a_I

j;\n-\€$*-'d

Chapter-6apter

F1: CyA"pV

2^ 4-97 4-91xA:-:-

Y VIvx VRe'^T*^C.f,,: #": 0'664

R"''t

h-xNu' : 1- : 0.332 Prl/3 Re l/2 4.91x

-Prl6VRe,

pv"- r-'-,J "J z

atDLD:ffi tr,l#, RB-,

"-la^rat s i,.. ) fRv"+: * Jo u(r)rdr rilr)Tlilra't lrt.r_' ttt v p1 l^' r\'_S " -'-

Ti- T, 'lI. - A4'n {nfiIj- Q:V{T,-})) .lflLT;lLT)t,: T, - (7, - T)cxp(- ILA,,hCp:; ,. ._U = ltA,.Ll t^ = titco(7, - T)

Q = 4,A,: rhcr(T, - Ti LPr:fB+ weu^p : vM,

16 u,;- - 0.05 Re D'lr, r-;.- - 0.05 Re Pr D = pr 1.6,"

t_L,t o,lhJltnt - lr rlrb!l.' = lU,

r=##i=# u(r) = 2v,,,(' - #J = "" (' - #)Circular tube:

. 0.065(D/L)RePrl\u = J.00I + 0.04[(D/t)Repr]1

Circular tube:

/RePrrtut4T'l.\u = l.dD l-----;-l l-l

\ L 'l' ^\*'/ r

Parullel plates:

t= (0.790 ln Re - 1.64)-r10d(Re

Do, ,/n

sp(T, - T*)Li1

sB(T, - r;L7 D*Rar: Gry Pr: 1 u::(#,) ,:-te),Nu: +:11:tPr/':cRai Pidral ss

I:- I+K

i,-.r.(I) : f 4(.77 - fx,(T(,\IJ*.. p**", : 2897.8 prn ' K' Eb(.T) -- oTa

['=. r."-lqr:oJr:o

I,(A,,b) cos g sin e de d4,Eh{.T) rrTaf/^

' b\.' t iT 1T

E.r : TIt_uJ : rr[r., [;\." d '\,'": -|;I

E= | gidAJri

Er..(i, T) : rrl61,{X.T)e.r n(r[. A, $, T) :

/,r,,(L 8,4r,7)

L,t(i,7")ee(0,,i,7):

I"{.0, +,T)

I

Dt.r\ | r^( f - T)Et,^( i.T) d-tr-ut't)-ltJE{Tt ,rT:

€(1") = rrJo-r,(?") * e1.fi,-r_(Ti + s.f,.-=(7)

/^ r5r(,\, B, d)r:1,6(,4. Y, q,.t = tlra;1rJ P;. a(i' 0' ,b) = /a;( A, 9, @)

1^..r(i, g. d) Gr *-(i)a,ll,,i./: mtJ.\ t. /\,,

G","r(i)P.i(,\) :

G;\{r\)

al-p*r:1 , G*r - ollu4not. od : frrGror* * eo(?-rae, - T; )

/-l,F VdA, - dA.- cos 01 cos 0,, - .i?f ur..1, +C{, : ---. J :

------;- rZi,

Qu" 7rr-*.1

cos 0r cos 0"

Q,t, -t u- r I. -.1 i

Qt, ^t J'i:

I cos g, cos 6,| ,, dltdAz.l{r 7i r -

Q,:'Z Qi n; : X a' F; -i o(T1a - Tit)Qr *t: ArFr -rrs(Ti - ry)

n.-Eui-Ji Rr 1-e;

>r R, ': A;E Q';'i:'rv_l1{i-j : Ai., Qi= Ail r,-,11, - li

J= |

| - o. 'Yolj = t, + i> Fi_/Ji - Jj)j= roTr: T,,,rt

v "ry i-er, I _1-r,Ar€r 'A,F,:' Arr'5 of32

t;

A,rfff - rli

*-')') " *(*"(*"*-

!̂/ r:. ,r, shiclds -

l&5He.

trlass franian o! sPecies A:tttt nllV Ftw^:i: ,,rtv-V Mas basis: iei'.t:+-

-PD^s-:t-

llole fractiortof sPecies A;-rq

Ii/V C,rh=T=m=T

Vt:V * V,ra.,t

Vn: v i' l'di$.sY-rtaV,t*rr'6lt

Thernral dil-fusivitY

I'n : *: fi --,W-tt aitfusivit):

fl^n., -^d{cArc)' = ----l- : -LUAA .1rllole basis: Jsn,t = A *'dlt

an --_ _\.u]-d dI

Pr :"* = )i.trsd* P = .vi [+4,'trb PisiTiPi':u 'iao)';-tiqoiusat - H

Pt'' - Ps'''Nrir.r.*u,t - DAalf t'aA ---T-

P't't - P't'z: gilA_*--L -

C;. otar* : ':f X P;. 1:s sida

rArt'

js: PaV * pnV&tr.s: nrr( j't + iil - pDa-ax

xr-+.t - 1r.l.r - ,-, -, P,l. r : P'r'Z

rir+ar..r.'*',n : PDIA ttT--- : D;aA -- L -

/,i6r..r."].r :'7a l+Dttffi : zon uPffifflf1. I - 14r-r

ri.51s.,r. r@ : A'l [ {yPD'* --t;=Z-

f t-t - P,t-z- *irr{tD.tr-7=T'

r, lftome'nruqtiffusliiy,nd Sh=l'T['I ivl0ilIi'lltUlll ullturrrr ""J \,h = #st =

D* = - I{o$ diffush'lly- 'ru

*t D$

rir.oo, -/ro-r.'lr(P.t, 7o,) - h*o'pAAlr"L1 - )ti'*)

t1o" :Nu : Sh or

t7.r. ,tE=! -r'g*! or { - t, - SL-*i-n----F-- D^'h

:,Genel kanai duzenlerihin verinr ve yiizev alania!'r

':D0z dlkdrirtgen kanatlar

,* = t/zw*t\]:r= L+ tPit&"a:2wL"

:::i 902 Uggen kenatlar

',', m: t/ifrlt:i

ii*l*.'= Zwt/ L2 + (ttz)z

L lJ.zrnL\i?rw= fr hW,rL)

Ln,.-..--:-i+\'Emrf+t

^ 2r1lmtz'= -;-----ti'c - ri'

tanh mL,'lrru -

-i-'frL"

2 b\znL)w-: ,LlJznL)

_ 3 tl4mLt3)'ttonil=r;l h4n,rcl

tanh mL,'ll|'d

^lrr.ec

i,.,Pltl lat"uotik ka,natlsr

;;"'*:1/2ffi;."*;"a: rryL[C1 + (t/t)ln(t/L + Ci)],'cq: fl ll[!

prof illi daireiel kahatlar

tn'= \lzil-kl:izc= ri* t/2e*;t:2ttlr!"- rf)

?tir r :,

r,j;'Dikd6rtgen profitll igne kanailar:j;.

m: \/4htkD= L+ D4

;&^;t= nDL"

ilFCSan prdtittt tgne kanattarin1 -=1Qffi

.nD

-

;{=+VL'+(Dnl'

farqbolik profllll lgne kanailar'n=;t/4611rfi

i.l* = Stc; c, - hr,xzacotL + q)l

',:,PqJabolik prolilli lgne kanatlart,(k0t uglu)

I'a_tf

I

,, 1.l '.:,:

J;.;

':.r

-'.ii

-!:i

tr-t \.1)

..t,

TDl

I

,rffi>

-r=1OA-l tt-.trZ)'c-r

oiI

--Ji\.4-,,;..::-!i:l

l;iirli;*" ffiiryrf------------ -1 /fr(r'-----u

---t-. 1 r'= r/:i I I - t/L I,ffi

Y*L--+.

-. _^ K{mr)llmr2)- lr(mr)Klmr2,)'tw'--z@

'tr

0.9

0.R

0.7

0.6

0.5

l- r--'+1,.= L+ tD I IA-=L-t-------.-

0..1

0.3

0.1

-1.I

I

tr

I .2 | .-1 1.6 l -8 : l'l l'J 4b i'6 -1

g=1_.1/:ir,.,14.)* $EKiL 3_12

Dikd6rtgen, iig.gcrt vc parabolik kesirli diiz 1xpn1lns1 verinri'

$EKIL 3-43Srbit kul rn I rkl r dairer'sel kanittlilnn veri mi'

().1 0.4 ().6 0.8 L4 1 .6 1.8

6 = 1,;1/rllrtd'tr'

T

si\ IN- =,1 ,-'- , I I

- rllJ--_ffillih

Wrrlr_fl-:-

1

i\ \. = rr-lrt i)

Nusselt number correlations for cross flow overtube banks for N > 16 andO.7 < Pr < 500 (from Zukauskas, Ref. 15, 1987)*

*All properties except Pr, are to be evaluated at the arithmetlc mean of the inlet and outlet temperaturesof the tluid (Pr, is to be evaluated at Ir).

Correction factor Fto be used in Nua,,v., - FNua for Nr < lG and Rep > 1000(from Zukauskas, Ref 15, lg87). '.-;-''- t'(a

Arrangement Range of Rep Correlation

In-line

0-I00 Nup = 0.9 Re$'4Pro'351P,'1P1r1o-25100-1000 Nuo : 0.52 Re8'sPr0'36(PrlPrr)o2s

i000-2 x,10s Nuo : 0.27 ReB'aPro'aslP/Prr)o-2s2x IO5-? x 106 Nua : 0.033 Re$'aP1o'+1Pr/Prr)o.zs

StaggeredQa?cn t

0-500 Nup : 1.04 Re$'4Pr0':61Pr7Prr1o'2s500-1000 Nuo : 0.7 I Rel'sPr0'36(PrlPrr)o'zs

1000-2 x 105 N ua : 0.3 5 (sr/sr1o'z p. fl'spp o':51pr7p1r1o-zs2x IOI-Z x 106 Nu, : 0.03 1(S/S,)o-z ps $-apr 0-36( PrlPrs )0'25

Nr I 2 5 4 5 7 10 13ln-line 0.70 0.80 0.85 0.90 0.93 0.95 o.98 0.99Staggered o.64 o.7 6 0.84 0.89 0.93 0.95 o.98 0.99

(a) In-linc arrangcmcnt

(b) Staggercd arrangement

60

40

20

t0Ei6

4

2

kl: o.8.E 0.6c o.;l

.'J n){t

o-t86

806040

20

l086

4

\. 1LEt2 0-E

0.6

c 0..1'll.:.,'cIr 0_2

.9, P--'1 *PL: SID G€?' 'lP.: SJD O,OPr: Pt

o-fo-2 0.6t 2 6to

(Pr- ty(Pz - l)

a 68;gl: 4 6s1g: 2 4 6E103 2 jt 6El0rr 2 4Rtr....

ttc^-.-:',CJll

.?t|]\ll\frot-Nrr /irt

\//--erdrd

0.60.8 | ? 4PrlP L

-#Sn: Sr

2 4 6stOl 2 4 68103 2 4 68103 2 16El0f 2 4

Rto.rt

7 4 a81go

0.5

0.4

U.J

0.2

Tk.t't-Ti

n, , _ I(r,t)-I-T;-T-

f tGURt 4-29\tariirt.itln of teurper':rtu re rvirhcL)o vc.cti ol) to :t rt c.nvironrrtent

Enpiric;l caiTel;tion-,'&r lhe i.,,el;gi i..lt5;elt numb;r icr frrce.l cJn\iari|err3v€r tircu!.3r and acrcir;uiar r.r'Iinier: ir! crnas ilniy ili.n Zr:|.:agskas. 1972 anCiekcb.1949)

U.UO

U-UO

0.o4

0.03

nnt

0.0'lo 0-1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 0.9 1 1.1 1.2 1 .3 1.4 1 .5 1.6

-r't- ?.lri

Positi()n at)d tinte in a senri-inf-rnite solid initially irt rentpenrtule 7] subjectcdat I* rvith a coR\jectiou hrat transl:er'coelficierrt of lr (ptotted u-sing EES).

ii J::.:lir'tr;ls

nuno?r 3nc lacltr i.3r isll!'iEyeiop:d !:ni:ia: :l.d !n tJbes,:i

;l.nrbisrt

-\\ \\ S \

\ \ $ \ ;\ l\\ \. | \.,\ \-.Llf, a\\

\ \ i\ N \\F

.02

\ I I

iA\t\i\}\IN N \

Cross-secticncf the r/linder Fluiri Range ol Re Nuselt nurnber

lc

/;€\-Tiiffi$*Fi !'*€Z__,

G:s orliquid

c.4-44JO40-40004000-40..JC040,ooc-400,000

tlu = O.gaoFea.::o Prl6flu - C-9llRecLIs PrL"t{u = o.6e3Ret.::5 PritlJu = 0.193Re0..!€ p.tahlu - c-oz7ReoN5 Pr:tr

5000-:00,000 t!u = 0.lD2Reotr'Pr!c

Squar: ,4r;-Tftf.,@i

Gas 5000-:00,000 l.lu = 0-246Pao iff Pr!!

Hsagon 5000-100,000 f.lu = 0.153Re0.6:a Pr:r"

I!i::"@Gas 50a0-i9,500

19,500-100,000l.lu - 0.I6r0Peo.5* PrL?llu - 0.03851ieo.7?2 pr:!

Verticalplsie Ilul Ges 4000-!5.000 Nu - C.228ReE]r: Pr1aEllipse Ges 2500-1 5,000 t'lu - C-2!.lqReosiz Pr:t

Tube

I

i aibI o,,r

'p, lia - 4,!C).r, 3n,:j i\-,J,,rL.gse/i lldinlrsy

tD,.!kl

i;'.1,-"Ir: Const rj5 = CcnstCircle

@J. Or 4.36 64.OO1Re

Re:tangle

-.4ffiWf-" -labI2

46ts

4.+4q 1a3.WAEA

c-ulc.4>8.24

,':! 3-61+. Ll4.79).JJ

56.92,JRe62.20,,Re06.JC/Ke7?.?aRe78.801Re82.32.lRe96.00iR:

zibi

8

?70? It5. Of,

4.554.885.09J. l6

6l.C01Reb ! .laHeI Z,lciK?tD.outH273.16,'Ra

lscsceles Triaogle

@0

i0'30'6C'9rl"

12C.

1.bll. za2.47

2.45z-t I3.11z.r6z-co

50.8OiRe

"z-zux253.32!Re)z.5vtt1e5O.96tRe

13 of 32

correlaticns fcr Ihe ar/eregg Nusselt numbet icr naturGl ccnvecticn ovs, sur-iaces

GeometryCharacteristiclength L Range of Ra Nu

Vertical plate

a L

10r-1 0elorJ_ l0r3

Entire range

Nu: C.S9Faf. (9_t9)Nu - O.lRaiE (9-20)

( n aATPat:o ' 'l 2Nu =

{0.825 *t;ffi} rs-zD

(complex bul more accuratej

InclineC plate

L

Use veriical plate equatior,s ior the upFersurface of a ccld plate and ihe lor.rersurface of a hoi llate

Replace g ! _g cos8 for Ra < 1O,

Horiiontal pla'le(Surface area I and perin)eter p)(a) Upper surface of a hot 9la1e(cr lower surface of a cold plate)

(b) Lower surface of a hot c.late(cr uppar sud2c9 of a cold plate)

llot rtrla:e

Hot surf:ce

A,iP

10.-l 0,lor_l or!

i 05_ Ior r

Nu = 0.54RaH (€-22)Nu = O.t5Rai,3 (9-23)

Nu - 0.27Rafa (9-241

Vertica! cylinder -r-II

L

I

l_

L

A veriical cylinder can be lraated as aveiUcal plate when

n-351 a--Gry

Hori2ontal rylinderReo < 10r? ru:

{o.o - n. l' (s-2s}

SphereRao= lgtt(P; > 0.7)

Nu=2+mffirr" (s-26)

14 of 32

i"lz,:l,t.od'! nibiicn iunci:'.r:;5 i'fis+ ir:i':: a:lii:sifs iit yrfl:i rJil:;Ei' ta;:lglit: ;i ii:ri: sirc i3'D!

lr, ..r I.FM' K I1

at'./J5400

5600

5800

7000

7?rsi4aa7500

7800

ac00E500

90c09500

10,0c0

i0,500i1.0c0! 1,5t'10

i2,0c0i3.0G0

14.000

1 5,000

t6,00018.000

20,0c0

25.m0Ji0,000

40.000

50,00075.,1r-10

100,000

ffi6$+:d$ri$#"r:jVis! iactar €x::ressiorrs ior ssrn: inliflitelu lonll (2-D) iexj.irelri€s

2004C0

6CO

8CO

1000

IJUU

1400

1600

i800?DCo

2200

24CO

2500

a003C00

32003400

3500

34004C'00

r.200

44C0.1600

4300

5DC0

5200

5400

5600

5e00

5000

C.0000110

C.00C0'10

c.0000000.000016

c.000321c.002i3+0.0077'10

8.019718c.03934t0.0667280.1008880.140256

0. i 83 !20a.?27897D.2i32i2u--\lctulri.Jo t .'r50.403b07

c.1433820.18Ca77

0.5 160 I 4

c.5487:j6.c.579280u,ou,/ f 39

c.633747

c.6589i0u.ccuiouc.701046

D.72Ci 58

0.73781E

0.i54 140c.i692240.7831 99

0.796r?90.8081C9

0.8i9217t).629527

0.8r91020.848005u.63Dltsd

0.374608

0.890029

0.903085

0.914i99U.:ZJJ IUn o?1 ccn

0.939959

0.945098

0.955 139

0.96289E

c.969981

0.9738i40.-o80a60

0.985602

0.992215

0.995340

0.997957

G.99E953

0.999713

c,.9999C5

CoDdrI llebt'on

.f[g!rt Ftlld Ed{|a

,,ffiAi;llffi

I

I=::t .ni 7= l?f

I . i-inlrrrrlr d;ri't +Er +?1i..:r.'"j,='.: r;li i. l..r.jrl: I rlili--

,.r,1 +Fil{ur-l - fu*' f-Iu-r Ii' il -lilr: )

Grui:! 6nil'J isk

,ffii:'qg iI !t

MJ(s€p,

l,= iL a X,= q/.!.

.,t+\z>I ^lt"'''-Ii a' c\t.

Rrad:cbrwr!r:ri:l r mcn dp

ReLrriorr

P3r:dlcl lrl!r(es r.irh midtinescoon€r(-{j h! frcrFcodicutnr lj oc

T- l-- h,, -----l .

-a

I

IIi

tti = Fj,/l a,r.f l'Vt: w,,iL

l.-. . __ [i!.q+ lp;t: + 4)r/: - 0v,- u.;): + airi:,_j "ry

Inclincd plst* of egual widrhaod rvitlr a cclEnlon edgs

,"'.-.?'z'-.'.?::___iF__r,______i

.tf. .: t - srrt =G.-'t !

Pct.t}:fDdiculs Flrt€s with a conulr-'n cdg::

-r-l'tl'rlIIl-h

{,-'- +{' - ; - [' -i+J=] "']

Thrcc-sidewl encletrrc

[__ F, _____l

P wl+ wi- wt- jt.,l

ln.li^ir plJnc md rw of cjrliodcm

Fi_j:t-['-t*)=l'"* !l-"-,ii -Jc)"'

15 of32

tr.

il..15si i = li)

L .= -lir*'.rll.r i -'.fi:-lt':i:lM-r , 1 ..='-; rifi !{ ;l iP! +v:\r!

. lriil r lllt.ti:r I rv:i r t rr'!.*ir:l lr'{ i l+t'iil' [(l+liriE"+grjl

-l l\t.z:rPi;r'1ilil+li:Eil:+ffjjl lJ

Sorall objed in a largp cavilv

'4?, r?, 12

Infinitely laqe penllel plates

Ar,Tr,e't

ArTz. 1

Qe= Agtirar-77) ( r 3-37)

.{,T-0A.)

F::=l

At= Az= AFn= |

; Aoe1_T:)cr: = l--;-

-l-+--l-- |tr 6:

03-33)

Infi nitelv long concentric cylinders

Arrr(11- ri)

.1,o(r{, - Tj)

Binary diffusion ccefiicients of dilute gas miritures at I atar{from Earrer, 194!; Geankcplis,197?: Perry. 1963; and Reid el el.,1977)

Substance A Substance IT,

K

Duor Do,mVs Substance .4 Substance I

\K

Du or Dt^,mzls

AirAirAirAirAirAirAirAirAirAirAirAirAirAirAir

AcetoneAmmonia, NH3BenzeneCarbon dioxideChlorineEthyl alcoholEthyl etherHeliurn, HeHydrogen, H2lodine, l.MethanolMercuryNapthaleneOxygen, O.Water vapor

?73 1.1 x 10-s298 2.6 x lo-s298 0.88 x 1O-s29a 1.6 x 10-5273 1.2 x to-s29a 1.2 x lo-t29a 0.93 x lo-s29A 7.2 x IO-3298 7.2 x lo-s298 0.&3 x lo-s298 1.6 x IO-5614 4.7 x lO-530o 0.62 x IO-s298 2.1 x lo-s29A 2.5 x lO-5

Argon, ArCarbon dioxide. COtCarbon dioxide, CO2Carbon dioxide, CO.Carbon dioxide, CO2Carbon dioxide, CO-,Hydrogen, H2Hydrogen, H2Oxygen, 02Oxygen, 02Oxygen, O,Oxygen, O2Vy'ater vaporWater vaporVJater vapor

Nitrogen, N2BenzeneHydrogen, H3Nitrogen, N2Oxygen, 02Water vaporNitrogen, N2Oxygen, 02AmmoniaBenzeneNitrogen, N,Water vapcrArgon, ArHelium, HeNitrogen, N2

293 1.9 x 10-5318 0.72 x 10-s?73 5.5 x l0-:293 1.6 x l0-5273 1.4 x l0-5298 1.6 x 10-s273 6.8 x lo-s273 7.0 x lo-s293 2.5 x lo-s296 0.39 x 10-5273 1.8 x 1o-s298 ?.5 x l0-5298 2.4 -x Lo-s29a 9.?_ x lo-s29ts 2.5 x 10-5

llctg: The eiiect ci pr*sure znd imperaiure on Orn can be accounled ior ihfough Das - T4!P. ils. nultiply OE vailes b.y 10.76 to convst thm io ii!is.

16 of32

At -

rt

E_El1'= I

(1 3-39)

Concentric sphercs

A, ,r,.:E_'T'Fr:=l

(13-40)

t.0|J.>

0.s0.70.6

0-_i

0.i

'!+l0.1

0.090.0s0.070.05

0.05

0.G4

0.03

0.02

0.J 0.5 0.6 0.9Ratio l-i /)

F]GURE tr 3-5Vieq, iactOf Ltel\ei1D t\VO

aliened parallel fectansles ofequxl si7-e.

FIGURE 13-6Vierv hctor betweetr l\1;o

perprlndicu lar rectfl ngles witha cotllntort ed.qe.

l0.1:

0.?

tr_J

-f,----------<

n-J

)J

-

0-4

0.5

u.on?0.8

-1

0.9t.01.2

1.4t-6{-R!-v

1-

5-6'8-t020

Rado LrlW

i 456 810

17 of32

3 4 5 6 I l0

FIGURt 13-7\,iew factor bqlr.een lu,o coaxialparrllel disks.

t.0

0.9

o.6

,. 0.-t

o..i

0)

0.1

00 0_2 0.4 0.6 0.s r.0 0 0.t 0.i 0..t 0.J 0.5 0.6 0.7 0.6 0.9 t-0,/h 'lr2

FTGURE t3-8 .Vjcx' factors for two conccntr-ic cylinrlcrs of firritc l,englh: (dl ouler cyl;oder lo inncr cylinder: (b;r rrurcr cvlinder ro iiself.

9inary diilt-r:ion cceff ici:nts oi .Jilute liqukJ sotuiicns and sciid s.lrrtions ei i atmiircm Barrer. 1941: Reid ai al., 1.977; Thomas. i99t; end vao 8laik. l93O)

\+Jf:i\ N,-I \o.:J i\

S

(a) Diffusioti threugh Liqu!ds. (b) oiffusion thrcug,t $lidsSubstance A(Solute)

Substance I(Solvent) m2r's

285 1.5 x 19-e293 l.O x 10-s29A 2.O x 10-e285 1.4 x 10-e283 0.84 x 10-e2AA t.O x 10-e29{3 1.2 x lo-329A 0.69 x 10-e294 6.3 x lo"e275 0.85 x to-e293 1.5 x lo-e333 3.5 x 10-e288 1.3 x to-e29a 2.5 x 10-e294 2.4 x LO-e29A 1.2 x lo-e298 0.18 x 10-,29A 1.3 x 10-e288 2.'l x lo-e

AmmoniaBenzeneCarbon dioxideChlorineEthanolEthanolEthanolGlucoseHydrogenMethaneMethaneMethaneMethanolNitrogenOxygenWaterWaterWaterChlorofcrm

WaterWaterWaterWaterWaterYYater

WaterWaterWaterWaterWaterWaterWaterWaterWaterEthanolEthylene glycollletlranoiMethancl

Carbon CiorideNit;ogenOxygen

HeliumHeliumHeliumHydrogenHydrogenHvdro6enCadmiumrtncZincAntimonyBismuthMeriuryCopperCopperCarbcnCarbon

Natural rubb€rNatural rubberNatural rubberPyrexPyrexSilicon dioxidelronNickelNickelCopperCopperCopperSilverLeadLeadAluminumAlumiaumlron (fcc)lron (fcc)

Substance A Sutslance IlSoluta) (Solvent) m:/s

?9A l.I x lo-to29A 1.5 x 10-!o298 2.1 x 10-to773 2.o x 1o-t2?93 4.5 x 10-1529A 4.0 r 19-ta?98 2.6 x 10-!3358 1'2 x 16-tz438 l.0x 10'i!293 2.7 x 10-te773 4.0 x 10-:8

7273 5.0 x 10-t3293 3.5 x t0-?5293 1.1 x 10-?o293 2.5 x lo-!e773 4.0 x l0-r4

7273 l.C x 1C-r0773 5.C x tC-15

1273 3.0 ;{ l0-rt

I 8 of32

Binary diifusion coeflicients cfsome Aases in air at 1 atm pressure(from Mills, 1995r Table A-17a,p- 869)

Bi na ry D ifi u s ian Coef f icient, *

mz/s t 105T,K 02 Coz

2000 48.o 39.+ 180 44-B

'MtrlUply by 10.76 to convat'o flzis.

ln a binary ideal gas mixiure ofspecies A and B, the diffusionccefiicient of A in I is equal iothe diffusion coefficient of E in A,and both increase vrith temperature

Solubility oi'rwo inorganiccompouhds in water al VarioUstemperaturrs, in kg, in 100 kg ofurafer ffrom Handbak of Chemistry(l.lew York, tulcGraw-Hill, 1961)l

So/uteNOHz

Drp , oI D1i,-g.eat I atm, in m2/s(from Eq. 14-15)at I atm, in m'ls Calcium

2oo o'95 o'74 '3'75 0'88 r o., (from Eq. 14-15) Tempera- Salt, Bicarbonate,3oo1.88L.577.77l.8o.-.fure,K...NaCl.Ca(HCog)z-40o 5.2s 2.63 t2.5 3.03 'O' 2.OS x 1O-55oo 4.7s 3.8s 77.1. .4..+?. . S . Z.I7 xro-s 2L.1.L.t . ...95.7 .1.6...15'eblb' s.ae 5.37 24.! g.g1 i; 2.2s x to-s 280 35.8 16.307oo 8.38 6.84 31.7 7.82 :: :':; l; ,:_. 29a 35.e 16.s3Boo 1o.s s.s7 3e:: ;:;8 15 2'33 x 1o-59oo 12.6 10.s 4i.7 tl.B t 2o 2-42xlo-5 3oo 362 L6'75

tooo r5.2 12.4 56.9 14.1 25 2.50 x 1o-s 31o 35-5 15'98120020.6 16.% 17.7 19.2 30 2.5g X 10-5 32A 36'9 L7'2O14oo 26.6 2I.7 99.0 24.s 35 2.68 x 1o-5 330' 37 '2 17 '43340 37.6 17.65t6oo 33.2 27.5 125 -++-____-__---4A-----4Jf-x+OE!------- 3'0=---3A:Z--W:8'--lgoo 4o.3 32.8 152 27 -O E^ . 6c v .r 1r_550

100150

2.96 X 10-53.99 X 10-55-18 x 10-5 373.15 39.8

36037.O

38.839.5

18.10r8.3318.40

Henryl constant H (in bars) for selected gzses in vrater ai low to rnoderai=pressures (forgas i, H: Prro.46olyguis4l)(from Mills, 1995r Table A.2l)Solute 290 K 300 K 310 K 320 K 330 K 340 K

H:Scozo2n2coAirN2

+40 56012BO 1710

38,000 45,00067,000 72,OOO51,000 60,00062,000 74,OO076,000 99,000

700 8302170 ?720

52,000 57,00075,000 76,00067,000 74,o0o84.000 92,000

1o1,000 110,0o0

980 11403220

6I,000 65,00077,OOO 76,0008O,OOO 8.+,O0O99,000 104,000

118,000 124,000

Solubiliiy sf selectedgases and solids(ior gas i,9 : Ci,uso-s6=lP1,s"4tl(irorn Barrer, 1941)

Gas Solid IK I kmol/m3 . bar

Analogy between heat conductionand mass diftusion in astaiionan/ mediunr

Mass Diftusion

Saturation pressure of vrat:r ai'raricus temoeratures

S?turationTernperature, "C Prjssure, Pa

HeatConduction

*13}: 20

?tO? RubberN2 Rubber

CO2 RubberHe SiO'H2 Ni

0.003120.001560.040150.000450.00901

4770

104. 151

218310439611872

72281705233911 FO

424655287384

l2,3soloI,330

1.55 x 106

298294294293358

T

k

,ic(

I

w1 ftpDes CDasIt I tDaa D*LL

MassBasis

MolarBasis

-40-36-32-24-24-?0-16-L2-8-4

o5

l015'zo2530554050

100200

19 of32

Tlplcal uapar psmearrE ol commonbufldlng rnateriafs (irorn F,SHRAE.199-3.. Chao. 22.Teble gtt

Malerialsand permeanceIts Thldrness ngts ' rn2. Pa

Analogy bei.veen the quantitlasthat aplrear ln the lormulationan4 solution of transienl heatconducilon anci iransient massdlftuslon in a st4ilonar/ medium

ConcrEte oZa r11. 1 11Erlcfi, masonry. l0O mmPlasirer on metal latn,

19 mm'

1.746

860

530

HetCond0cibn

lr'l;5S

Dif-rusic,nFlasler on 'rvood b0l,Igmm

Gypsum vrall Doard.9.5 mtn

Plyr,locl, 6.4 mmSUll air. I ,ntllneral v/oot tnsutatlon

(unprd€cteo. f mErpanded polyurettuneIrEulatbn board. I m O.SA-2-3

Alumhum toll. o.o25 mm o.oAlumlnum loll. O.ffXt mm 2.9Polyelhyleno, O-O5l mm 9.1Polye|hflpr€, O.2 mm 23Polyesterr O.l9 mm 1.6Vapor r€tarder htex palnt,

O.O7O mrn 26Exbrloi aqyllc hous€ andtrlm palnt, O.(NO rnm 313

Bulldlng paper, untt m6soi O.16-0.68 kg/ri O.l-ZrtOO

T C,y,pofyto Dr"

^ VJ, n - T_ - walX, i) - ryr.-o.=- 4_T-, a*= = -l{it ryal-

285040-tog

774

245

AnaloEf between tl'r€ guar[tltt6tlrat apped ln tne tolrrrutallonand sotuUcn of heat convE€tlonanrl mzss conv€c'*lon

Heat lvtasConvegtton Convectjon

Tg,0 - T,I- Ts

rvAx, tl - ru^wnt-Vrc-sms - 2yGi

/r"-o Iu,** = -4-DA.JIt=-1,

Varlous exprcs-clons for enporafion rate of a llquld into a gas thrcugh aniniefnce iln A, under varlous approximations (subscript r stands forvapor,s iof llqulGgas lntaiace, and @ aray from surfacel

Assutnpilon Evaporation Ra'te

General

Assurning vapor to be an ideal gas,P,: p8,T

.Usl ngSh ilionJolburn.analqy,hr,^: pcrtrou,Lea

-x2Vat

o,-&*Lk

-dla:E

T'h*

4a^ ut<

pr-! tt -a?

-h-Esrn..E ----

h^^ L._. _ __E_Sh - /(Re. Sc)sh - f(G(. sc)

usrnsf - i=+,rzhere r: L+an

Prc peii es zi Va riou s lem oent i; res t K'i.Dr-noriip< a+ itl1 K .(V/im . K)ice{Jiiig:' l'ii

MaliingPoi ni,

r\

i; axi06pkeln: 40c 600

i000Ccmtcsition

Bisn'uih

Sercn

\,rtrm . K mlis r00

Lt=v

I 854

545 9780 i22 7.ZE 5.59

?573 2500 i 107 z-i.a 9.7E

'I74qQar ifil 1D12t3 i 1 i.1. 2I9 !

th h t hH

112 rzDI tC Anr'l

15li JUIC

10.6 -q.60 9.85rltli, z:rED. tlt't,

'i.c4

I?7r O.O

i453''

-... i', Y4- /' ,

' an c, .,.

'484 .,:'_Atr4

.:-l..' .r ."':.:J 'ec.Z '71'.3 65..4';' 542 ; '.,58]' '6r6i

"i67.r4 : 58.? 5?.1 ,' -^; ' --^ .'.1.;-;

I

'i79 3i6 3171358 893-3 385 4Ci I17 182 4i3 393252 -355 3-e7 1i7 132 451

Cornnsrciai trcnzs \?9'3 8gD0 €2Ci90i?, Cu, 1.3% Al)

Pi;':spiicr ga:r brcnze i 10.4 874.i 355iE9% Cu. 1i% Sni

:i.3 / a J= .LJ r'36C 395 3?5

5.71. i i' i9

I ."- -4!:

785 iiO 3454i aa 74

\.:+ Y:_-:,,:.-.. !----uat U tuE: Jt s>:

i;-0% Cu, 3C% Zn)] i 6d c:'ru i3u r i u

t493 89?D 384 ??(5!.?! Cu, 439f l.ri) ?37 362

lrcn: ii--pure rsrc 7870 447 ec.? 23.': i;: ,:i o

":: t u;f;t uli.= ,ii

.

A.rmcc

7?.7 20.7 95.6215

:3. i;tn

2l of32

t

a

Cajrnjrrii : r'; ,..,'i,, :,i,,, 594,', ',',eoSC. :,. .23'r' , " ':36-.3 ,t. j'..::il . , '..r. j" r.1"'i ,l:: = '.,,1 .;'..., .i , ': i';,;.,; ,y,i.r: ,: , :., ._...'.::.:.:. , ,: . ,,,ctrrcnjui. ', ,..'':; ,27'1i." |,,.t iiqc,, . :14j ', ,,, 93,i ''

7Z7A

Fropetiia a; J.! XPnD:d'ies ai laicrs Te!xleztr;Es i.ii;.

(oJ.h . F.)/.,(JAB .K;r :r iOs

4S.?

i?.?

Jg.:

49?45.4

192

5;-b

2t>17.1

f/l

,55i' ., :9.3 '547 ,'

556

€,ag

3e.3

cs

za.>

--it?8.3

9€i9

142

')'!!.

?'6:e4

t?3

!c21

?5!.

:1.5Lai619t?-ai41

3fu

' 5=-q .5l_4

:{9i i70

275

!4.,530

32c,'!7 0

f,i u

^^.

^-4.

53j-:

..14.2!45

;! sq

)18

57.t-i]e!?l

zg.5

,ai.i,

E6,?

i5.6.:.1C55'

l.5i1ta?93,

.:;

7':.8.

!:) i91.?

t=!a9

4.1.615;!?l

?t I

?6.7:?5I5!:934

:!.,

,:D.D

fi.} ."

't5:2 "'

' i.i5,8:'.

34.n

i074134261

E9, Z

n9?

48C'! 3.5

! t--3'.1f,-l

;?.5!2: ,

:50 .'52

:'!46 "i.'lx ,,

.4,U J2.4.:Df rouo2?,b 25.,i

5?2 alt.''' z:,: !+.1

J/J I EUr

i'lick!i:Pun

6.7 l0-3?iz

,rgp 2ns:, !58 ??7

77.i . "72,e:,i30 .125

' t'.:. ..5a,9' I :r.cr,.,e7i,:,, !27; -'-iqe . !lF4,i

.',,'147,'-t. 2rO , ,t

Proecti.s cf scild me:als (CcncluleC)

PrcDerli2s at 3aA KPop=riles ai Varicus Tsmperaiures !.lii,

A{'rV.h.Xi/c,{rltg.KiM€ltingPoini. p cF k ,rx i06

lmposiiicn . K kg'm3 Jikg. K tATn . K n:/s iOC 20O 4C0 SCC 800 1000

22 of32

i.lelting

.: j-: .i,., ..,,,

r,.l

i cr- i Masi (C.lto; c.).6'c% Cr,0.!3% h1o,3.6% Si!lir-iMo{t.15% 0, j,b cf,r:.i4n |Jo,c.39X Sii

l at-,tB-?\ C, !.O2't *.

87.5ita

r3a

, - ieC.).,:.' ii ii ,, .1

=' 'i. z7a ','.';',''9r: t"93F -

:, ?C< n iaTO I

:t0 133 7L! !d6 t39 !53;hsium 2C23 1!,7iO ]'i8 54.C 39.i 53.a 54.6 54.5 5S.8 5€.9 5€.9?9 I1? 'L?4 1-?4 ics t56Tin sos 731c ??i 56.6 4c.! .::.? -72.j -17,?tb utl !4i

-ii-tniun !9:3 {5OO aZ2 2!.9 :.3? lC.3 ?!.5 ?C.! l).1 t9.7 Ze..}3!C 164 55i 591 533 fr;3

iur'E:i:n 3560 \9,3oC \Z? lil :8.3 ?08 t86 i59 ilt L?3 tt8137 142 f.i6' i,t€i.,'.,', 1,,t.,':'i+d6,,.,,,

: r i l.. r .'r,_r i-

;, ., I ': ,':,:r''::21sii ":- .r ,.. ,,.,,11...,, i.: l-..,j ,i ;': ,,, "i-- i : ii,ir,'' ,lr.rli'-,, :' z?.,..'rlt?',3qt,.i,rl.,,.,,,i0.8'll1,.l]!:,:.:ll' |,19i,,., ;,. ,'.,,

Ft$r iaa'i. ?. lrice-! liC Defic P D{i'*il, F|rtsfi.aizt ci Hrz,'",.8 l,je$ t?*,W. jd sd- :934. ih! f;€lgii! i: up: b;- i{rftarirJ .Jl jffi lyit€r &t:r. ria

s cf solid ncne'!etals

?rcDeni.-s at 3OA K

Piag"-lttes at Various Tenpeqtaes iKt'| (!'rtln . K)lcu(J,rkg ' K)

ca I c;(106e. Kwlnr , 'rl rnzjs ioC

32:4.:94c:.' '' 2E:4'940 ,;'I98, :

L 49C)

2.28nEn

lPq'

,'1110 ;. :

1 i il-'',,i!'1 -

' '159q1i.3

lEEC

47.

E.,on fibr, .oory 39t-i(30% vol.) ca;i'i;osiieir. ll to fibe:sk. .i. ic fibe:'s

. . . 1.

?o8t

+JJU :iJU :J=,-'

, ccralce ii.s. ,.:. .; :. . .

"i..[Lt;bvj+-td.fi.D:rs....l.,.j':.';'.0.87:'c;c.1..Fyrcreian, 1a2? 26OC E08 3.9.8 1.89 =.25 4'.78 5.54 3.28 3.08 2.SG

Ccrning 96C6 908 10-38 7'122 i197

'Grashit=li'Ear,' 45C' i.1CC:Ecxy'(25%"vc.l. i

3.7C 16.8 -:.23 4.09 2.6E 2-0i. i..60136 - 4il 9-c,2 1406 1650 1793-,.i

Siliccn:erbids 3iCC lL50 675 4gl'r 23C 8; ic; rr; rri;Siiicon ciicxid:, 1383 255C

':ui TJrcrrri ri r.'.{uor La-li:, ll to c-axis 10..1 39 15.4 7.6 -.C,r 4.2& r to c-:xis 5.2i 2C.g 9.5 4.7C 3.4.: ? 1.D t4. BB; io7;':ti 125;''

Siiicon nitricie 2\73 2400 691 i6.C 9.85 13.9 i 1.3 9.88 3.7657.9 77e 937 1063 i i 53

Suiijr 3s2 zgTa 7c8 0.?0s 0.1.4i 0.165 0.iE5403 504

!= i 3 !: lu lJa ti D.! I0.2 6.6 4.7 J? 68255 274 . ?e'r 295

ihcrium ci!cxida

,-, tr' lii:nlU,Ti,ClOXlCe,,' Pc!1'cti5tdiline.r '

2i33,..4157.-7't0, '.,.rr. , ::. . '.,..i ., i' .':

23 of32

600400

',.',.''.i

Preperiies oi ouiiciing inaterjais (ai a'mean

Thickness, LThermai

Conduciivity, iV//m . K

SpecificHeai, c,

R-value(icr lisreri

thickness, L*),K . rn2,'\ry

Density,lr o/ir 3il,iaieriaI

Building Boardslsbestos--cement boardGypsurn cf piasier board

t lyliood (Douglas tir),

insulaieJ boarci ani sheating(reguler densiiy)

Hardboard i ;righ densi i-v. standardiempereci)

Pariicle boarc:f,4edium densitirUndei.layment

V/cod subfloor

.K

6 rnmi0 mrn13 mm

..,o mm,lOir:nm.13'nrn;,zu mmi3 rnm20 mni.

15;n.,20 mm

800800

Proper-tie-s of insuiating m=teria ls(zt a niean tenoe i'aiur: of 24'C)

li ateri a IThickness, L

mm,

TherrnalDensity, p Conductivity. k

kglr-n: vJ/m . K

R-valueSpecific (tor lisiedHeat, c, thickness, lv?),kJikE.K K.rn2,'!!

Blanket and EattMine;'ai iirer (iibrous fcrrn

crccesseC irom ru-*k. slag,cr giass)

Sprayed or Formed in PlacePciyuretha;re ioamGlass fiberUre'rhane; tv,,o-part mixiure (rigid foam)Minerai vrcoi granules r"ith asbesios/

inorganic bince:'s (spra5'ed)

Lirose Fili:,,.' ., "', '.-'.,' , .;;;;i'iit;,..r,.i&,'srul, or sr;ss) r ',r l:'..;

Rool InsulationCellular glassPraformed, icr use above deck

50 to 70 mm 4.8-3275 to 90 nrrn 4.&-2?

l.35 tc 165 nrrn 4.8-32

0.7 i-{.960.7i-!.960.71--Ct.95

fSrn*25 mm50 mm

?4-4C A.C2-3-C.O265'c-72 0.038-0.0397C q.025

l.:90 0 046

I Q'a-2;?'^: ) ^--'.;;

l AA o.058 i.uta,

?.!J.>

*to.490.93

26 of32

L.z5I.94

i

I

I

I

i

I

i

, ,'';..'-.'.,'1'. t '.,'-, '1,,'.' i.,r'i:i,.r; ,: : . r: .,:...- .i -... it i rr

','-! 's, ii'; t i_ .

Frc,eenies oi miscellaneous maieriais

ScuE€': aoriioiisJ ircrn variilus souic-

lues are ai 300 K unless indicateci otheruiisa)

Thernral

Delrsity, p CcnCuctivit-v, fN.iaierral 'lJim . K

2325

2645

,: , ,,.tr.i:.

SpecificL{o:i r

.i\

ThermalDensity, p ConductiviiY. f

\{im'K

Speciiicl-.lc=i r

.K

i.0i.i!.i

1.4 is2s1i7L'1845

1 i0c

- ea e

..,.t90.:' ':",j'500'r :

;'1500 '.i, '

:1900'" ' ;.1 OUU

0.i30.i6

v.z- : .v.U.OU

't''t "

il''. !.L

'1.0,

ri.35

201 0

800.

1900?204

ri-,';.1 :, j':.;,ii; ::'.1 550i4951350

I _1UUcb

i.40.048rJ.UD

0.i7

=A'- n lC42A 0.14i45 0:05

27 of32

Clay, dryClay. wetCoal, anihraciieConcreie istone

rnii:)uOrX

Cottc'n

LexanNylonPoiyprop,vlenePcilto-Ei.tP\tC. vinyi

PorcelainRub'ber, naturaiRubbp-j, vulcanizei'Soff :

Hard

Sugar'l'issue, human

bKtnFa: iayerL{ usc le

Wood, racialuai(Fir

VToo!, snip

'r' ' '! tr.: nih. : ', ;,. ,. !LJv- r.

li_ !-r. - ...r..: 1.

-, -

1 lou':2AO

910I. JYf,

ZJVJ-i ttru

o.i9c.290.i20-i50.i

c.2a

-s(-t -TftbLns^

Salun1iorr iiersityFstr: p.{gjT:P*,, kPa L:qlic ,|aSnr

Enrnatp.J Speciiic2i Heat

Vapcriiaiicn i, J..l{g. K0ynamic Visc6itv

a, lrgm .s

. \bluinePErCt, EtpanstcENumber C'--tiicienl

Pr p, vr

ThemElCancir'.ivig.

k, Y#n. K,1!,kJ/(e Liq'Ji6 V5ptr LicuiC VaDq Liquic Yeoct Ucuid 'J:Fn. Liquid

o.o:

.ic,:5

:5?c

l.i Uf, 12.331J. 1b5

ilu I?490

j. ir

4217

4!:.4clE:slSa4l a0

t e5.1

I e62t gDi

L5 IUta/J

c.t7tc.58Cr.589

0.O17'r

Ii )9.45

I.00i.G0L.OC

t.0cl.oo

9?9.3 0.cc'.18CCQ a. n .'ft?

999.i D.CO94cqa I n^!rccs i n nr:=997 .A 0.o:3:

l.?9? :r !O'!I.5i9 x l0-r1.307 x i0-t1.:38 x:t-tl.O0? x :0-:0.e9! x '.:C-l

n c?? r 1n-:0.934 x iD-:0.966 x i0-:G.959 x i6-:L'1.9;3 ;{ !D-30.96;- :/. -:A'3

-C.065 r. i0-rt.,315 x l0-rc.:33 x to-:0,.135 '^ l0':n:CE.r' 1.,-!

0.:.a: >: lO-:996.O +tta z4.673 C.0!9? 0.i?D x lc-l l.Ci6 x I0':

x t0-:4.8.3 l.D0

I 0r-r

l.cor-00:.cot.00: .0L1l.cG:.cGf.i)D!.0c:.co:.or)i.00:.0c:.01!.o?

r.gf!.07i.uv1.tl

!.21I --

i.49

L.a i?.!3Ji.7 -i

o.::.j7 x lu,u? li : n:: ./ i ^-!

f,_l

ED

,-c

SDE5

tii3cICI ial':30

:40r5cI ni,

r8G

?CO

?2Q

ZiU2ZA?ta:20

3 r- 1.14

t 2.35! 5.;5! 9.9425.0:?-:.'t'!3.3.,i517._39

:i E:

44.5 3:tJ ! 3:!73.2ii _r5.::?iQ.'!

!7 3.6at /-57r!.i

i.o.1?.!i.2i1.4

.i,c€

6.4 i2ts :A:

:l,z;+i 4,5e'5I J.D3 I??.cr90

9e-9..i c.oe:ii1t< i i r.rc

983.3 0..r3c4980,4 0.15139i;-.5 O. f 9e3-.7a.7 0.:.12:a;l c n ?cr=9e€.i i.,.3:36o;( : n j1a=n6) i n i.rr:ii? c n E3tc

350.6 0.326r?s43.j ).!2i9:4.4 1.426

r16.6 2.5469C,a : 'j.71.,ee7 .7 4. i l.;e87.S 5.!53875.4. 6.i38ocs.J ;,cale40._? ! 1_5CFtr T 1< t:7e3.7 ?3.69:-;i'I 2 12 liil3.a 4€.15567.: 63.576i0.5 92.6152Ei i44.0J:i7.0 3:.?.C

c.o?o43.O20Scl.O?12o.0?150.o2?1o.02?5c.0?.3i)'.t.u1:J

'o.ozJir

u.vlEzt-t.u! ! :o.azeec.c3c I

o.0.3470.o35.1

c.a40t

0.0487c.0540v.uouf,u.ubvfn nts:-.i0.t:o

0.599 r t0-:c.547 x lc-?9.504 x lC-lc.46; x lc li.433 x tC'li,4a+ x !?-,C.i73 :t 1g-tO.355 ;i lC-rC.333 x l0-t0.315 x lc-3C.?97 >r 19-:A ?Rl'r tn_ j

C.?55:< 1g-:o-z3z x r-0-r0.?i3 / I0-30.197 x :.0-.r0.183 z-16-:0.1 70 x. :.0-:0.ltlO:< 1P-:O.l5C ir !0-!0.1.i3;q 1g-rC..134 z :.0-rc.Ie2 x i0-:0.il: x lo-r0.1o2 .{ 10-,0.094 x l0-:0.C86 x 1i-,-0.073 x lc-lC.C;C :< 10-?C.O50 x 1g-:0.rA: x lo-.!

1.0a6;,. l0'3':.O6? v lC-t!.c77 y to-51.C9_? x l0-::.ilo z lc-t!.i26 x to-!!.t4? x. to-,I r=O y r.,-3l.l7i: x lO-:i.t93 x 10-:i 21n Y 1n_:i.??'i x 13-ii.2E: x 10-:i.?96 x lr't-:1..330 x 10-:l._455 x 10-:1,399 x tO-51.434 x lo-t1.45e x i0-51.5C? >:19-s1.537 >r !0'51.57i r:1C.-:1.6+1 x 1g-:1.712 x t0-t1.7s8 x to-51.87C ,( lC-:i.s65 z !o-!2.C94 x !0-s2-255 x 10-5Z.i7! r. !C'.4.31: , ic-5

0.a31 x:c-?0.434 :{ l0-?0.517 Y !0-:0.!a8 >z 13-:c.578 x !0-:0.6t7 ): !.0':0.653 x.'f9-r0.670,. IC-l0.70? ...i !c-!o.7!6 x !0-:n )qa \ i-5n ?qF v la-tn qq2 v r.-3

9.5i3.{ i0-:c..97C :< 1C-:| 1t< v r^-!

1.1,15 x l0-1l.i?8 x l0-3l.?lc x tc-:1.280 .\ l,J-31.350 x lt-ll-52O x lC-3i.7?0 x l.-1-!2.000 x ]0-32..3E0 x io-l2.94.0 x lo-5

J.)5

?.71J.f::.3S?.22?.oB!.?6i.e5:.,::.Jd1.4i

1.24t.rct.D91.03

c.983c.947

u.6t5o.9360.9320.85.1

'J.-aA?1 4,1

Z.UO

15!>

llD:?34S!3342.32 i

?2E13

??7d?2172?30zzei

2l!<t-'t4.489.o.427

l€i€ i" K:n:traib visc:s;i-v I 3r!c ihemal rJih.r;iviiy c can be calcutaled t,om ih3k csiinirt.r rs, v * p.p and d - Htrcn- y,?r. The ,"oJlli=a El-3nd.?74.14.cara:hgirio|e.,boi|in€.,anccr.tica|.poinireriFretJ,esol9/alel''esp€cii.€i},-T;spro;rihs|6tecabo/3(exc€Pt.!1e3ny prsssure :{'iL\ ;iegligi.ble errci crcept ai tsrirersfurgs nea, il3 Crttis].pini r"lug.ilcie i: The unit iJ,"€ . '; icr slr.iir heet;s ecui./aie.i ." kJ,*g. K, and i.!r. untt !1rlrr . "C ,cr ii€finat conduc.J./il-v is 3qui./algnt t" w.im . t{.Ss.jr.*. ',,fsccs;t/ e nd ihernal ccno'u:tvii riii3 ar: frcr,1 j. V *ng3rs acd J. T. R- $;:lsrn, ]icu'.'l?l o! ?hi,s:cei an.j Chenica{ Relercnce Dziz l5 {l.986},:.i. i 29:-i:2". aJti,gi i;.ia 'EE octaiieC frcm ecicus s,:urcas o( ;iiubf3d.

28 of32

I

'

i

!

I

/+Aul+ -TABLOJA

-_)

29 of.32

Emissiviiies of sUr-iaces(a) h,'ietals

Temperature,n

Temperaiure,K

3C0-50C3OCL4OC

30c-2000OULLdLJU.i

3O0-1000500-i000600-io00

30c-500500-1 20GJUU300

Emissiviiy,

nrrant^,u,v.,-u.ti0.09-0. t 2

0. i 7-0.300.3c_0.400.70\-0.80

0.08-0.14c.2,}-o.32

0.c5

Aluniinum' ,." '; ,: -. ,'.. j'','Pcrishbd. , :5oo-gcio;',i,.Commeiciat Sheet "' . 400 '

-;,,'t ,,, :" - . .., .;.'

Hsavif;e'oiidizuq ..,,': , ao0-800'r;i ,Arioc'ized'. ' ,, ,.. '' ,.i,300-, ,,,"i,,,,,'

E;smutti, brigniHr:

Inissirities ol- sunacrs (Cinc judzc )iDi Nonrneials

ilaTeriel

Alun'riaa

.Alurhinurn bride .Asbgstos , -: !"isph3ll Davament.

a ) 't.Comn:nr .. .iiireil:.y ' ;

C€rh:n ?-ilar:ren'rClothConc:e!eS las:

$lindcw

Pyroc:ram

" c,5:-r1:45,'

', u.9:J+C! +i D.gE -,ri ..

u.5:{.:J'. :. ,. .. '.!'. >-LU.vC'rrt:7i .' ' '

J.; )-t.=tJ0.88-C.94

0.82-O.52u. r:J-r.3,'c.95i.99ri.o:Ji.::. .c.80

'0.i10-4.:O

9 9t ,. ^-". -u.54{.ytr .0-9i' r'll .,g.99': ': ' t'

-

o:90 j; : '

; attr, r,'hriePi?ster, wililaPorc:iairr. giareiQJari:, rcugii, iJseJ

t.9L-)

c.?z!).920.-53

u.v5

'U:YU

u.o/-u:5tr, u.:3' 0.8CFC.93

n Q=rn qR

c.85-C.:12u.v:tsi.:o

j.9cii. yu

TemDeraiure.ii

3ot-14oii,

3CO, ',r3C0 .,

inisivity, 'i:mpera:ure, En':is,

=

'-

ai-l{i{

€.e E a! 3lr = - ;.= r-i==9€33E.I=a5

;l=!9.=;3:Ez7?1+44i.=F3-'i);,3ai7ai

4

f

ehciilsn-?

.= ,'Jl_

qa€

,r1o::e: uortlu; ./crzq

32 of32

E

d

o

tr(J

1.0

0.9

0.8

0.7

0.6

05

1.0

L! 0.9a

J 0.8=

F

Q 0.6

0.5

"'35ffih1?u1',P1.0

0.9

0.8

0.7

0.6

0.s t o.t 0.2 0.3 o'4

6

o

3)tr

O

0 0.1 0.2 0.3fr I r | ' l"_1,0.8 0.9 1.0 e=7:-i,

l-'l ,l

jlr{iqt i !o.rr. gaa( lerr

ti--Fo.z 0.3 o?- o:- fi- fi o't o e r'oI 2, etc. (any ntultiple ol' 4), tube passes

-

11

ffior='{}ffi^ I..t-,,ncaittl! QaYo.T

okrl

1.0

0.9

0.8

o;7

q

dE

't

toU@

Correction factor F charts

tor common shell-and-tube and

cross-flow heat exchangers (fiom

Bowman, Mueller, and Nagle' Ref' 2)' +-L g,crflt I

a rmq

R=4.(tl

3.0I

tnI

.5\

i.o b.s-b.or\t \l N 0.4 _0.2l\

T):!lr- ttrl

0.-s 0.(r 0.7

2;c,6

-t - l--t+ -t--..1-]-+F-F4 = 4.0 3-O 2.1 1.5

J\L-\=L\:Li rr rr r r) 6 0.40.2

T, -7"K=:------r f t'

I:

)

.o'- i.or I ll

i.0_1.5\ l\ i$Rrl'.r''ilr

tl

It=3t2 -.o l

ttl

ri = h.ortl [-Tii ii-] i bdlp p'\l r \l N I l\ l\l

-0.4l\-0.2

l\

o_ | -- 12-'l

ttl

ff;;,;;u*^ aryr) u-qrffi-1*-qdfra"nsl I i I ll I ll I-lI r-l- I -L '-'-" -'-

-1.0 ,,-'fi' 0 0.t 0'2 03 04 (,t) uo w't

(/) mfrrra/

Effectiveness relations of the heat exchangers typically involve the dimen'

sionLess group UA,/C,.,n' This quantity is called the number of transfer units

NTU and is expressed asUA" IJA,NTU=^:^Lnri,r (rILl,r,nirr

( I 3-39)

where u is the overall heat transfer coelficient andA, is thc heat transl'er surface

area of the hcztt exchanger' Note that NTU is proportional to A". Therefore, for

specified values of U aticl Cn';,,, the value-of NTIJ is a measure o'f the heat lrans'

fcr sttfuce area A,- Thus, the larger the NTU, the larger the heat exchanger'-

In heat exchtrnger analysis, it is a|so convenient to dcfirrc ano|'her dimen-sionless quantity called the capacity ratio c as

Cl'niu (13-40)(r _ Z:-

It can bC ShdWRTI1aI the el'tecfivcnc,sstf a-hcat.e'xchttngel' is a-futretion ot{he-

numbet'of transfer units NTU an

j jo:irl-^ o\-Y-

,u

I Shell tluidI

100100

3eoo'E

+o,o

s6 -.,oOU

'3 +o

,9

r00

80

t234sNumbel of transfer units N'l'U = ArUlC^in

t2345Numbcr ol'transler units NTU = II,UIC,,,,,

(c)c@

12345Number o{'transl;. on11s SftJ = /"U/C.;n

t2345Nunrber of transfer units NTU = ArUlC,ntn

I v 0.2:-''*'E.)

0.7:1.3:

/72Mixedfluid

tjnrrixed fluid

Vltg

I

t2345Numlrcr ol ransf'cr units NTU = r{.U/C,,,,,,

(/1cffie

(l) T.llt=rhe}Fflswand 4. 8.t12. ... tube passcs' * A""* S€e{rl Iil^iffi

2345

I | '-o\ --[t#rt /l/ | v-2'ffik/7

Shell lluid

+I

100

80

oOUo3 ott

'8 +o

,9)

20

bS

joooI

e

t{tr {lc{ -trTLantrl I th*l*sglgg*-tt*,.'6"-* A'f' ."#3-r*kSress

ror n*, *";;ffi; otm.{

8i otrtknn,^ L^"qt'q'c{W cok'at V*t'n fcrtlana drlr

QAP rat eilLtX

j 7 v6f$-'nT

Shell fluid {.1,

tl [--+

'_a

TTllllt'Frrhp f-

;'::;; -. --*-----rI

Nurnber o1 transl'cr units NTU = A"U/C,,,;n

rS

at

,st

u]

!

ffii'i;,1':,,...;:,i.'l;''..l::'.;..,ii'i;.1ii;.1.ifi;'.;.....'u.,''";'i.i..it;i*|'.l....1,i*i,Nl'U relations for heat exchangers NTU = lJAslC,n,rand c = 0,n,,,/Cu.,,, =[ilCtJ!!4i1ct),,,,,, (Kays ancj LoncJon, Ref . 5 )lleat exchanger type NTU relation

Double-pipe:Parallel-f Iow

Counter-f low

Shell and tube:0ne-shell pass2, 4, . .. tube passes

NTU=_

NTU: I rnlc-llc-l \cc-1/

I+c

NTU = ---L rnt/7 + c23 Cross-flow (single-pass\

c,.. mixed, NTU .., -," lr .* In (l - t'c)l0.-,; unmixed- "' ll -' - c : I

2lt-1-c-t/T:lE2lc-t -611.2f1 c2-

r',_l,l -4_l gll

C*. unmixed4 .All heat exchangers

'ir,'lfh C = 0

Ntrr- In[cln(i-c) +l]c

NTU=-ln(1 -e)

Note that rhc rclations in'l'able l3-5 rr.c cquivalenr to lliosc in ?rble i3-4.&,Lrth sels,r'rf relations are given lbr convenience.'rhe relations in T,rble l3-4

.: