to the condensate

accumulation tank. Using this system it was possible to maintain

pressures from 8 psi absolute to 20 psi absolute, corresponding to tem-

peratures from 180'' F. to 228^ F.

In all, 13 temperatures were measured using thermocouples.

22

These were: (l) storage tank, (2) inlet fluid, (3-10) tube wall, (11)

outlet fluid, and (12-13) steam in heat exchanger. Leads from all

thermocouples were connected to a rotary selector switch manufactured

by the Minneapolis-Honeywell Regulating Compare . Measurement of the

e.m.f. output of the themocouplep was accomplished using a Leeds and

Northrup potentiometer. Type 8662. This potentiometer was equipped with

an automatic temperature compensating mechanism but more reliable

results were obtained using an ice bath as a reference junction tempera-

ture. The tube wall thermocouples were calibrated before they were

installed by checking td.th N3S calibrated themometers. A calorimeter

was used to maintain constant temperatures of 32° F., and approximately

100 F. Boiling water was used as a third check point. The values of

e.m.f. obtained agreed with those given by Adams in the International

Critical Tables, Volume I, within - 0.^%, Temperature - e.m.f. curves

were plotted using the data from the I. C. T. with scales readable to

0.1 degree Fahrenheit. The thermocouples used for measuring the fluid

inlet and outlet temperatures were withdrawn from their respective wells

and were calibrated in the manner described above. All thermocouples

were sufficiently alike to justify using the same temperature - e.m.f

.

curves.

Other special apparatus were prepared to measure other quanti-

ties related to this investigation; the appropriate apparatus are

described in the section devoted to these meastirements.

C. ExperiiT-ental Froc^du^e

The black liquor used in these experiments was obtained from

23

the Palatka, Florida Mill of the Fi'udson Ftilp and Paper Company, a

company engaged in the production of unbleached kraft paper for use in

bags and guiuiied tape. The liquor was taken from the last stage of the

multiple effect evaporators and contained approximately 55^ black

liquor solids (b.l.s.) with the balance water. The liquor was trans-

ported in 55 gallon steel drums and remained stored in these containers

until used.

Since the black liquor was a water solution, liquors of various

concentrations could be easily produced by diluting the concentrated

material with fresh water. The solids content determinations were made

by drying at IO5 C. a sample which was absorbed on asbestos in a

porcelriin crucible. In this way no crust was formed and a constant

weight was obtained in 2^ hours.

In order to avoid usinc excessive quantities of the concentrated

black liquor the plan for operations was to start by using the most

concentrated liquor and then^by dilution in the stainless steel storage

vessel, prepare successively lower concentrations. At each concentration

complete sets of data v?ere to be taken so as to eliminate the necessity

of repeating a particular concentration. Actually, however, the appa-

ratus was first run using water since it was felt that operating

difficulties could best be investitrated and corrected when using a sys-

tem on which considerable data were available. Following the runs using

water, black liquor nins were made using 30.5, 33.0, 25.1, 16.8, and

9.2^ b.l.s. At this point in the investigation it was decided to obt-ain

a new sample of black liquor from the Hudson Pulp and Paper Company in

2k

order to investip.ate higher concentrations. Experimental runs were

made using; this new liquor in concentrations of ^9.3. ^1.9i and 33«0>

b.l.s. As a final check on the apparatus and the calcxilations another

series of runs were made using water.

The procedure vrill be discussed only in relation to the black

liquor runs since these are- of major imp-ortance in this investigation

and since the use of water in the apparatus offered no additional diffi-

culties.

Concentrated black liquor was poured into the 80 gallon stain-

less steel storage tank and sufficient water was added to bring the

vol\une of fluid up to approximately 60 gallons. This volvime of material

was sufficient to provide fluid to fill the remainder of the apparatus

and still leave a safe quantity in the storage vessel. It was necessary

to provide agitation to obtain a hcsnogeneous solution of the black

liquor and this was accomplished by circulating the fluid through the

rotary pump and preheater and back into the tank. Several hours were

allowed for this operation. Heat was sometimes added in the preheater

and the storage tank to increase the fluidity of the very concentrated

liquors and thus improve the mixing. Several samples of the liquor were

taken and analysed for solids content.

In preparation for a series of runs the liquor was usually cir-

culated through the entire apparatus for a period of from 30 minutes to

an hour. The steam to the storage tank and preheater was turned on and

regulated to about 5 or 10 psi. The circulation of the liquor served

to heat up all piping, pumps, tanks, etc. When the liquor in the

25

storare tank reached the desired temperature the steam to the preheater

and stora(7e tank was usually cut off. During the heating up period the

potentiometer and ice bath were prepared and the 13 thermocouples were

checked for response and agreement.

With the fluid circulating through the heat exchange test

section the steam was admitted to the annulus and adjusted to about 10

psi. A brass cock at the opposite end of the steam space was opened

and steam was bled off for several minutes to rid the steam chest of

entrained air. The vacuum pvimp was then started and the valve to the

condensate discharre line was opened. Tap water was turned on the coil

condenser to prevent flashing of the condensate with accompanying loss

in vacuum capacity. A bleed valve on the vacuum rump and the — inch2

Foster pressure regulator on the steam line were adjusted to give a

steam chest pressure slightly below atmospheric. The pressure was

used as an approximate indication of the steam temperature.

The temperature of the storage tank was allowed to inci-ease to

the desired level and then was held at this point by adjusting the

fresh water flow in the cooler follov;ing the heat exchange test section.

With all apparatus in operation and having been checked, a run

was started by adjusting the flow control valves to give a desired flow

rate as indicated by measuring the rate of discharge into the weigh

tank. With the flow rate fixed, at least 10 minutes was allowed for

equilibrium conditions to be reached. Equilibrium could be detected by

following the variation of several thermocouples during this period.

When successive readings failed to show significant deviation the

26

return pump was started and the fl\:id in the weigh tank was pxomped back

to the storage tank in order to make room for 100 to I5C pounds of

fluid to be collected during the test period. The pump was then

stopped; the quick opening valve was closed to prevent dr&in back

through the pump into the v^eigh tank; and the stop clock was started

when the pointer on the scales passed a convenient point on the dial.

The thennocouples were read and recorded in rapid succession in the

follovdng order: (l) storage tank, (2) inlet fluid, (3) outlet fluid,

(^-11) wall temperatures, (12, I3) steam space. The timer was then

stopped and the weight collected at this point was recorded. During

the early stages of this investigation a second set of readings were

taken after a several minute interval to serve as a check on the results

of the first set. These two sets were found to be in agreement in most

cases, thus, indicating that equilibrium had been established before the

first set was taken. Therefore, in the remaining exi>eriments, adequate

time was allowed for equilibrium to be established and checks runs were

made only occasionally.

At the completion of one run the flow rate and steam pressure

were readjusted slightly and after the necessary equilibrium period a

set of data was taken. The flow rate was, thus, gradually increased or

decreased to the maximum or minimum flow obtainable in the apparatus.

The complete range of possible flow rates was traversed at least twice

with each liquor concentration. After all the necessary data had been

taken using the highly concentrated black liquor, a portion of this

material was pumped out of the system either to the drain or to storage

27

drums. Tne voliime was made up with fresh water and the fluid was cir-

culated to obtain thorough mixing. Samples were taken for solid

contents determinations and the apparatus was ready for another complete

set of runs at this concentration.

Several days were usually required for a complete set of runs

to be made at each concentration. Each time the apparatus was started

up the procedure outlined above was followed. At the end of one days

operation the entire quantity of fluid was pumped back into the storage

tank and the remainder of the apparatus was allotted to drain. Each time

the liquor concentration was changed, an extra long precircvaation period

was allowed so as to prevent the presence of pockets of different concen-

tration in any of the tanks or lines.

D. Data

Descriptive and experimental heat transfer data for all runs are

given in Tables 1 and 2, respectively. The tube wall temperatures as

shown in Table 2 are the temperatures at the extremities of the heated

length of the tube and are extrapolated values based on the readings of

the eight tube wall thermocouples. Plots of the thermocouple readings

versus tube length made for each rxin indicated in iiost instances an

approximate linear relationship. It will be noted that the point of

measur«nent of the tube temperature lies within the wall and that its

exact position relative to the temperature gradient through the wall

remains to be determained.

The avera.^e steam temperatures shown in the last column in

Table 2 were not used in the calculations but are given for general

28

TABLE 1

GBIIER/U. INFORMATICM OK FLUID SYSTEMS

"

"Weight per centRun No, Fluid System Black Liquor Solids

1- 22 Water

23- 55 Original Black Liquor^ 38.5

56- 30 Original Black Liquor 33.0,

Sl-103 Original Black Liquor 25.1

lOit-131 Original Black Liquor 18.8

132-163 Original Black Liquor 9.2

164-191 New Slack Liquor^ '^9.3

192-202 New Slack Liquor i^l.9

21*4-223 New 'Slack Liauor 33.0

22*^-236 Wat-^r

Original Black Liquor was obtained prior to operation of theheat exchange appai;atus and was the material used in all physical pro-perty determination's.

New Slack Liquor was obtained from sajne source as the originalmaterial in order to secure runs at higher concentration of blackliquor solids.

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36

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37

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38

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39

infornation as an indication of th^ overall driving force. In soine

instcinces the steam temperatures are only slif^htly higher than the

extr^ipolated tube wall temperature at the outlet. Such a small temper-

ature difference is an unreal condition and resulted from the fact that

the straif^ht line used to extrapolate the tube wall temperatures was

slirhtly misleading in this region. This condition occurred whenever

the plotted tube wall temperatures indicated a slight convex curvature

with rer:pect to the horizontal axis.

In several instances runs which were actually completed and

recorded vrere voided due to known factors which would have made them

in error. Thus vacancies appear in the Tables of data for Runs Number

13, 166. 173. and 203-213.

E. Samrle Calculations

Run No. 184 was chosen for these illustrations since it is

typical and showed, in general, satisfactory results. The fluid em-

ployed in this ran contained ^9.3^ black liquor solids. The calculation

to be presented in this section will include data from Tables 1 ^j^d 2

as veil as the results of the physical property studies discussed in

the followin? sections of this dissertation. In addition, other

properties detenr.inable from the geometry of the apparatus are neces-

sai^. These properties are tabulated as follows:

Inside diameter of tube: D = O.51/12 = 0.0^25 ft.

Outside diameter of tube: . 0^= 0.75/12 = O.O625 ft.

Thickness of tiike wall: d = O.OlO ft.

Heated len?th of tube: L = 6.00 ft.

Inside cross sectional area of tixbe: 3 = C. 001418 so. ft.

Total inside heat transfer surface: A = C.SO sq. ft.

Total outside heat transfer surface: Aq» 1.176 so, ft.

Log mean heat transfer surface: A =C.975 sq. ft.

In order to systematize the calculations, a data and work sheet

was prepared for use with each run, .'In example of this sheet with the

data for Run No. IS^^ is shovm in the ap;)endix. The sheet was designed

for the calculation of all dimensionless groups to be used in the heat

transfer correlations a? well a« the j factors.

As pointed out in the section "Data" it was necessary to deter-

mine the exact position of the tube wall thermocouples with respect to

the temperature fradient. The thermocouples were located at the botton

of grooves milled C.0625 inches deep and C,0625 inches wide, Feened

into and completely filling; the groove vas a strip of soft solder.

Mathematical calculation of the position of the thermocouple with

respect to the temperature gradient was complicated by the goemetry of

the cross-section and the fact that the thermal conductivities of the

stainless steel (Ty{?e 30^) and the solder are different. Some investi-

gaticHG are reported in the literature wherein the physical position of-

the thermocouple in the wall was taken as an indication of the position

of the temrieratui'e measurement. This assumption can be grossly in

error, as was shovTi by this study, and it is accentuated when tube walls

are composed of materials of relatively low themal conductivity thus

causing large temperature drops aci-oss the wall.

In order to avoid a complex mathematical analysis of the tube

41

vail temperatuTf^ it vas decided to use a seini-empirics.1 methcxl of

attack. A themoco'iple was to be mour.t^d in a flat plats of Type "^Ok

stainles? steel in a manner similar to that used in the tube wall ; a

temperature gradient v-as to be imposed; and measurements of the vail

tem];ierature -inc the two surface temperat^jres were to be made. Having*

in this way, determined the thermocouple position relative to the tem-

perature gradient in a flat plate a m.athematical treatment could be

used to locate the thermocouple measurement in the tube vrall,

A groove C.0625 inches deep and C.06^5 inches wide vas milled

two-thirds of the way acr-oss a h inch by ^ inch piece of Type 3^^

stainless steel C.125 inches thick. A copper-constantan thermocouple

vas installed in the same way the tut>e vail thermocouples had been done

and additional thermocouples were soldf^red to the surfaces a1x)ut 0,25

irches ax^'ay from the groove. Rubber hose was used to direct atmospheric

steam on the grooved side of the plate in the area of the thermocouples.

A stream of water was directed at the opposite side of the plate. The

three temperatures v.'ere read over an extended period of time and aver-

age values tcere determined. The temperature drop from the wall thermo-

couple to the cooled surface vas found to average 80% of the total

temperature drop across the wall. This is in contrast to the fact that

the thermocouple was physically located very close to the center of the

vail. Most of the difference can be attributed to the difference in

thermal conductivity between the stairless steel (9.^) and the solder

(19. C), Additional effect is caused by the fact that the bottom of the

groove is at the midpoint of the wall and therefore the thermocouple

42

which is aMJ,-c.-=^rtt to the bottom is actuall;/ somevhat off center.

The rrrblera of deteminine; the ther.riocouple locc.tion in the tube

^Tilx bri5c»r' on infor-TTiHtion gainf^u on the fl^t piste tests is simj-lified

by a.^svnninp; that the v;all is of uniform composition find that the ef-

feetivs physical locition of the thennocour.le is one-fifth of the way

throuf;h the vhII. In order to deteri-.ine the proportion of temperat^jre

drop from the thermocouple at this loc^ition to the inside surface it is

necessary to devel \o an e -iTeso-ion for the temperati:re distribution

th.rough the tube wall when heat is flowing throo.-h th<=- wall at a steady

rate.

For a lonjj tube of the dimensions used in these' experiment's, let

t , t , and t be the temperatures at the radial dist5nces r , r , andO v S O VJ

Tg respectively (see Fipiire ?)• Vnen the tube has length I, the he£t

transiaitted in unit time, c, is given by the expression

q = 2TrrL.„fi =. 2iru:„3fi; (10)

where k., is V.ie thennal conductivity of tho wall. Int-^gration of this

equation betveen the limits r and r and between t and t givesso soq = ?1TLkw a, - t^^

^^^jInr^ - Inr^

Integration betv/een the lirnits r and r and between t and t givess w s w '^

q = 2TrLk,(t, .-t^)(^2)

Inr .- Inr

.3 W

Since the v.'.lue of q in the equations 11 and 12 are equal, the equations

•"nay be solved si.-aultaneously to give

Figure 7

Cross Section of Heat Transfer Tube

Wf

t„ - t. Inrg . Inr^,(13)

(

Using r = 0.235, r^ = C'.375 and r =0.351 there resultsso w

-2 Si , 1:!- = 0.83 (1^)

*s - ^o ln°» 255/0.375

Therefore to calculate the actual inside tube surface temperature

the overall temperature drop must be multiplied by 0,83 ^^d this value

subtracted from the temperature of the tube wall as indicated by the

thermocouples. As shou-n by Figure 8, a plot of the tube wall temperature

versus the tube length, the data are well represented by a straight line.

Over the small temperature rise encountered the thermal properties of the

black liquor may be assumed constant. Thus the variation of the fluid

temperature through the tubs may be represented by a straight line be-

tween the inlet and outlet bulk stream temperatures. Since the heat

being transferred is proportional to the overall temperature difference

it is obvious that different amounts of heat are being transferred in

different sections. However, a mean value of the temperature drop across

the tube wall may be calculated from the dimensions of the tube, the

total heat flowing and the conductivity of the tube '>;all. Thus from the

basic heat flow equation

At. = t„ - t, = ^^oJ^Zl („)"•A

where A^^ is the logarithmic mean of the inside and outside tube

and (r - r ) is the thickness of the tube wall.o s

areas

^5

0)

cc o +> *

1

1

O-P HO -P

r

! 1

'

•o1

1

l'

1

1 1ill

to|

HpP3

1

11

i

ll1

1!

1

1

c oIT) f-< 0)

^ X 4J nr^

<2^ «T1^m

0)

<D cJS •Ho

ir\ a o• •Ho * ^J^ +j <fl

0> •HH J-.

^ as

>e <l)

u^ n f^•

(^ 3<H -!->

mV Jh

o (i>

c(0 S+j <u^ w

'io • sanr^BJSdiaei

1*6

A^ = ^o " ^= 2Lir£ojJs) (16)

lnf2 In '^o

A r

A - (2) (6.0) (3.lh) (0.0312 - 0.0212) ^ ^ ^^^ ^^2

'

In 0-031?^

0.0212

Using a value for the thenr.al conductivity of the tube wall of

9,k BTU/(ft.^) (Fr.) (°F./ft.) there results from equation (15)

(0«0312 - 0.0212)

^*w = *o -"^s

' ^ O.k) (C.975)

= 0.00109 q (17)

Conbiniup; ecuations (1^) and (1?) and solving for (t - t ) an' w 3

expression is found for the mean temperature drop between the tenpera-

ture Indicated by the wall thermocouples and the inside surface

temperature

.

t„ - tg = 0.83 (to - tg) = (C.83) (0.00109) q

= 0.000905 q (18)

The quantity of heat transferred per unit time, q, may be found

from the mass rate of flov, W, the heat capacity of the fluid at its

average bulk stream temperature, Cp, and the increase in temperature of

the fluid from inlet to outlet, AT = (T^ - T ). Therefore,

t - t = 0.000905 WCp (T^ - T^) (19)

For run Mo. IS^, the mass rate of flo^: from Table 2 was 2632

Ibs./hr. The inlet bulk stream temperature T, was 159.8° F. and the

^7

outlet bulk stream temperature To was l6?.l F. and these gave an

average bulk stream temperature, T , equal to 160;95 F. The values ofb

the fluid heat capacity for various concentrations and temperatures are

given by Figure 13 . At the average bulk stream tempera tur-e and concen-

tration of this run a value of Cp equal to C,738 was found. Thus,

t - t = 0.00905 (2632) (0.738) (162.1 - 159.8)VJ s

= ^.1 °F.

Based on the assumption of uniform heat flux along the length of

the tube, the inside tube surface temperatur-e at the inlet and outlet of

the heated section may be found from the extrapolated wall temperatures

at these points. These extrapjolatcd wall temperatxxres, as shown on

Figure 8,were found to be 202.5° F. at the inlet (t ) and 2QU.<f F. at

the nutlet (t ). Thus the inside tube surface temperatures at thew2

inlet and outlet were calculated.

Inlet: t = 202.5 - ^.1si

= 198.4 °F.

Outlet: tg2 = 204.5 - 4.1

= 200.4 °F.

Referring to Figure 8, it may be seen that the mean temperatvire

drop through which heat was transferred from the tube wall to the fluid

will be the logarithmic mean calculated from the inside tube surface

temperature and the bvilk stream temperature of the fluid both evaluated

at the inlet and outlet of the heated section. Thus,

At - ^^2 - Ati (200./+ - 16?, 1) - (198.U - 150.8) , ,

Zit, (198.^ - 159. S)

Actually, in this cass the arithmetic Average temperature differ-

ence would have been satisfactory since the ratio of the terminal

ter^peratura differences does not exceed 2,

The avera^^e coefficient of heat transfer bet\veen the tube wall

and the fluid v/as calculated directly from the rate of heat transfer, q,

the mean temperature difference. At , and the area across which thetn

heat flowed, A. Thus by definition,

q a hAAt =• WCpAT (21)w

where h is the coefficient of heat transfer based on the inside surface

area . Thus

,

h . '"^'Cp ATAAtj^ (22)

(2632) (0.738) (2.3a)

(0.80) (38.i^5)

h = liii5.0 3TU/(hr.) (ft.^) (^F.) ,

The Stanton number, St, was used in the correlations to be pre-

sented in later sections of this dissertation. This number can be

calctilated from the heat transfer coefficient, h, the heat capacity, Cp,

and the mass velocity, 0, which is equal to the mass rate of flow divided

by the cross-sectional area. Thus,

49

h h^' ' WhT] ' Sfl <23'

A more corivi^nient method of ralculatinr the Stanton nunber is

four.c by rearr- n-ietif^rt r.f equttion 21 after multiplying each side "by .'5.

CpVv CpG A ^!>t„

JL = 0,»-Ci:;l8 ^_ ^ C.OCI77AL (,r..)

CrG C.eO At„ At

It i^ evident that >.e Stcnton nun-^er r.:ay be calculated directly

from the two te.'nperature diff'^rences. Thus,

_h. ^ (0.00177)^ (::,30)

= 0.0001058

The Prandtl number, Pr, barbed on the bulk mean fluid tejaoeratare

was calculated fron values of Cr, k and/* obt.^.in«d from Fij^ures 1;, 2C,

and 22. Tliese values are Cp equal to 0.73'', >U equal to 18.1 contlpr^ise,

and k equ-al to O.306 3TU/(hr. )(ft?)(°F./ft,) . a corrvf^rsion factor of

2,^2 vas .T.ultipliod tines the viscosity in centipoises to obtain vis-

cosity in consistent unit'.

ir -. Bi^- = (p-?3:-) (rM) (2.^2)(26)

k C.3O6

= 105.5

Th« Reynolds number. Re, b3.-:ed on the bulk mean fluid tempera-

ture v:a2 found to be.

50

. Pe = ^ = Lpi (,7)

(la.l) (2.42)

= 1800

The Oraet* number, Gz, can be evaluated from the Reynolds and

D

LFriindtl nuonbers and the — ratio as follows:

- ' if) m (r) (?) -'^

0. = («,, «.,(£|5«5) (..)

Gz = (Re) (^Y) (O.OO56)

Gz = (1300) (105.5) (0.00556)

Gz = 1057

The ratio -^^ is fcind by dividing the fluid viscosity at

the average surface terror erature by the fluid viscosity at the bulk mean

temperature. The avera^^e of the tube surface tejnperatures at the in-

let and outlet was found to be 19^«'+ F. and the viscosity at this

temperature u'as found from Figure 22 to be 9.05 centipoise. Thus,

ill = il25 = C.50M 18.1

Tlie coefficient of cubic'*! expansion, j3 , may be calculated from

density or specific gravity measurements. By definition.

51

^ _ ^ exnan.^ion(30)

(31)

/-. ... ^^

In terms of density this may be written

1 1

y5 = p2 Vi(S-^n) 1.

In tenns of tre specific ^Tsvities of the flui^^ at the terminal

bulk temperatures

^2 (T . T ) 3 3

^^'"^

2 112The values of specific gravity at various temperatures and con-

centrations may be obtainetJ from Figure 23. Thus,

/3 =(1,2590)^ - (1.2582)^

2 (162,1 - I5G.P) (1.2590) (1.2582)

fi = 0.000288 ^/*^.

The r.rashof number, Gr, is calculated from the inside diameter of

th? tube, D, the density of the fluid £t the bulk mean temperature, fi ,

the gravitational constant, f, the viscosity of the fluid at the bulk

me&n temperature, ^a , the coefficient of cubical expansion y5 , and the

temperature difference betv.-een th'^ tube surface and the bulk of the

fluid, Atp^. The equation ''or the Grashof namber with all constants and

conversion factors includ*^.-! becomes.

Or

52

= 2.13 (10^) ^'/^ ^Sn (33)

At th*=» bulk mean fluid temperature, the specific gravity from

Figure 23 was 1.2S66 and the visco^3ity from Figure was 18.1 centiroise.

Thus,

^ _ 2.13 (10'') (1.2586)^ (0.000238) (JS.'-^)

(le.l)-^'

Gr = lli+O

F, GalculatH'd, Re3ults

The complete calcul-ntea results for all experimentdl runL^ are

tabulated in Table 3, The variables tabulated and their ranges of

values are as follovs:

Hest Transfer Rate, a: JU-'C - U52OO 3TU/Hr.

Log Mean Tempemture Difference, Lt^: 13.9 - ica.50^.

Hea* Transfer Goe^'ficient, h: SO - 33M? 3Ti;/Kr., Ftv. <V.

Stanton Nunher, nt: 0.0000753 - 0.00239

Prandtl Number, Pr: 3.^9 - 3^-. 00

Reynolds IJuniber, Re: 1^5 - 755i^'0

Viscosity Ratio, A's/yU : 0.211 - 0.391

Graetz Number, G2: 65 - 1^61

Grashof Number, Or: li?5 - 33^000

It will be noted that the Graetz and Grashof numbers were calcu-

lated only for tho:-.e runs with Reynolds nximber values less than 3^00

since these variables v.-ere to be used in viscous region correlations

only. The results of several intermediate steps in the calculation of

53

«H fn

^ i?n« Pu J.'

C3

rt t.J i0) .O

&

o

>iJH oor M-4

4J

jU

CTv O O O (^ O O O^ <Ts r%r- 1^ fH tH ^j i^ ^^^ a —' riV V r- r- c- f - c- r c no

\D o iTN. vr\ CO C^ xTir^ >r\ f^. C^ o m:i r-«C5 qO o C^ 00 cc vi;!

^ f- (^

>iJ \o O

C x:

co _

fO

•^ to .r-»

n) c V^

o

p

o c o c o o o o o o

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o c» o o o o oO C' O r-NONrH C^H O: rH 00 \f\ tV Nc; r~- c^ -:t ^ (^ o>H

OOQOOOOOOC5 OOOOOC~- cv ^ c- o cn( CN ctn -y- o) NO r , ir> NO c>^ Ox <i^ if- ^ (M CCVA u^ rH Q NO C> rH -^<«^ 0-^ (-N -f ^ u^ ^ ^ ^ u-^ 3- CO C^ C^ On

rH <M < A -* <f x^ii fv a) OS OK t^ C-- 1^ r- i^ N t-- Jn oC'1-^ r-t r-t r-i ft rt t-( t-i r-l i-i

r\^ X.-N.NO !>. CO On Oo: ?. o; cc cjC 00 oo CT.CO ocH r-i r-i r^ r-i r-t r^ i-t r-i

rH CV C^^ •AUN cr> (7N ijN 0--

rH rH rH rH H

61

t g

^ (!' »\ CO o I'J OC. cs.1) <> f -r 'X' c c^ fN.-^ f C; t>- e o f J-Ih ri r~i « • • • •

o X O O iH r-l rH

o

c

6-< C

9) Vc *•• ^ia p c

O ii. <.^

t) aH

li

f--

o c> o* k •

On

o

O, on u? ov Oc^' (I rj r\? r\

C; Vf , 0> r'\ tM vv r-t ^- vo o; CM t«. i-t o 00 Hr » vr> .;j- u^^ to (M «n r--c Jt ^ t^ c^ vo c^ r- ^-

L (.J o o o

IM r-l r-t VQ C^V) t-i <"^ nO a.

r-^ Ow <. o; > .

o c; o c. c> ooooooooo

(• _i ir\ \j~\^ r-- u.

m o «• CO w-^ <r) to CO uv o o v£» Cv C-- r- -y

M 00 O O HM5 --J :<i r-{ ar-t r-l H r-t r-i

r-* ON r- O O'J O C '

(; n • _? W \ U~>, u'\ vr\

C^ CO r^ <v) vf> o u^vO »^^

<\t oT CN PJ C^ <^> V N r-i -3f , vr> OJ _i -J CO vO vA -1

o o o o o

crN >AvO CO

rH f-t pH fv.

u> u"\ u"^ ir\ u^,

O C; O CJ CJ O o COO»-^l-^^HlHr-t^-!

uA C\ "v; -y vr\ c'\ ^-v; c^ o CO t- .rr o

o c^- ^ r- <M o o t'^ f^ij r\ tr\ a) to o a^-u^ -^

r-. u^ u^vo c- 0- r-< rM r-( i-l f-i f' \ vo P H rNH r-t H H tH

U^ C3 U^ t-. U^ VTvO f-l 0^r- vT (T'^C' fy r-i c^ o r^

C \ Vi ) ^ r-t

+i <^. a) o o O CJ O o o o o o o CJ o oin in *J <> o < > <AO <.:> o o o o o o o o0) c ctt U' * r. -•-1 On r^ C\ cu fA C-- rA rj a« (~- CC oIT! '•I rt; H ^4 o C> c:> r-l C'> (, (V v^^ r-, M 0.. -J vO or.

i-, '.n s: rH rH iH <H iH H C\' H in. rv o; Cvj CJ <VJ

VO C^ CD (>. OON aN vi"- ON or^ H H l-( fNJ

O O O H r-l H f-l H r-( o;in: t\i (\i i\i fv: iNj o.- '•J r< (M

c^ NO \o r • r \ ^ -y cN c ^

o o o o o c> o oVN. vo t^ OJ vo '-f vO r-t

c- C5 c o r\ V tNi ^^ ^ (\; rvi 0^ c^i

r-* <M c\^ u^ vja r- 00 gvC J C-J {Vj CVi CM (M <Ni <%' CVJ

r* OJ (M <M <v.' CV (\i iM CM

o u

^3 f^

<D X!

o ^

o

c

62

Io

r\ (^ OJ O 0\ COi-t cv --t cf vb t^00 or cr r^ 00 00

O O O O O <::i

C^ c\j Csi or,; c^ \r\

r \ r > r r> r^ r^

cc o o C^ CO ^H f' O —* CO C^^ ^ C> O'.C^l C-i

r-i r-i r-* r-i r-{ r-t

•f^ V 1 C

tk:<o w -' c^ ^0 vo o f^ r-^<t C <i- c^ 00 O OC 00 O OnX w <« cnlfa. ^ SO 0-. H ^ CO O

t- <i)j

H f-t rH cv; r J cj c--»

c- o {-

C" ; •

A) i' i:^C U OiC r< c4JJ 4.

i3 ^ u ^^ C^ c^^D o ^^o 00L. a- • cvJ \r\ 1^

' r-.sc a- -"tho 0) <~J

t • *«••*•c c. <n

a) Oo s*J d i-t C7- C^ vOf . CM CJ f\; M cH H

f-

k)0)^ << (D o o o o o o o

c? « -p o o o o o o o£2! ?^ ^Z • CO r>- o t^ o cj CO

f-. i. kTN C^- C^ (J^ O O^. m a: ^ (^ c-1 r^ f'v^ -aH

C • ^aa oS

Cvl (\» CM f^j cvj Ovj eg

63

the log me.m temperature difference are not tainslated since only the end

result is of significance and the procedure is straight forward.-

Q« Anal/sis qf Result s

The discission in this section vill be limited to the general

reasonableness of the calcjlatarj resi'lts and a complete analysis of the

interrelationships of the data will be presented in the overall dis-

cussions at the end. A^ stated previ(''ui5ly the consistency of the data

will be indicitted by the def^ree of applicability of the well established

methods of correlation.

In res^arr! to the experimental accuracy involved in these measure-

ments it can be stateii that effort was made to obt'iin a reasonable

ntimber of significant figures at all times. It is well established that

even under ideal conditions and vdth extreme care heat transfer corre-

lations may have deviations on the order of - 20%, This cannot be

interpreted as legitimate reason for careless e>:i>eri-'nental technique but

does justify the use of slide rule accuracy in computations and

measurements. However* particular care roist be exercised In measurements

that involve detennining small differences of relatively large numbers.

Thus temperature measur«anents were accui*ate to four significant figures

or a tenth of a degree fahrenhelt. Temperature differences of 10 to 100

were thus accurate to three significant figures while those below 10

vere accurate to two significant figures. '^?o temperature differences

were encountered sirallsr than approximately Z'^F,

It is in the evaluation of the tube surface tenperature that the

greatest error may occur, firrors are introduced due to the tmcertainty

6U

of the position of the wall thermocouple with respect to the ternperatm-e

gradient. The teraperature drop across the tube wall was relatively

large riue to thp lov thf^rmal conductivity of the stainless steel and

varied from 3° F. to as hirh as *-^C° F. Corresponding differences be-

tween the tube surface temperature and the bull: fluid temperature were

perhaps ^4-0° F. and 20° F., respectively. Since the tube surface teir,-

peratvu-e u-as found as a function of the total wall temperature drop and

the drivin'-' force temperature difference vas then found by difference

betv.'een the tube surface temperature and the fluid temperature, it is

evident that any error in tbe tube vail texperature v/ill produce an

error inversely proportional to the ma^itudes of the temperature drops.

Thus, an error in the 3 ?" vail temperature drop would produce an error

only T^ as great in the kO F. driving force temperatiire difference. On

the other hand an error in the ^C*^ F, wall temperature drop would pro-

duce an error -^ or 2 times aj great in the 20*^ F. driving force20

temperature difference.

Efforts were made to ef.taibli.'sh the possible error in the location

of the wall thermocouple with res.-^ect to the te.-iiperature gradient. It

was concluded that the maxi-num exi^ected error was on the order of - 5.0'^.

Thus, under the most extreme conditions the maximum error to be e?rpected

in the temperature difference beti/een the tube surface and the fluid

v^'tjij) was - 10.0 >, An approximate evaluation of the error in each run

may be made by dividing the heat transfer rate, q, by 221 times the log:

mean temperature difference. Usin<r this method it may be seen that the

error for runs in the viscous refion is on the order of t 1.0-:£. In the

65

transition region the error varies fror. t 1,0;^ up to t 3.5-;^ and in the

turbulent repion the possible error may increase to 1 IC.O^ at the very

high Reynolds na-nbers.

The fluid flow measm-enents v;ere accurate to = pound and ~2 10

second. The weight of material collected wa.> usually around 100 pounds

but at very low rates was occasionally as low as 20 pounds. Thus, the

weight measui^enents had a maximum error of - pound in 20 pounds or2

- 2.5:^. but was usually on the order of - 0.5^. The time of collection

of the fluid was never less than ICO seconds. The maximum error in

these measurements was therefore - 0.1^,

Usinp; the exioerimental heat transfer coefficient on the fluid

side, the thermal properties of the tube and the overall temperature

difference, values of the steam side coefficient were calculated and

found to be on the order of 1000-2000 3TU/(Hr.) (Ft?) (°F.). Such

values were considered ouite reasonable.

CHAPTER III

SiECIFIC '-EAT irrViSTIOATIOXS AND R^^SULTS

A. BackgrouqH

The specific heat as well as the other properties of the black

liquor should be known as a function of temperature and solids content

in order to have sufficient information to use in conjunction v.lth heat

transfer equations.

The literature contains v^ry little inforrriation on the specific

heat of sulnhate black liquor. Kobe and Sorenson (l?) determined the

specific heat of sulphate liquor from the puJ.ping of western hemlock.

They used liquors of four different solids content over the range of 77

to 200 F. The results were correlated as mean specific heat as a

function of solids content only, there being no api>arent correlation

with temperature indicated by their data,

Stevenson (3I) gives a value for the opecific heat of black

licuor solids as 0.23. The same reference also gives values of specific

heat of black liquor solutions of various solids cont°nt. These values

are equivalent t*-> the sa-n of the component parts on a weight fraction

basis wherein the srecific heat of black liquor solids is O.5O and water

is 1.00. At least one other value for black liquor solids is in common

use, namely O.^k,

66

67

The literature contains nvunerous methods of determining the

specific heat of liquids, many of vjhlch are modifications of the classical

methods. The jnethod chosen for this work was similar to thst given by

Williams (32) and was selected because of its simplicity.

This method is ba-^ed on the mensurement of instantaneous rates

of heating and cooling' during alternate heating and cooling periods of a

sample in an insulated vessel. Kobe and .Sojrenson (1?) measured the

average rates ov^^r a 10 interval in a similar apparatus.

B. Arparatus

The apparatus is illustrated in Figure 9 and is shown diagram-

ma tically in Figxire IC. The sample vas contained in a 2C0-ml, Deuar

flask fitt.-d with a cork stopper which was covered vith aluminum foil to

prevent '.%'ater absorption. The heating element was; a coil of 20-gage

Chronel "A" resistance wire, ihis v.-as contained in a small ^-lass tube

bent to form a horizontal circle of 1 -^ in. diameter with tho two ends of

the tubing ext-ending up into the bottom of the cork stopper. The ex-

ternal copper wire leads extended all th-; way into the heatinf^ coil in

the circular portion of the tubing. A glass stirrer vas centered just

belov' the he.itinr element and rotated in a glass tube bearing in the

cork, A 3C-^are copper-constantan thermocouple was held firmly between

the cork and the flask and extended into the center of the sa^mple.

Sealing wax was used to seal arotmd the heating element and stirrer

bearine- openings in the aluminum foil. Although it softened during each

use it remained in place and formed a vapor-tight seal. The entire api a-

ratus vas set up in a room maintained at the constant temperature of

cd

o

•ri

O«

0\

69

350 R.P.M.

MOTOR

TOPOTENTIOMETER

THERMOCOUPLE

HEATINGELEMENT

TO POWERSUPPLY

200ML. DFWAR FLASK

Figure 10 Cross Section of Specific Heat Apparatus

70

72° F. i 1.0° F. This enabled equilibrium conditions to be established

v.'hich otherwise woxild have been im}-)Ossible v/ithovit the use of an addi-

tional insulated vessel surroundinr the Dewar flask.

The heating current ivas supplied by a 6-v. lead stora^^e cell of

which usually only two cells v;ere used giving slirhtly less than ^ v.

The voltage was measured by a calibrated General Slectric voltmeter

accurate to C.Ol v. The current was measured using- a General Electric

tnillivoltmeter across a j-^i^I • • 200-rTv. s?unt, s<.nd was accurate to 0,006

anp. The temperature v;as measxu'Hd using a Leeds snd Northrup potentio-

meter. Type 5662, and plots of temperature ver.sus e.if.f. taken from the

datci in the I.C.T. by Adams (l/. The temperature measurement? vjere

accurate to 0,05° ^«

C. perivation of Equations

The ba.'dc equation of calorim.etrj' foi* a batch system is,

Q = WC AT, where Q is the heat added to a sample of weight, W,

refiulting in a change in tenperstur*-, AT, and where C is the heat

capacity or the specific heat referred to vmter at 60 F. Since the

heat camcity of water at 60° F. is 1.000 3TU per pound per °F., the

specific heat is numerically equal to heat capacity but has no units,

IVlien heat i« added to a syster.1 which includes a calorimeter vestjel a

portion of the heat is absorbed by the vessel and some is lost to the

surroundings due to the teiTi]>erafure elevation of the apparatus above

ambient. The equatlc^n beccxneii

Q = f^ + (C.K.) ] AT +F^ (34)

71

v:here C. T. is the calorimeter equivalent and includes all the heat

requirefnents of the system other than the substance unciei- study and H,

is the heat loss.. Eqvuition (3^+) expressed differentially as a function

of tLTie beccxnes

where TT" represents the rate of heat loss to the suiro>jnding.«r , Rnd is

dependent on th*-- teniperature of the deten-iination. Thus at any tempera-

tuj-e level, if the heatir.<; is discontinued, ~ = 0. and —h may b«d© dO '

deterr^ined as

§'- KM=..,]t (36)

where the subscript o designates the no-her.t poriocS. Therefore,

K.cc.K.;] [S..||] (3,)de

wherein C*K» is detomint^d using in the apparatus; a material of known

specific heat, the rate or" heating is determined from acciu-fxte electrical

ir.easuranents during the heating period, and the rate of change of tem-

perature for the heating and coolin.^ peiiods is deterrdnec^ from the

slopes of accurately plotted temperature-time data.

D. Ex^-.erin^ental I^-or-edurfi

Samples of various solids contents were prenarf^d by dilution of

a concentrated liquor sa;-aple and v;ere e->ecked by drjdng at 105^ C. a

STTuall quantity which vas absorbed on asbestos in a porcelain crucible.

The procedure followed in makire a test consisted of the

72

following steps:

(1) A sample of knovm solids content was added to the tared

flask and accurfttslj weighed.

(2) The apparatus was assembled and the heating current was

turned on to bring the entire system up to the desired

tempers.ture T. The heating current was reduced and a

half hour was alloved for the system to attain equilibrium

at T.

(3) The terr.pere ture was allowed to drop to 3 to 4*^ below T

and the heating current was a<rain turried on. Tenperfcture

and cuirent measurements were taken at one-isinute interval f.

until the temperature had passed T by a degree or two.

('j-) The current was shut off and tempert-ture measurements

were again taken at one—'^inute intervals until the system

was a few degi'ees below T.

(5/ Steps'i

and h were repeated until con.'Ustent results were

obtained.

(6) The system was raised to the next higher temperature and

steps 2, 3« ^* snd 5 were repeated.

(7) After the test at the highest temperature had been finished

the entire system i.'as reweighed to detect any loss in

weight due to evaporation.

The heating and cooling curves for each run were plotted as tem-

perature versus time. A typical set of these curves is shovm in Figure

11 which is for a liquor containing 52o6^ solids at 150^ F.

73

/

//

//

J/

/\/

?.^ Oo

1

^, 1

^\^

1 ^N,

1 /

*^\

/1 /

r

//

//

*\\..

1

V^ V

u

-V^— ^

^ ^

<§

0)ato

u5

w pl

a> C^cv p

3 toc c•H ^

o Si: •^* oc oF

CO •H TlH H c

05

vn cH •H

•H

•^ 'aan^jBJsdwax

74

The slopes of the heatinc; and cooling curves were determined and

average values of the most consistent slopes were used in the calcula-

tions.

Ej« Data

Table k contains the tabulated average heating and cooling

curve slopes and the rate of heating for rmis made at solid content per-

centages of h,n^ 9.?, 13,h, 21.6, 32.2, k2,h and 52.6 and at ter.iceratxares

of 100, 125, 150, 175 and 200° F. The data used to plot the heating and

cooling curves were considered too voluminous to be included.

F, Sample Calc\)lations

A typical calculation for a 270.0 gram (O.596 lb.) sample

containing 52. 6::^ solids at 150*^ F. is shown as follows:

The rate of heating by the electric current was found from the

equation

4i- « 0.05692 3 I (38)

where E is the voltage, I is the amperage and the constant is the nunber

of BTU/min. equivalent to one watt. Thus, with 3.6^ volts and 1.53^

ampers the rate of heat \ras

^ = 0.05692 (3.64) (1.534) = O.3I8 .3TU/min.de

The rates of tempersiture change during haating and cooling at

150° F. were deterrdned from the slopes of the curves plotted in Figure

11. Thus,

75

-.9

'".2

la.v

21.6

32.?

t T^rar'eratur :• ^ :r;F:

.

V » / (Ib.s.)

ICC O.i.85

ICO n,US51.-5 C.Ufis

125 C.U3515C CA%130 C.'iBS

.500 C.kr^

100 < .^S5100 o.iic.5

125. O.^fHl'-5 0.'.'".5

150 O.ic.

130 0.'495

175 0.-95375 O.J^95

200 O.Un^• 2C0 O.ifS-5

100 0.319100 0.519135 0.519125 0.519.

100 c .508100 C.5O8125 C.5C9125 0.503150 0.503150 C.<08

175 C.5OS200 C.5C8200 :.508

100 C.'iOO

ICO 0.^30125 c.^30125 0.530150 C.530150 0.530175 C.5-5O

Heatinr 'e-^tisr ^olin?-

(:3TI/Jiin.)

0.3295C.3;:?9

C.3252

0.32500.3230C,?2''0

0.3135

0.3i;56

0.3'^ 56C.3^5:. ?U3

c.3iilP

0.3-'j56

0.3^560.3^132

0.3/11?

C.3309

0.32390,3270C.3250

0.3516C.35I6C.3403O.'i^CS

0.33930.33Q3C.3357C.3337

0,3357

0.-607C.3609

0.357^0.3579

0O537C.3537C.3523

C^F./Min.) (^F./Hin.)

0.5^5.

'•6'*.

0.^56C.35CC.3bl0.122

0.5r>i,-

0.591C.527c.530C.Clj0.:.21

C.32IC.316

0.1820.130

0.5710.5670.';35

C.'-67

0./-30.'>.6

0.530C.5';2

C.ii26

0.^'«2

0..?f6

C,12C

0.139

0.6690.662C.56C0.5640.i;70

0.459

0.352

0.053C.O530,1^--:

C.ii,3

C.230. >*') ?.

C.058

0.0570.1280,130cay0.2210,31.-:;

C.326

0.46^

C.C500,0600.1-^2

C.I35

:.05if

o.O';6

C.1U5

0.1420.234C.231

0.36IC.5130.5I8

0,0540.056C.1520.144C.2i42

0.2340.350

!(>

TASL'^ :—Continued

5c 1 id:"

Content Temoerature''.-ISf, ofSanrle Hfstinr

Rate of Ter'

Heatinr;

rer^ture Change

(.0

^2,^

',1.1

171-

2002CC

100100

123

l.':5

15c

15c

175175200

200

100100

12512515c

150

175175200200

(Lbs.)

.' .530

C.53O

:.552C.552C.552C.5520.S52c.552c.552c.552c.552c.552

C.596C.596

0.596C.596

0.596C.5960.596c.596c.596

0.596

(3ru/Mip.) C^F./Min.)

C.3523c.350t|

C.3504

0.3075o,30?3

0.36660,3652C.36580.3658C.'^639

C.3639C.363IC.3623

0.3329C.32660.319^C . 319'i

C.3I820.3170C.3I55C.71J0

0.3109C.^103

0.3500.199C,223

0.567C.5780.623C.6^2C.525

0.529C.^Oi*

0./il5

r.263

C.2S1

0.61^4

C.632C.5it2

0.539

C.ii52.

0.3^6C.339

0.2020.203

(^./Kin.)

C.357

C.ii6C

0.05'-

0.0570.1290.1250.2200.2160.3280.31a

C,0h6C.QhSC.I230.121C.2C3

0.2030.298C.2950.419

d0

77

= O.V+i4 °F./min.

fis = -0.203<= F./min.de

The calorimeter equivalent, C.&., was determined using pui'e

water in the system. This valtie was 0,0655 3TU/°F.

Therefore, by substitution into equation (37)

0,318 = (0.596 Cp + 0,0655) (O.WW; + O.203)

Cp = 0.717 3TU/(lb.) (°F.) at 150° F.

G« Calculated Results and Discussion

The calculated resxilts are tabulated in Table 5 for the range of

solids content from ^.9 to 52, 6y^ and for temperatures from 100 to 200® F.

The values of specific heat in the table are averages of two

determinations. The maximum weight loss due to evaporation was on the

order of 0,2^ of the original weight of the sample and did not affect the

results.

The data are shown graphically in Figure 12 v/hich is a plot of

specific heat versus the per cent solids with temperature as a parameter.

The specific heat was found to increase with increasing tenperature and

to cecre&vse with increasing solids content. This is entirely consistent

with the nature of all the organic and inorganic constituents of the

black liquor and shovild, in fact, continue in similar manner beyond the

range of temperature and concentration studied.

An empirical equation was sought to fit the data and relate the

78

©0-.

o 00 ^ vr\ r\ r\ben $ § CO E^ ^M * • t • • * •

«J c:.' O o o o o o^

u"^ it o-> CM r^ vn,

Oo so, ^ ^ g: r ?fM • • • • «

o o o o o o

<y> • H H l-l CO C^U^ •^ ^ «\i CO H IVr- . (7^ o 00 t^ IN ^^

tj\ H • V »o O • o o o O o«: HH .J

Q S JH E- •*»

g|to o

>r\ ^g o P^. C^*

COo o cv

•

4'.^-^

Cd(X. ft. c- cr • m GO

•^

^f5 ^U C-- o • o o o o o

bJOa, <: C r-»

H COtn

fc- 5-J-

•O 1

^?; u->OC'

o Fl K^00 oo H

o c^o S rj o- a OS OC re r- r -3 ^^

t-. iH • • • * « • • co o o o o o o o o o

(ti •

§^

O n s^ s ^ HcS

oo CO•> X

O c a- CO CO CO c^ f^ ^ >>or-» « • « • « * ^

C' o c> o o o c; o

1/! tt «Tj a Oj ^ vD CV} ^ t^ o S II

r-i « • • * * • •-;!fH J (?N 00 ri ir>( r\. (SJ o

<8l-i OJ f^ ^ \r\ oH > a,

•H (^

o%P n)

c 0)

c ffio<i

u •Ho «> «M

(X,

O

CMo Hr\

a>

^^^11 3Tfjfoads

80

specific hf?at, Cr , to noth tempers ture, T^ F. , and the solids content as

the weight fraction, C. This eouation was found to be

Cp = C.9^C 4- S.C X 10"% - (C.<39 - 6.i. X 10" 't) C . (39)

and is shovm a^ the solin li^ie • '..n Figur-? 12. In dealing ^;ith a series

of calculations wherein the tcnperature range is not too large or if for

si.T.plicity an av^rare value is desir?id at a particular temper'j ture level

the equation may be sL-nclified. For iniitance, at 200*^ F, equation 39

reduces to

%C.O^ F. = ^'^^^' ' (".511) C (kO)

wherein Cp is a function of solids content only.

The equation for Cp as a function of T "nd C has been used to

errtrapolate the data to the lOC,^ solids axis as shov/n in Figure 12 by

brokt^n lines. These values of Cp are tabulated in Table 5 as ab . 1 . '=^

.

function of ter.perature.

The method of calculation used in most of the kraft mills con-

sists of assvrniin.q; a str^ir^ht line relation between pure vater v.ith a

Cp = 1.0 and black ] iquor solids of an asruned Cp, , valu?. Thisb.l.T.

relation is

Cp = l.OC - (1 - Cp^^^-^^„^) C (iil)

and is used irrespective of t-^nper.^tv.re. As stated abovr-, Stevenson (3I)

gives two values for Cp, , , namely C.P.8 and C.5C. These values areo . i . s

.

in use in the mills as veil a? another value of C.3i.. Equ&tion 41 is

81

plotted in Fi^re 12 for the Cpj.^^-j^,^^ values of C.28 and C.'j'.. The line

for Cp^^i^.,^ of O.5G falls approximately on the 200° F, line of the

present data and was left off the jlot to maintain clarity.

The results of these experL^-ient-i indicate that at the tempera-

tures u.3ed in evaporators (I60 to 265° F.).only the value of Cp, , =

0,50, of the ones currently in use, gives nearly accurate results.

However, this yields values wnich are too low at the higher temperatures

which are necessary at the higher concentrations.

The eri-or involved in using one of the lover Cp, , values

will naturally increase even T.ore at the hicher concentrations.

The data of Kobe and Soren'^on sre plotted in ?igurs 12 using

their equation,

Cp = C.98 - 0.52c (42)

This sins;,le line represents the average of data obtained over the range

77 to 200 F. Their data indicated no correlation with tempera tui-e and

pave considerably lower value? than the 130° F. line which is the

approximate 'avera^^e of the present data.

On the ba-is of the present data the corr&lat.-on of Kobe ; nd

3orenson gives values much too iov- for the temperature conditions used

in evaporators.

If equation 3?. which relates Cp as of function of T and C, can

be assumed corr-ct over the ra.-e of temperature studied, it may b, used

with due reservation, to extrapolate the data beyond the ran^e obtainable

in the laboratory apparatus at atmospheric pressure.

82

The straight lines in Figure 12 indicate that the specific heat

i? linear with the solids content when temperature is fixed. It follows,

that these data can be represented on a line coordinate type nomograph.

Figure 13 is such a praph and may be U5;ed more conveniently than Figure

12.

83

1.02 -T-

1.00 - .

.98 - _

,96 - .

.9^ - -

.92 - -

.90 _ _

.88 - .

.86 - .

.m - .

.82 - .

.80 . _

.78 -

.76-

-

.72 -

.70 -

.68-

.66-

.64 -

Speci fie Heat

,0°

Temperature, °F.

^60

--50

--40

--30

--20

--10

loPer Cent Solids

Figure 13 Nomograph for Specific Heat

CHAPT2R IV

THiiH'IAL CONDUCT IV ITY IW^STIOATICIB kim R^,3ULTS

A» Backgro^jnd

>. thorout-h search of the literature revealed a complete lack

of therr.ial coriiiuctlvity inforrrLation or. sulphate black liquor. It is

necessary to know values of thermal conductivity at various temperatures

aad solid concentrations Ln order to interrel^ti--* the heat transfer data.

Sakiadis and Coat=s (2?) surveyed the literatijre and compiled

all the available thermal conductivity data on or|-anlc liquidT, inorganic

liquids and solutions of various liquids. They critically evaluated the

data and gavn ratinp-s of excellent, very g'X>d, fair, etc., based on the

methods used, the precision of measureiT,?nt and the general aj^reement

with other data. Although these data do not include black liquor it was

rossible to determine the freneral range of val-ues to be exi:>ected» Most

organic and nonmetallic inorganic liquids have ther-nal conductivities in

the range of C.C5 to '-"..IS 3TU/(Hr.)(Ft?)(°F/n.). Notable exceptions

ar6 antnonia and water which have values around -.3O to O.i+0 3TU/(Hr.)

(Ft;)( F./^t.). Jakob (13) states that in general aqueous solutions con-

duct heat less well than water and that their conductivity decreases

with increasing concentration. The data compiled by oakiadis and Coates

for aqvieous solutions indicates that this is usually true. Hov/ever,

84

85

aqueous solutions of sodium compounds freouently show the reverse

tendency. Thus, solutions of sodium hydroxide, sodium carbonate, and

sodiun sulphate shov; increasing conductivity with increasing concentra-

tion. Other soditim compounds showed either constant or only slightly

decreasing values of conductivity with increasing concentration. All

aqueous solutions of organic materials had conductivities which decrea.-^ed

rapidly with increasing concentration. The effect of temperature on tlie

conductivity of various cowpounda cannot be generalized. However, water

has a positive temperature coefficient up to approximately 260° F.

Stevenson (31) states tliat most of the alkali in the black

liquor is present as sodium caroonate or as organic sodium compounds

with chemical properties very similar to sodium carbonate. The greater

part of the organic matter removed from the wvX)d in cooking is combined

chemically with sodium hydroxide in the form of sodium salts of resinous

and other organic acids. In the sulphate process, appreciable amounts

of organic sulphur comjx>unds are present in association with sodium sul-

phide. The rest of the alkali is present as free sodium hydroxide and

sodium sulphide. There are also small amounts of sodium sulr.hate,

silica, and minute amounts of other impurities, such as lime, iron oxide,

alumina, potash and sodium chloride. The proiX)rtlon of total organic

matter varies but will generally be within the limits of 55 to 70 per

cent of the total solids in the black liquor. The black liquor used in

these experiments was analyzed and foiand to contain 7C.3/J organic matter

in the total solids present.

From the above considerations it was apparent that the themal

86

conductivity of black liquor '.-rould begin at low concentrations at the

conductivity of water. Further, since black liquor is largely organic,

but since the inor?:anic material i:3 composed largely of sodium compounds

it was supposed thst the conductivity would decrease moderately with

increasing concentration.

The literature was' studied in an effort to find the best avail-

able method of determininfr the Lhem.al conductivity. This study failed

to reveal any unanimity in the methods ns^d in the past. Sakiadis and

Coates (28) have reviewed all of the published methods and have investi-

gated the various factors in the c'e.dgn of therm^J conductivity apparatus.

Their survey disclosed that mo:-.t investif;'£tion.s reported in the litera-

ture were made—

. . . with apparatus involvint; heat transfer through thin films,of the order of a few hundredths of an inch, to eliminatedevelopment of convection cur-rents. However, this practice limitsthe accuracy of the deterr\ined coefficients.

A scirvey of investicrationr. i-elating to heat transfer mechanismindicated th&t the development of convection curr^-nts is dependenton the direction of heat flow, temperature drop across the filmas well as liquid film thickness.

Their experiments x^ere designed to determine the existance of

convection currents in horizontal thick liquid layer? when heated from

the top. Their results proved:

. . . that no convection currents develop in V.orisontal thick layers,of the ord?>r of one to two inches, heated dounward, . . . Convectioncurrents were found to develop during heat transfer in thick liquidlayers when heated from below by horizontal surfaces, and byvertical surfaces.

An apparatus w^s desic-ned incorporating the alxjve conclusions

and the best features found in other apparatus reported in the literature.

(2, 2, ^, 12, 2<?) It was decided to use downward heating through a

87

moderately thick horizontal iiruid layer. A layer thickness of one

eighth of an inch vas considered to be well vithin the safe limihs for

pure conduction and \^as also thick enough for exierimental accuracy.

Thennal conductivity is expressed a- a qusnlity of heat floving

through a unit thickness of material per >jnit time per unit area and per

Uiiit tc.Trerature gradient. Tho quantity of heat flowing is the only

factor that causes any real lifficulty in rnr-asurf-.Tient. To avoid the

actual meisure-nent of ih^ he^.t flotin:- it vas decided to use the tempera-

ture drop caused by a quantity of heat fioving through a material of

known th-rinal conductivity as ..n indication of the rate of heat flov.

3y arranging the heat flov^ in series tlrou^ih both the material of known

conductivity and the test materi-d the s^me Quantity of heat would flow

through both.

The ratio of the thennal conductivities could then be ex-pressed

as functions of the temper-iturs drops acrors the two I'^yers.

Very reliable data are available on the thermal conductivity of

water at t^mperatur-s from 1;:0 to 200" F. This material w^ns chosen as

the standard and all therm.-^l conduct Iviti-:. v.erc determined with refer-

ence to it.

3, Apparati^.q

Th.? assembled thern-.al conductivity apparatus is sho:^ in Fjgure

1'^. The large box in the center of thei icture contains the thermal

conductivity apparatus which is shov,-n in Figure If. A dia?rainatic view

Of the assembled apparatus is shovn. in Firura 16. The apparatus shown

in these illustrations consists, of an infra-red la.T,p which served as the

•H

I

Figure 15 Themal Conductivity Apparatus out of Insulated Container

90

f> n* TJr-l « ^3 m 3« CO crc »- -HM OP ^

^ m+> o

» 0) oJcamea>

J3 XH to

.g m

"O B0) moi 0)

JQa nh <«M

91

heat source, the insulated box which contained the main thermal con-

ductivity apparatus, an internally cooled plate on vhich the apj:.arc'tus

rested, a constant teTm-erattjrft ^J.-i^p^ or oil batl-, a circulating piunp,

thermocour-'les and a poti^ntiometer.

The radiation from the infr^-red bulb var. absorbed by a brass

disk six inches in ciarneter and -4 of an inch thick which vas attached

to the lid of the inj-xlated boy. It vas coated vith black crackle paint

and thus had a high absorptivity and was of such thickness that a uniform

temperature on its under yide could be assumed. The under side of this

disk reradiatec to the toi. disk of the thermal conductivity apparatus

which was approximately three inches away. Both of these s'jrface.'; were

also coated with black crackle raint . Thus a uTiiform tempei'aturft of the

top disk of the main apparatus was vertually assured. The irain apparatus

was embedded in foara glass insulation with the exception of the t^p disk

whirh had to "see" the under ride of the heat source di.sk. The main

apparatus which is shown in Fip;ures 16 and 1? was constructed of brass

which was heavily coated v.ith nickel to prevent corrosion. The appa-

ratus consisted of three brass disks, the lower two of which were

actually bottoms of shallw^ cupy. The sizes, which are show in Firnire

17, were adjusted so that the three tieces would nest vith one eirhth of

an inch clearance all around. The sides of the cu]>s vere made of very

thin brass and served to retain the liquids in the spaces betvreen the

disks. The sides were made higher than necessary, for retention of the

liquid in order to provide insulating air spaces which would retard

possible heat loss from the sides. Small pieces of plastic were used as

92

93

spacers to adjust lh» vertical distance between the surfaces to one

eighth of an inch, ''oles were drilled fror. one side into the centers of

each disk and snail brass tubes were inserted just large enough to

receive the "O-^aupe copper-constantan therniocour-los which vere used.

The thjree assembled disks rested on top of a core'' briss plate through

which a fluid of regulated temperature was circulated. Good met:d-to-

metal contact was insured by very accurate grinding and lapping of the

two surfaces. The pattern of flovr of linuid throunli the cooling plate

was so as to insure a imiform temperature at ever;^' point on the surface.

This was accomplished by havinf the fluid circulate toward 'he center

and out apain in concentric spirals.

The coolinc fluid wa^; circulated with a sm^ill laborstory pump.

A constant temperature bath was u<^ed to maintain a supply of cooling

fluid. The fluid used was either water or oil depending on the tempera-

ture to be maintP.ined. •

C. Df-rivation of Sgu^tions

The relationships used to calculate the thermal conductivity of

an "unknown" liquid v.ere derived from a knowledge of the thermal con-

ductivity of water which was used a? standard, the dimensions of the

apparatus and the thermal conductivity of the brass.

Denoting the areas per]: encficular to the heat flow at tne oottcan

of the top disk as A^. at the top of the middle disk as A„. at the "bottom

of the middle disk as A^, and at ths top of the bottom disk as A. and

letting Xg, X^ and X^ be the respective disk tydcknesses and X and X,

the upper and lover liquid layer thicknesses; an ex^^ression can be

9^

wri tten for the heat flow across each liquid. Thus,

\2=

"12 \2 ^\2 (-1^3)

and q34=

'3U ^U ^V (M)

where q. and a.,^ are the rates of heat flov. "12^^ ^'^ are the over-

all coefficients of heat tran; fer, h2 and A^^ are the mean heat flow

areas and At^^ ^"t^ ^S^ ^® "^^® temperature drops across the liquid

layers plus hilf the thicknesses of the two adjacent brass disks. Those

equations may be rearranged and written in terns of the in-Ji-ziJu..l heat

conduction coefficients based on the mean ar^.as.

^1 o U12 ^12 ^2 •^a h ^M \2 \ ^'^

+; f~ +_—J2 (^5)

At„,1 (0.5) X^ Xi (C.5) X—-— -- -'''- + •: + —., .... .—

X

-^ 34 3^ b 3 ^ :i^ c ";

Using the dimensions given in Figure 1? the follov-i.v-r values

were determined

:

\ '^ h ^ ^'^^5 in. = O.OlUl ft,

\~

''b"

''c~ '^•3125 in. = C.C2605 f.,

A^ = 19.63 s^;. in, = 0.136it sq. ft.

Ag = 21,60 so. in. = C.I5OO sq. ft.

A^ = 22.08 so. in. - 0,153^1 sq. ft.

A^ = 2.1 ,20 sq, in, = 0,1681 so. ft,

i „ 0.1'(6i, + O.lcAO

\2=

'—J*"" ^ °*^^^'' ^''' ^^'

A^. - 0.15?^ + r .i6fiT „ T,-Q/*3il ^ , = 0.1603 sq. ft.

95

The exact conposition of the brass was unknov.-n but a reasonable

value for its thermal conductivity (23) was assumed. Thus,

^a = ^b =^c = 65 BTU/(HrJ(Sc. Ft.)(*'F./Ft.

)

It was assumed that all the heat passing through the upper

liquid would pass through the lower liquid. This was reasonable due to

the insulating effect of the concentric nickel plated sides of the cups

and the surrounding foam glass insulation. The fluid used in the cooling

plate was also circulated through tubes located in the insulated space

so as to maintain an insulation temperature near the desired temperature

of operation which at tines was 100° F. above ajTibient . Based on the

foregoing discussion, q,2 was assumed equal to a^. Dividing equation

^5 by equation ^6 and inserting all known constants there results,

(C.5) (c. 02605) r.om 0.5 (0. 02603)^\2 ^ (65) (c.i:'64) "^ k^ (C.1M3)

"^

(65) (C.15C0)

^^34 (C,5) (C.02605) ^ c.oiUi^

(c.5) (c.02603r(65) (C.]53^) k3^Tc.l608) (65) (0.1681)

0.098^^^12 _ 0.001U68 + k^ + 0.001334

'^*^-- C. 001306 + 0.0878 + 0,0011923^^1

At 0.0984^12 0.002802 +—iT—

" 34 0.002^498 + 0.0878

This equation can be further simplified by consideration of the

relative sizes of the two terms of the numerator and denominator.

Assuming a value for the liquid thermal conductivities of C.30 the

96

eqxiation becomes,

^^1? _ 0.002f}02 + 0.323

At^i^^ 0.ro2i^93 + r,.293 " *

By neglecting the smaller terms in the numerator and denominator

the ratio becomes

^^12 _ C028At3^ " 0.^92 " '*''''

Therefore the terms in eouation i*7 representing the cr;-,dv)Ction

through the brass may be nerylected and the simplified equation beco»nes

^!H = l!l^8^L^l = 1.122^2. (48)

^V (0.0873T\ \

D» Syt'rimental frocediire

Sauries of "olack liquor of various solid contents were prepared

as before hy dilution of a concentrated sample . Before each run the

nickel plated sxirfaces of the three i>arts of the main apparatus were

polished in order to maintain similar fiL-n properties and emlssivities.

A measured quantity of one of the liquids to be used in the

apparatus was added to the lover cup. The amount was just sufficient to

cover the three small plastic iriacers. The middle cup was carefully

placed in position in such a v;iy that no air coiild be trapped underneath.

A similar procedure was follov;.>d in adding the other liquid and the top

disk. The level of the liquid in the annular spaces was checked and any

excess was withdrawn if necess iry to prevent the level becoming deeper

97

than between the plates. For high tender^tvrs runs more liquid was

r'-;moved '"ror. the annular srace so that \fter h.»atin3 the expanded liquid

Wv-^uld have: a depth of approrrimntply one elf nth of an inch. The top of

the mnulir spaces was partially sealed by nreosing alutninutn foil over

the openings. Th.is precaution was t:'ken to prevent evaporation of any

of the liquid siimple-. If evaporation did occur it would soon result in

hir bubbles betv;een the plates v/ith .i corresponding- decrease in the con-

ductivity across the licuid. Such an occurence would be rapidly detected

in the temperature measurements.

In sone of the earlier runs it v.'^:; noticed th£it even when little

or no evaporiition occ-orred air bubbles were formed in trie water layer if

the water had not been properly deairated. (^oneequently, the water was

always boiled just prior to u.^ing it in the apparat.is. JAr bubbles were

never found in the black liquor layer.

The thermal conductivity assembly was placed in the insulated

box on top of the con'=;tant temperature platen. The insulation was

arranged, the tVu-ee thennocouples were installed, the top was placed on

the box and the infra-red heat lamp was positioned vertically aVx)ve the

black brass disk in the box lid and was turned on. A cylinder of an-

bestos paper enclosed the i^th of radiation and prevented convection

currents across the face of the disk. The constant temperature bath was

regulated to a ternperature lust bolow the temreroture to be maintained in

the test liquid and the circulating puiT-p was started. The values of

e.m.f. produced by the thermocounles at the centers of the three brass

disks were measured over a period of time until equilibrium was established.

98

The time for equilibrium varied from a half : our to tvo hours

depending on the tempera tiire of opera-tion. Once constant readings were

obtained over ? period of 5t least an hour the run was comv-leted.

The relationship between temperature and e.T. r. for the thermo-

couples was approximately linear over a short tempera L'-ire range.

Therefore, the ratio of e.r.f. differences wis used in equrition k8

instead of temperature differences. This procedure eliminated the intro-

duction of errors due to conversion of e.n-..r. values to temperatures.

CalibratiDn of the apparatus was a.ccompli>3hed using water as the

upper and lovjer liquid and with ethylene glycol and glycerol in con-

junction with water. Values of thermal conductivity predictec using

equation k3 showed maximum variations on the order of - 2,0,?^. No

difference wa=5 found in values by interchanging' the upper and la»rer

liquids. Thus, for consistency, water was used as the upper liquid and

black liquor was the lovjer liquid.

E. .. Data

The experiniental thenaal conductivity data are shown in Table 6.

In columns two and three are tabulated the average temperatures of the

black liquor and water layers, respectively. Column four shows the

average of the ratios of the e,y.r. differences ror the water layer over

the black liquor layer. The averages in these columns are for all

measurements; taken durinn the period of equilibrium which may have been

an hoMT or more. Column five has tabulated the values of the thermal

coriductivity of water at the average temperatures of column three.

These values were taken from a graph in the Appendix which represents

99

T.^SLS 6

EXPERU-ffiNTAl, /J.'D CALCLXATSD TFEff'.fil, CONDUCTTV'ITy DAT.

Avei-sge Temperature Avert re liilio of ry .ermalSclirtc of Lic,uid Layer 6,%,f, Differences

Watnr/Bl^ck LiruorConuuctivitv

Content 31ack Lifucr Vtater Water Black Liquor

(°rj ('^-) (BTU/Hr , 3r.Ft.*^F/Ft.)

12.68 101.3 lOi^.l l.OiiO 0.3636 0.337126.0 128.1 1.064 0.3730 0.35^1?P..6 13^.^ 1.052 C.375O C.j5215<^.9 156.3 1.074 0.3v820 0.36515".'+ 156.- 1.074 0.3320 ':.365

151.6 I'^'^.'i 1.123 0.3315 C.382165.

7

16^.1 1.047 C.3352 C.359175.6 17^/.'' 1.06? 0.3330 G.367

'3.55 101.6 i::>h,h 0.^69 0.3638 0.31410i>.2 IOC .

- C.037 C.366O 0.3221?5.6 12^,.-) c.^98 0.3730 C.33212^^.7 127.7 l.OOB 0.3730 0.335153.2 IS- '.3 1.013 0.3825 C.14615^.3 156.3 I.OU C.3A20 0,34417'-. 3 176. i^ 1.019 0.3870 0.351

3?. 60 1^1.8 155.8 0.Q68 O.38I5 0.329176.7 1^0.5 0.969 0,3880 0.33519'^,^ 202.0 1.003 . 3930 0.353

:3.75 101.7 10i*.3 0.924 0.3640 0.30012^.6 127.7 0.952 C.37'^0 O.3I6153.3 15^.3 0,922 o,^?:z^ 0.^1515:^.3 15?.^ 0,^31 0.3823 0.313

h2,oO IC1.6 lOii.6 0.890 0.-'639 C.28912C-.0 12*^.4 0.^02 C.^730 0.300153.3 IS?.^ 0.887 C .

'>325 0.102151-7 155.^ 0.919 0.3815 C.3I2176.5 17^.9 0.^31 C.388O 0.322

•^-^ . :?0 lO-'.O lO-i.l C.S29 0.3644 0.269105.2 111.7 0.825 C.-^672 0.270126.5 12^.4 C.811 0.3735 0.270126.4 12<^.3 . 827 0.3735 0.276126.6 12^.7 C.328 0.3735 o.^7612fi..U 13"^. 6 0.^55 0.1750 C.286l^-'.h 15P.''+ 0.S21 0.3825 0.280151.3 1*1=;.

4

0.866 O.38I5 0.295176.

U

I8C.3 0.385 0.3880 0.30619B.3 200.1 0.907 0.3925 0.317

100

the mean value.3 of all of the food quality data on water reproduced by

oakiadis and Coats (2?).

F. Sample Ca lculations

The run using black liquor with U<; .QO)l solids at 126.0° F. will

be used to illustrate the method of calculption. !Lcuiliorium concitiona

were maintained over a period of approximately two hour?. Over this

period minor fluctiuitions occurred in the e.m.f, readings v-hich were

taken at ?0 to 30 minute interval?. The e.r.f. differences across the

liquid layers vere evaluated and the average ratio of these differences

for water over black liquor was found to be C.902. Individual values of

the ratio varied by a maximum of t 2.5^. The thermal conductivity of

water (k^) at the averSf^e temperature of the water layer was found to be

0.3-^30 BTU/(Hr.) (3a. Ft.)(°F./Ft. )

,

The thermal conductivity of the black liquor (k, ) was evaluated

using equation ^^8 when the ratio of e.-n.f. differences was assumed equal

to the ratio of temperature differences.

(0 "^730) (C '/OZ)

^l = *'' /322' "" ^'^^^ BTU/(Hr.)(Sq. Ft.)(^./Ft.)

G. Calculated Results and Discussion

The calculated values of thermal conductivity oi" clack liquors

containing from 12.68 to 53.20.^ solids at temperatures from 100 to 200° F.

are tabulated in the last column of Table 6. These data are represented

graphically on Fi^urp If, which is a plpt of thermal conductivity versus

per cent solids v.-ith temperature as a parameter. It is noted that the

temperatures of the sanples varied slightly froni the dei-ired tenperatures.

101

O.i+0

eg*

i?

0.35

g 0.30

0.25

ko 5020 30

Per Cent Solids

Figure 18 Thermal Conductivity versus Per Cent Solids

60

102

of Tnea-jrement {ICO, ]2 =, I5O, I75 and 2C0° F.). A cross flol of

theirmal con(5uct.ivity versus temnercitiire was prepared ^nd vslues of the

thermal condiictivity at the dfisirnd temreraturrty weie re-d frcm the

smoothed curve.s. These values wfr<3 uaed to locate the line*-, in Figure

18* The slopes of theae lines were found to varj- linearly with tenpert-

ture according to the foliowinp; relation.

Slope = 0.2096 - 0.000:338 t (®F.) (k9)

Interpolfition of the 3 ires of Firure IS was accomplished using knowr*

values of thennal conductivity of water at intermediate temperatures and

the relation of eouation ^9, The interpolated grapih is shown in Figure

i"^-. For convenience these data are presented in the form of a line

coordinate chart in Figure 20.

There were no published data with which to compare the results

of the?-- exp^^rinenti'. However, the values were considered consistent

with v;hat night be er-Tcected from aqueous solutions of the materials in

the black liquor.

103

20 30

Per Cent Solids

40 50 60

Figure 19 Thermal Conductivity versus Per Cent Solids

104

0.i42 -r

0.40 --

0.38

0.36 --

0.34

0.32 --

0.30 --

0.28 --

0.26 --

0.24 -L

Temperature, F,

t60

-50

--40

-30

--20

--10

Per Cent Solids

Thermal Conductivity

BTU/(Hr.)(ft?)(^/ft.)

Figure 20 Nomograph for Thermal Conductivity

chaptf:r V

VISCOSITY

A. 3ack;;r9una

The literature contains only two references on th« visco&ity of

sulphate black liquor. Kobe and McConaack (16) reported valuer for soda,

sulphite and sulphate liquor obtained from pulj-ing westei-n hemlock,

Fedluiid (11) reported vali:es of viscosity for black liquor frctn two

diiferent raills-»one a typical kraft black liquor and the other low in

organic matter.

Kobe and KcCormack reasoned that since the viscosity for all

types of waste liquors was due largely to the dissolved si^g&rs and col-

loidal lignin molecules some general relation might erlst for all thru^e.

This vas substantiated by their results vhich sho^v-ed that the three

licuovr, could be represented on the same corr«lntion v;ith an accuracy of

5^. They reported that the liquor.'., even in low concenti-ations, pos-

sessed a certain amount of gel-like properties below 63° F. They used

the Cstwald viscometei- for their determinations ovei- the temper? t\u-e

range of 32 to 200<^ F,, but did not indicate whether tubes of different

capillary sizes were used. Thus it was not possible to determine

whether their results showed any differences in viscosity with different

rates of shear. Such differences could be displayed by gel-like materials.

105

106

I-t was nssvmec- , th^r^forp, thst the liquors which they exarsin»^d at

tempera t'a*ep above 63 F. were Neiwtcnian since they did not i-eport any-

thing to indicate other..'ise.

Hedlund reported that especially at lovr tempera tureo there was

a difference in viscosity at the sane concentration betv'een the lienors

of different org&nic content. However, ht» did not indicate any differ-

enfe>' of viscosity with rates of shear. The Hoppler type viscometer was

eir.j-loyed in these experiments over the teTnpei-o.tur'f» ranje of 65 to YjO F,

KoV>fc and McConnc,ck used an Cthmer (Zl) plot to correlate their

data. In this net> od tie logarithm of viscosity was plotted against the

logarithjn of t)ie vise )sHy of vi^ter at th" same tenperature. Straight

liner, were produced in t.hia way for each concontiction, Friwj this

diagrajr. and an A. --.T.M, Standard viscosity-temperature plot they inter-

polsted their data and plotted it at; the logarithm of viscosity ve^Tus

temperatiire. This method of plotting resulted in lines whicn had slight

curvature at the lower tenperat'.;re;;. Thus the temperature axis was

modified so that the lines were .straight ovei their cntirf- Id-npth, When

the data of Hadlunci were plotted on the diagram pr^par- ' '•'/ Kobe and

McCormack straight lines showing fair agreerient were found at concen-

trstions below 50^' At higher concentrations the linos reprei-entinf- the

data gradually became curved. Considering the differences in wood and

the probable differences in the cooking process it was renarkable that

even suc'i close agreement should be found.

3« Apparatus and rpocecUure

The values of viscosity were deterrr.ined at various temper?. txares

107

using Cannon-?enske-Ostwald type vlsccsneter tubes in conjunction with a

constant temperature bath controlled to - C.l*^ F. The tubes were pre-

calibrated at 100*^ F. and 210^ F. V-ilues of the calibration constant

for intermediate tempers turec were determined by interpolation. Vis-

cosity tubes of the ICO, 200 and 3^0 series were used in order to cover

the entire ranc^e of viscosity without excessively long efflux times.

Standard procedures were follo^^ed and the average of several consistent

readinc-s was determined. The average efflux tine was multiplied by the

appropriate constant to obtain the kineniatic viscosity In centistokes.

The kinematic viscosity was then converted to absolute viicosity in"

centipoises by multiplying: ^y the density or sp-ocific gravity.

The calculations are illustrated using the data for a mn using

1?.6S% black liquor at 100° P. An efflux time of 83.2 seconds was found

as an average of 10 runs on 2 samples. The calibrs^tion constant for the

100 series tube was 0.01^06 cent 1 5 toV.es per second, Thu5,

Kinematic visco:..ity = (33.2) (0.01406)

= l,l69 centistokes

The specific gravity found from Table 8 or Figtire 23 was 1.060.

Therefore,

Absolute viscosity = (1,169) (1.060)

= 1.24 centiix)ise

C. Calculated Rejults and Discussion

The exTJerimental data and calculated results of viscosity' of

108

black liquor are tabulated in Table 7. Usually the viscometer tube was

used which gave from 100 to ?.0Q seconds efflux time. However, in two

instances two different size capillaries were used vrf-th thp same con-

centr£tion of black liquor. Thus values of viscosity wpr= obtained for

a sample containing 33.7,c solids at two different rates of shear. Close

agreement was observed for these values. F\irther. no discontinuities

were found for any of the samples on which more than one size viscraneter

tube was used. For ir.stance, if the data for the 53,2!h sample had

indicated a different straight line for the points determined using the

200 series tube than for the 3OO series tube the obvious conclusion

would be that the viccosity varied Tvith the rate of shear. Such was not

the case and the conclusion was drawn that over the range of variables

studied the black liquor behaved as a Ne^rtonian fluid. Thus apparent

agreement on this point exists between these data and the data of pre-

vious investigators.

The data of Table 7 were plotted on a modified Othmer(£l)

diagram similar to that used by Kobe and McCormack. The viscosity was

plotted vertically on a standard logarithmic scale. The temperatui-e

was plotted horizontally on an arbitrary scale so that a straight line

resulted when the data for water were plotted.

A cross plot of the loparitl^jti of viscosity versus solids content

was prepared and lines of slight curvature resiilted. From this graph

values of viscosity at even increments of solids content were determined

and plotted on the modified Othjner diagram (See Figure- 21). Straight

lines resulted for all concentrations over the temperature range

109

TABLE 7

5XP5RIMETTTAL IND CAT cri. 4t-^:d V. 3(^0.SITY DATA

Sol'.r • Vi .^cor-.et'T Absolv>9-r,::1...,v,t Sc rl-?s Mo. Viscosity

(') (Centincises)

12.68 100 100 1.2ii0

1?.5 100 C.953

150 100 0.763

175 100 0.639200 100 C.5^3

23.55 100 100 2.I185

1?5 100 1.819150 100 I.U09

175 100 1.121200

.100 0.9 23

33.75 100 100 (.27100 200 t.l9125 100 ^.22

135 200 h.ZZ150 100 3.06175 100 2.31

32.6 200 100 1.68

i^2.9 100 200 21.89125 200 1^.00

150 200 S,k6

175 200 5.37200 100 h.2k.

5?.

2

100 300 245.20125 300 97.90150 300 i*6.80

175 200 26.00200 200 15.92

no

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55

50

^5

100 125 150 175Figure 21 Viscosity versus Temperatvire

35

^5

2C

15

10

200°F.

Ill

investigated. These data were replotted on a line coordinate nOTiograph

as shown in Figure 22.

The data of Kobe and McCormack were checked against these data

by plotting on Fi^re 21. The overall aa:reement was found to be on the

order of - l.O'^. General agreement of their data with those of Hedlund

has already been pointed out. Mo analytical data were available for

comparing their black liquor to the one used in these exi>eriments which

contained 70.8^ organic material in the solids. However, considerable

evidence exists upon which to draw the conclusion that sulphate (kraft)

black liquors exhibit similar viscosities irrespective of the nature of

the wood used and the normal variances in mill operation.

112

100.0 --

5C.0 --

10.0

—

5.0-

1.0--

0.5--

Per Cent Solids

Viscosity, Centipoises

Figure 22 Nomograph for Viscosity

220

-210

200

190

190

170

160

150

140

130

--I20

--U0

--100

Temperature, F.

CHAPTER VI

SPECIFIC GRAVITY

A. Apparatus and Procedxire

The specific gravity of black liqvor was determined over the

complete range of pei- cent solids and temperature used in these experi-

ments. The procedure used was to measure the veight of black liquor

contained in a IOC ml. volumetric flas!-; and divide this by the veight

of water cont-tined in the same flask at the same temperhture. The flask

was first filled with black li nior up to the line and immersed in a

constant temperature bcith controlled to i 0.1° F. .\fter the flask and

content.*? had assumed the ter.perature of th*? bath the level in the flask

was adjusted. The flask was dried and wei?h<>d aft^r arrain immersing in

the bath to recheck the level of the liquid and the temperature. The

flask was then filled with distilled v:ater and a similar procedvire was

followed. The weieht of the contents in the two cases was determined by

subtracting the weight of the flask. The specific gravity was then

detemined by dividing the weight of black liquor by the weight of water

contained by the flask.

3« Data and Calculated Results

The specific gravity measurements are tabulated in- Table 8 for

the solids content range of C to 53,20^ *nd at temperatures from 100 to

113

11^^

TABL?; 8

SFRCIFIC 'l^ATV^ D.i^A

.;>oii.ds .-'cificContent Temperatur-? Gravity

{D (^.)C 100 C.Q93

125 C.987150 0.930175 0.972200 0.963

1?.68 100 1.0601?.63 125 1.0331?.68 15C 1.01^7li:.58 175 1.03812.68 200 1.030

2?.. 53 100 ia?32?, 55 125 1.11623.55 150 1.10923.55 175 l.iOO23.55 200 1.092

3^75 100 1.184^3.75 125 1.17733. "^5 150 i.i6a3:^.75 175 1.15932.60 200 l.ii*5

U2.O0 100 1.2iil

h2,9C 125 1.233k2,9Q 150 1.225^2,90 175 1.217^^2.90 200 1.208

53.20 100 1.30453 . 20 125 1.29753.20 150 1.2855^.20 175 1.27753-20 200 1.268

115

200 F. These data are plotted in Figure 23 as specific gravity versus

per cent solids with temperature as a parameter.

A cross plot of specific gravity versus temperature was prepared

(not included) and a linear relationship was found.

116

1.30

1.20

V. 1.10

1.00

10 20 30 kO 50

Per Cent Solids

Figure ?3 Specific Gravity versus Per Cent Solids

60

CHAPTER 711

INTERRELATION OF THERMAL AND PHYSICAL PROPERTIESAND THE HEAT TRANSFER COEFFICIENTS

The diniensionless ntunbers calculated in Chapter II and tabulated

in Table 3 were employed to detennine the j factors as given by equations

4 and 6 for all runs. The calculated j factors are tabulated in Table

9 for runs with Reynolds numbers f^reater than 3000 and in Table 10 for

runs below 3OOO. These values are plotted in Figure ZU as log j versus

log Re., ,

From equation ^ it is evident that by this method of plotting

the predicted J factors in the turbulent region should be linear with a

slope of minus 0.2. Inspection of the data in this region of Figure 2U

shows it to be in substantial agreement with the Sieder and Tate line

(equation 4) which is also plotted. It is to be noted, however, that the

data show some divergence at the high values of Reynolds number and that

this divergence increases with the solids content of the black liquor up

to a maximum of 33^ in a few cases. Also, close examination of the data

for any one concentration shows that it falls on a line vrith a smaller

angle of inclination than the Sieder and Tate line. In effect, the

results indicate higher rates of heat transfer than are predicted by

equation h at the high Reynolds numbers.

From a practical point of view these results are considered

117

118

TABLE 9

HEAT TRAJTSFER j FACTORS—REYNOLDS NU>raERS A307E 3000

Run Rejiiolds j' Factor, Eq. 4 Run Reynolds J 'Factor,No, Number

(lo3)

No. Number Eq. 4

(103)

1 IO96O 3.75 68 4230 3.^92 II36O 3.90 69 3380 2.23

3 15860 3.5s 73 3880 3.19k I586O 3.62 74 3I8O 2.79

5 24270 3.52 77 4290 3.786 24270 3.33 78 6290 4.40

7 31720 3.29 79 8370 4.288 3278O 3.31 80 8530 4.46

9 41940 3.15 31 7100 4.1110 42560 3.17 82 7470 4.2111 20000 3.^9 85 4690 3.9012 20330 3.^3 36 5700 4.11Ik 56430 3.04 87 7260 4.2115 59670 3.12 88 9130 4.1916 59050 2.32 89 11180 4.2517 3356O ?.09 90 13640 4.2418 43560 3.01 91 16810 4.2619 78O5O 3.05 92 19550 4.0320 3068 5.00 93 23910 4.2421 7080 3.37 94 24320 4.1822 13260

. 3.55 95 12400 4.3427 7490 5.18 96 15150 4.2228 8040 5.1^ 97 I825O 4.2747 3500 2.79 99 5290 4.7148 3600 3.23 100 8300 4.11^9 5020 4.64 101 11590 4.3451 33^ 3.05 102 16200 4.2352 4830 3.79 103 21990 3.9953 53^0 4,16 104. 11240 4.1854 5804 4.20 105 11790 4.2355 7360 3.'30 106 8130 4.2759 .3300 2.61 107 8220 4.3960 4140 3.53 109 5/J40 ^.6061 4170 3.53 no 5500 4.4262 5120 3.91 111 13260 4.0563 6000 4.02 112 13260 4.1064 7610 4.22 113 14/^90 4.1c65 9980 4.42 114 16260 4.1366 10400 4,11 115 16320 4.1467 4590 3.70 116 20150 4.32

119

TABLE 9—Contijnued

Run Reynolds J 'Farter. Run Reynolds j' Factor,No. Number Ec. 4

(IC')

No. Number Ec. 4

(lo3)

117 20720 4.46 152 55100 3.69118 2231c 4.10 153 55100 3.76119 26390 4.?1 154 3870 4.22120 27840 4.50 155 10410 4.21121 32570 4.26 156 I69OC 4.18122 32670 4.70 157 I796O 4.1012ii 3545 3.76 158 18940 4.06125 9093 4.19 159 24170 3.91126 l>,o6o 4.11 160 27890 3.93127 14540 3.92 161 33340 3.77128 17720 4.20 162 41770 3.87129 21490 4.08 163 49350 3.91130 25240 3.89 201 3350 3.57131 39990 4.^5 202 3650 4.23132 4220 3.95 214 3580 3.96133 3550 4.21 215 4700 4.5013^ 6350 4.22 216 5180 5.40135 6250 4.19 217 5840 4.43136 10020 4.12 218 6770 4.43137 10020 4.12 219 7850 4.55138 14520 4.03 220 •9650 4.45139 14230 3.39 224 29000 3.411^+0 18210 3.98 225 29300 3.37141 I836O 3.79 226 11300 3.831U2 2O86O 3.86 227 17620 3.631^3 2O86O 3.76 228 24550 3.^^!

IkU 25I8O 3.76 229 29100 3.30145 25250 3.35 230 32100 3.24146 3O86O 3.76 231 37700 3.25147 3O66C 3. 80 232 42800 3.24148 35500 3.77 233 52300 3.02149 35670 3.62 234 58900 3.02150 42780 3.36 235 67900 3.03151 43150 3.86 236 75500 2.98

120

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3B.S%

Water before Black Liquor RunsWater after Black Liquor Runs9.2^ Original Black LiquorIB. 8^ " " "

25.156 " "

33.C

38.5:^ " " "

^9'3lt> New Black Liquor41.9^ II M n

33.

(

Equation k

J I I I I I I I I

600 aoo 1000I I I I I I I ll J \

I I I I I I I I I I ill2000 4000 (,000 aooo 10000

,RejTiolds Number

Figure Zk j Factor versus Reynolds Number

(roooo 00000 looooe

12k

satisfactory since general agreement with the theoiy is demonstrated

plus the fact that, for design purfioses, equation i^ would yield "safe"

values. Frcwi an academic point of view some discussion of the diver-

gencies should be offered.

Examination of the data in Table 3 shows that the quantity of

heat transferred to the fluid, q, increased directly with Reynolds

number. Likewise, the deviations of the calculated J factors increased

directly with the Rejmolris number. It is recalled that the pipe surface

temperature was calcxxlated from a knowledge of q, and thus the magnitude

of any error in this calculation would increase with Reynolds number.

In the "Analysis of Results" section of Chapter II the error in the pipe

surface temperature was evaluated at - IO5S based on an assumed possible

error in the thermocouple location of - 5»^'^- An error in the pipe

sxirface temperature would also cause an error in the viscosity ratio

term in the same direction. However, this error would be very amall

since it would be raised to the C.lit power in equation ^, Thus, these

factors would not account for all of the deviation found at high fieynolds

niunbers, nor do they seen probable since the data for water are in good

agreement with the Sieder and Tate line.

The only other possible experimental cause of variation in the

tvirbulent region j factors would be errors in the thermal and phj'sical

properties or the temperature at which they were evaluated. Over the

entii^ range of these experiments the specific heat and thermal conducti-

vity varied no more than about 30^, whereas the viscosity varied 100

fold. However-, in the turbulent region alone, the viscosity variation

was only about 3 fold and about the same variation was found in the

125

Prandtl nvunber. On the other hand, for a single rur the maximum vari-

ation of the viscosity and Frandtl number from inlet to outlet was about

15:*. The inlet to outlet variation of the specific heat was no greater

than Z%. Thus the J factor deviations cannot be rationalized on the

basis of using an incorrect temperature for the evaluation of properties

in equation U, Errors in the properties themselves of such magnitude as

would be necessary to accoxint for the j factor deviation seem highly

improbable

.

3y elimination it would seem that the only possible expjlanation

unaccounted for lies in the fact that equation k does not apply equally

well to all materials. However, from the engineering view point, it is

desirable to have only one equation which represents a mean value for a

variety of materials. The Sieder and Tate line (eqtiation U) is therefore

accepted as representing the data for black liquor sufficiently well in

the turbulent region.

Referring again to Figure 2^ it is seen that the experimental

points plotted in the viscous region are considerably scattered. The

solid line drawn in this region represents the Sieder and Tate equation

6 for the particular ^ ratio used in this work (- = liil), A close

analysis of the data showed that the gresitest deviations occttrred when

using a material of low viscosity at a low velocity. Also, it was ob-

served that the greatest deviations were all positive, thus indicating

higher rates of heat transfer than predicted by equation 6. The devi-

ations could be easily explained as due to natural convection, since the

occurrence of natural convection currents is favored by low velocities

126

and viscosities. Also, any increase in the circulation rate would

result in a higher heat transfer rate.

In Table 10 the predicted J factors (equation 6) are listed

along with the calculated ones. Also shown is the ratio of the calcu-

lated to predicted j factor values. Examination of these terms will

indicate how many times greater is the j factor or heat transfer rate

when natural convection occurs. These terms are therefore the desired

values for the S and <^ natural convection factors of equations 7 and 8,

The natural convection factors, (^ and (|> , proposed by Sieder and

Tate (3) and Kern and Othmer (15), respectively were evaluated and are

listed in Table 10. The "tentative" equation of Eubank and Proctor (9)

was rearranged to have the same form as equation 6 and a corresponding

natural convection factor, (t , was calculated from it. These values are

also listed in Table 10.

The data in the viscous region were replotted using the natural

convection factors <i, <j>' , and ^ in Figures 25, 26, and 27, respectively.

Inspection of these plots in comparison with the uncorrected data in Fig-

ure Zk revealed that the Sieder and Tate factor was the most effective in

rectifying the data with the line of equation 6. The factors of Kern and

Othmer and of Eubank and Iroctor both resulted in elevating the j factors

consJ.derably above the Sieder and Tate line. The values of (p varied from

0.738 to 1.150 and (|)*'varied from 0. 871 -to 1.010 with the higher values

being associated with the r\ms with the greatest natural convection

effects. Therefore, the net result of these two corrections was to

increase the j factors for runs with little natural convection up to

127

I'

I'

I'

I ' II

I^ [

ouo

c+r-i

CO

O

n

u c

1 (4

1r;

^

^/ f

128

X!u c

.it

tn v^

H UC 0)

^i

&

0)

I .1 I I I I

P/ f

129

130

the rims vdth appreciable natural convection. On the other hand, the

Sieder and Tate factor,^, which varied from C.876 to I.634 effectively

lOT-rered the data for runs with appreciable natural convection down to

the line of eqtiation 6 and did not cause much change in data which were

already near the line.

The fact that these corrections yield values less than 1.00 in

some instances does not propose a hypothetical flow condition with less

than zero natural convection. It does propose that in these instances

there is less natural convection than was present in the data used to

establish the constants of the Sieder and Tate equation 6. Therefore

the correction factor,^, must be less than 1.00.

The differences in the effectiveness of the natural convection

factors can be explained by the different pipe diameters used by the

various investigators. Actually, it is the | ratio that is important

but the length, L, has not been varied over as large a range as the di-

ameter. D. Sieder and Tate used a length of 5-1 feet, Kern and Otlimer

used a length of 10 feet, and a length of 6 feet was used in these

experiments. Sieder and Tate used a 0.62 inch diameter tube as compared

with a 0.51 inch diameter pipe used in these experiments. Kern and

Othmer used pipes with diameters ranging from 0.622 inches to 2.^4-7 inches

and Eubank and Proctor based their results on works of other investigators

with pipe diameters ranging from 0.i;94 inches to 2.4? inches. It is not

surprising, therefore, that the Sieder and Tate natural convection

factor should be effective with these data. The fact that the other

convection terms were less effective suggests that the pipe diameter, or

131

more correctly the t ratio, is not entering into the expressions in theD

proper way.

Further evidence in support of the above was found in the work

of Kern and Othmer, When they applied the Sieder and Tate correction to

their data they found that while it did fairly well on the small diameter

runs it grsatly over-corrected the large diameter runs. On the other

hand, their correction was designed to more acctirately correct the large

diameter data wherein the greatest natural convection effects are en-

countered and thur, the greatest corrections were necessary. Their

result yielded corrections which were only slightly too large for the

large diameters and had little effect with the small diameters.

Referring again to Figure 2k and examining the data for the

various concentrations separately it was noted that the data fell on

different lines for each concentration and that these lines apparently

converged around a Reynolds number of 3OOC, It was further noted that

the data for the most concentrated liquor fell generally about the

Sieder and Tate line and the more dilute liquors fell on the lines in a

clockwise direction from this. The Grashof ntmbers were found to have

only moderate variation for the runs of any one concentration. There-

fore, the Grashof number alone coxild not be counted on to apply the

proper correction over the full range of Reynolds numbers. Since for

any one concentration the necessary correction factor increased as the

Reynolds number decreased, it was logical to conclude that some function

of the Reynolds number should be included.

These same observations were made by Kern and Othmer in their

132

experiments and thus lead to their inclusion of the log Re term in the

natural convection correction.

The applicability of the Kem and Othmer type correction factor

to the data of these experiments seemed logical. To test the method

specifically for the pipe diameter used in this work it was decided to

evaluate new constants and see how close the corrected data could be

made to agree xd.th the Sieder and Tate line.

The log Re times the desired values of ^ ( =— ) were plottedJp

versus the one-third power of the Grashof number. A linear regression

line was determined for these data and the new natural convection factor

of the Kem and Othmer type was found to be,

3'^3.- _ 2.ip (1 ^ 0.0;342 Gr '''')

, )t" - log Re ^^ '

Values of ^ were calculated and are shown in Table 10 . The data

in the viscous region were recalculated using this factor and were

plotted in Figure 28. Both from theory and inspection of the Figures it

is obvious that the use of this factor gives the closest agreement with

the Sieder and Tate line.

The essential difference between this factor and the original

Kem and Othmer factor is that the coefficient of the Grashof number is

approximately 3.^ times as large. This added weight given to the term

containing the Grashof number is necessary due to the difference in

diameters for which the factors apply. It is possible that if the way in

which this coefficient depends on diameter could be determined an

1 . Ill

The standard eri-or of estimate using ^ was found to be0.000629 for the range of j values from 0.00170 to 0.01200.

133

l'3^

equation equally effective for all diameters would result.

The region of viscous flow was found to extend somewhat beyond

a Reynold number of 2100 which usually marks the beginning of the tran-

sition region. In most instances viscous flow was maintained up to

about 3000 Re::,'nolds number. Beyond this value a sudden change to the

transition region was noted and the j factors increased rapidly and then

finally leveled off and became asymtotic to the data in the turbulent

region. This behavior, in the transition region, was entirely as expected

and needs no further amplification.

Additional support to the occurrence of viscous flow up to a

Reynolds number of 3OOO can be found in the literature. Kern and Otlimer

(15) found viscous flow in some instances at Rejmolds numbers as high as

38OO. Bosworth (5) states that the viscous flow may exist at a Re^Tiolds

number of JQOC for cases of undisturbed flow. McAdams (19) cites data

indicating the beginning of transition at a Reynolds number of 25CO or

slightly higher.

The general agreement of the calculated and predicted j factors

over the entire range of experiments is considered to be prima facie

evidence in regard to the reliability of the thermal and physical proper-

ties as well as the applicability of the interrelationships of the

variables used in this work.

CHAPTER VIII

CONCLUSIONS

The results of the foregoing investigations have lead to the

conclusions which are itenized as follovrs:

1. Complete data on specific heat, thermal conductivity, vis-

cosity and specific gravity of sulphate black liquor were determined

over the range of to 6O5S solids and 100 to 200*^ F.

2. The specific heat data for sulphate black liquor found in

the literature were neither complete nor consistent and the new data

give for the first time the specific heat as a function of both per cent

solids and temperature.

3. No thermal conductivity data were found in the literature

for sulphate black liquor, therefore, these data represent an important

contribution.

^. A thermal conductivity apparatus suitable for aqueous so-

lutions and other relatively non volatile liquids was developed.

5. The viscosity data were found to agree with data for sulphate

black liquors from widely different origins. They were also in sub-

stantial agreement with soda and sulphite liquors.

6. The general use of the thermal and physical data is

recommended, in the absence of specific data, even though they have been

135

136

determined using black liquor from only one mill. This is possible

since specific heat, thermal conductivity and specific gravity would

not be expected to vary much with different liquors. Also, from number

5, above, viscosity can be assumed the same for liquors from various

mills.

7. The calculated j factors were found to be in substantial

agreement with the values predicted from the Sieder and Tate equations

in both the viscous and turbulent regions. For engineering design

purposes, the Sieder and Tate equations yield "safe" values.

8. The j factors in the transition region increased according

to predictions and became asymptotic to the txirbulent region values at a

Reynolds number of 10000.

9. Natural convection became appreciable in the viscous region

for fluids flowing with low velocities and with high Grashof numbers and

caused as much as 100'^ increase in the j factors.

10. The Sieder and Tate natural convection correction was found

to be more effective than the other factors given in the literature.

11. The Sieder and Tate natural convection correction was best

probably because it was developed based on data frcm a heat exchanger

similar in size to the one used in these experiments. Other natural

convection factors found in the literature were based on data from larger

diameters and different lengths.

12. The Kern and Othmer type natural convection correction was

very effective when the constants were reevaluated by the least squares

method based on these data.

137

13* Further work is necessary in order to develop a correction

for natural convection equally valid over a wide range of diameters and

lengths.

14. All of the data in these experiments were determined using

an — ratio of 141. It can only be assumed that si:nilar results would be

obtained at different - values. The effect of different h values is

predicted by equation 6.

BIBLIOGRAPHY

1. Adams, L. H., Int. Grit. Tables . Vol. I., (1926), 58.

2. Bates, K. 0,, "Themal Conductivity of Liquids", Ind. Sng. Chem, »

25, (1933). ^31.

3. Bat-^s, K. C, "Thermal Conductivity of Liquids", Ind. En?. Chem. .

28, (1936), i^9^.

4. Bates, K. 0. , Hazzard, G. , and PaL:ner, G., "Thermal Conductivity of

Liquids", Ind. Eng. Chem . Anal . Ed. . 10, (1938), 31^.

5. Bosworth, R. C, L. , "Heat Transfer Phenomena", Jolin Wiley and Sons,

Inc., New York, (1952).

6. Colbum, A. P., "A Method of Correlating Forced Convection Heat

Transfer Data and a Comparison with Fluid Friction", Trans. Am. Inst,

Chem. Engrs .. 29, (1933). 17^.

7. . "Mean Temperature Difference and Heat Transfer Coef-

ficients in Liquid Heat Exchangers", Jnd, Sng. Chem. . 25, (1933)

»

873.

8. Dittus, F. W. and Boelter, M. K., Univ. of Calif.. Pubs. Eng. . 2,

(1930), ^3.

9. Eubank, 0. C. and Proctor, W. S., S. M. Thesis in Chemical

Engineering, Massachusetts Institute of Technology, (1951)

•

10. Graetz, L. , Ann. Physik . 25, (I885), 337.

138

139

11. Hedlund, I., "Indtmstad Svartluts Viskositet vid Hoga Temperaturer",

Svensk Papperstidning . 12, (1951). ^08.

12. Hutchinson, E. , "Oi the Measurement of the Thermal Conductivity of

Liquids", Trans . Far. Soc .. Ul, (19^5). 8?.

13. Jakob, y. , "Heat Transfer", Vol. I, John Wiley and Sons, Inc., New

York, (19^+9).

1^. Kern, D. Q. , "Process Heat Transfer", McGraw-Hill Book Comp&ny, Inc.,

New York, (1950).

15. ., and Othmer, D. F., "Effect of Free Convection on Viscous

Heat Transfer in Horizontal Tubes", Trans. Am . Inst. Chem. Engrs. .

39, (19'^3). 517.

16. Kobe, K. A., and McCormack, E. J., "Viscosity of Pulping Waste

Liquors", Ind. Enp. Chem. . 41, (19^9). 284?.

1?. . , and Sorenson, A. J., "Specific Heats and Boiling tempera-

tures of Sulphate and Soda Slack Liquors", Pacific Pulp and Paper

Ind. . 13, No. 2, (1939). 12.

18. Latzko, H. Z., Natl. Advisory Comm. Aeronaut.. Tech. Memo , (19^).

1068.

19. McAdams, W. ". , "Heat Transmission", 3rd ed., McGraw-Hill Book

Company, Inc., New York, (195^).

20. Morris, F. H. , and Whitman, W. G., "Heat Transfer for Oil and Water

in Pipes". Ind. Entr. Chem. . 20, (1928), 23^.

21. Nusselt, W., Ver. deut. Inc. . 6? (1923), 206.

22. Othmer, D. K. and Conwell, J. V/. , "Correlating Viscosity and Vapor

Pressure of Liquids", Ind. Eng. Chem. . 37 (19^5). 1112.

11*0

23. Perry, J. H.. (Editor), "Chemical Engineers' Handbook", 3rd. ed.,

McGraw-Hill Book Company, Inc., New York (1950).

2k, Prandtl, L., "Eine Beziehung zwischen Warmeaustausch Stromungswider-

stand der Flussigkeiten", Phvsik Z. . 11, (1910), 1702.

25. Reynolds, 0., Proc. Lit. Phil. Soc. of Manchestp^r. Vol. 14, (I87U).

26. Rumford, E. T., "An Experimental Inquiry Concerning the Source of

Heat which is Excited by Friction", Essays: Political. Economic, and

Philosophical . Vol. 2, No. 9, (1796-1802).

27. Sakiadis, B. C. and Coates, J., "Studies of Thermal Conductivity of

Liquids, Part II", Bui. Enp. Ebq^ . Station. Louisiana State University .

35, (1953)

28» • and . , "A Literature Survey of the Thermal con-

ductivity of Liquids", Bui. Eng. Exp. Station. Louisiana State

University. 3k, (I952)

29. Schmidt, R. J. and Milverton, S. W. , "On the Instability of a Fluid

when Heated from Below", Proc. Ray. Soc. . I52, (1935), 586.

30. Sieder, E. N., and Tate, G. E. , "Heat Transfer and Pressure Drop of

Liquids in Tubes", Ind. Eng . Chem.. 28, (I936), 1429.

31. Stevenson, J. N., (Editor), "Pulp and Paper Manufacture", Vol. I.,

McGraw-Hill Book Company, Inc., New York, (I95C)

32. Williams, G. C, "Specific Heats of Volatile Liquids", Ind. En^.

Chem. . 40, (1948), 340.

Appendix

142

«>

V

\

C 00

\O ctf

(0 «]

\1

'

^^

N

\^

\\\

\

\\\

pU ct

ItEh H

J^ ?R

(•^i/*iQ)(n£*bs)CJH)/aia • 'C^xat^oupuoo iBuixeqx

1^3

i.uo

1.30

1.20

:^1.10

cl.OO

.90

,80

.70

-

\

\

^

\

\Data from ! IcAdam, (19)

\

100 120 l-l+O 160 180 200

Temperature, F.

Figure 30 Viscosity of Water

1^44

Run No. (SH- Material ^9.3 7a S.L. Date t/^'^^^Q 2/, 'f^¥

Flov; Rate Remarks

Lbs. /QO

Sec. I3(^-S

w, Lbs/Sec. 0.121 —

W, Lbs, Hr. ^^^2.

1.Temperatures

2. /^%S3. /C2Jh. J^^2.i-

S :io3.z

6.

7.

6. sos.sc 31^5-^

10. So^.l11.

12.

12. sc^s:/

G ^ I f3o3ac>

\ _Z£^^1

AT

ISf.g

2-3

t^ - tg = 0.000905 W CuAT = ^/_ t 207^ t 20<h.S'

t /^^J' t /i'^./ (t - t ),ii^(t - t )^4^V_

At^ Ji'is t jfr.s t ^ :ioo.^m g^ 32

\ /^^<P T2 /^^'^

At- ^if ^ At 3^3

Cp >^ k

T^ ^.7^^b

/// 0.3OL

tj, ^-7^^ /^^ 0. 3m

^sf:c^5

r-vM\ =_Zf£^_/£p^j = 7/.7r

/d7^7/y^s'\ _ ao^ /wcp N -

lyubj IFl^

/D G] = /SOO / D G \ = ^^^^

Ji = 0.001770 ^ = g> OOP/OS?Cp G At„

Cp G I k /b V /tbi

i = h /Cp>u\^/3 _ o.Ooc/oS'S 17.Z = O.oo/fl,Cp G I k if

Figure 31 Sample Data and Work Sheet

BIOGRAPHICAL ITEMS

The author was bom in Louisville, Kentucky on October 15, 1922.

He received his elementary education in Louisville public schools and

was graduated from the duPont Manual High School as Second Honor student,

in 19^. He persued his undergraduate studies at the University of

Louisville from which institution he received the degree of Bachelor of

Chemical Engineering in 19^3* The following year he received the degree

of Master of Chemical Engineering from the same University. During his

graduate studies he was engaged in research work on synthetic rubber for

the Office of the Rubber Reserve. For the next three years he was em-

ployed by the University of Louisville Institute of Industrial Research

and did research for the Quartermaster Corps.

In 19^7 the author accepted a position as Assistant Professor of

Chemical Engineering at the University of Florida, where he has also

persued a course of study leading to the degree of Doctor of Philosophy.

The author is a member of Omicron Delta Kappa, Sigma Tau, and

Theta Chi Delta honorary fraternities and Triangle social fraternity.

He is also a member of the Technical Association of the Pulp and Paper .

Industry.

145

This dissertation was prepared under the direction of the

chairman of the candidate's supervisory committee and has been approved

by all members of the committee. It was submitted to the Dean of the

College of Engineering and to the Graduate Council and was approved as

partial fulfillment of the requirements for the degree of Doctor of

Philosophy.

January 29, 1955

(^D^'n, Cdilege of'^ngineering

Dean, Graduate School

SUPERVISORY CO^'^IITTSE:

Chairman

f'^t-i

/I

a~

C<.A.*itit/\, .^

'£j^

UNIVERSITY OF FLORIDA

3 1262 08666 940 4