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AIN SHAMS UNIVERSITYFACULTY OF ENGINEERING
NEW ENGINEERING PROGRAMS
Heat TransferData Book for Manufacturing and Material Departments
Prepared By:
Prof. Dr. Eng. Gamil W. Younan
Eunwction,ri ii.,i
*'t,d
:.
1ffi
HadialionI
f uniform cross-sectional area
)t:irl
*!*Heat Transfer From Extended Surtace (Fi;, t
'T'' lt
/// 9conv
_tD-I
P=2w+2tAc= wt
'(a)
Tip Condition(i=L)
transfer:hfu(L) = -kdeldxl,-L
Adiabaticdlldxl=r= 0
Prescribedtemperatule:0(L) = 0t
Infinitefin (L-+ oo):
A(L) = g
0=T-T*0o = d(0) :'l',,- T-
Ac= nDzl+
(b)
Fig-3.1 Straight fins of unifonn cross section. (a) Rectangular fin (b) Pin fin.
{ 2n'/ f''wThe differential equation for the temperature distribution is
d2T 1, \
= -'mz(r -T*)=o
dx'and tle general solution is;
e=@ -T*)= rF-* * c2€ruSpecific solution for different boundary conditions are given below;
Table 3.4 Temperature distribution and heat loss for fins of uniform cross section
Fin HeatTransfer Rate q,
A Convecdon heat sinh lal + (fzlne,t) cosh
TCase
cosh rnl + (h/mk) sinh
M tanhmL
(cosh mL - 1) ,0,.tirl, *L I
e,
b:![i-.]
nf'= ltP/lA"M = \/tF6"0,,
cosh'm(t - r) * (hlnk) sinh m(L -.:r)cosh rnL + {hlnlk) sinh mL
cosh rn(l - x)
cosh nL
(Br./0r) sinh mx * sinh m(L - x)ff
sinh rrzl
iil lt1t:t.
illl
*.L-
Tlre foregoing reslllts are stllnularlzed in table
flinction is provided in the tabie 3.6
Tire hvoerbolic functious are defiued asrL
/ \
sinlt x-%l.u'- r-*)/\
cosh x -%tr' * u-* )
3.4. A table of lryperbolic
r-li,t
iI
I
t.:trtt-.*kii
i,lliii:
ex - e-xtanh x -
ex' + e-x
Table 3.6 hyperbolic functionsf?al
H
F:j[']
,
sinhx cosh r tanh x sinh r cosh.r tanh x
t
f'r
I
r.Cl
[.;
tt
i,
0.00 0.0000
0,10 0.1002
0.2a 0.2013
0.30 0.3045
0.40 0.4108
0.50 0.5211
0,60 0.6367
0.70 0J5860.80 0.888iD.9D )..D265
1.00 t.17521.10 1.3356
1.20 1.5095
1.30 1.6984
1.40 1.9043
1.50 2.t2931.60 2.3756
1.70 2.6456
1.80 2.9422
1.90 3.2682
1.0000 0.00000
1-00-50 0.09967
1.0201 0.19738
r.o+s: 0.29131
1.0811 0,3:7995
1.t276 0"46212
1.1855 0.53705
1.2s52 0.6043"1
1.3374 _q.664M1.4$1 Dl16i$
1543t 0-76159
1.6685 0.80050
1.8i07 0.83365
1.9709 0.86172
2.t509 0.88535
2.3524 0.90515
2.s77s 0.9216i2.8783 0,93s4i
3.107s 0.94681
3.4177 0ss624
2.50
2.60
2.70 -
2.80'1.9$
2.00
2.10
2.20
2.30-2,40
3.00
3.50
4,00
4.50
5.00
6.00
7.00
8.00
9.00
10.000
3.6269
4.0219
4.4571
4.93'10
5.4662
6.0502
6.6947
7.4063
8.1919
3s53<
i0.018
16.s43
27.290
45.003
74.203
24t.7 |s48.32
1490.s
4051.5
11013
3.7622
4.1M34.56i95.0372
s.5569
6.1323
6.7694
7.473s
8.25n3,(H<
10.M8
16.573
27.308
45-014
74.21.0
24r.72
548.32
1490.5
4051.5
I 1013
0.96403
0.9704s
0.97574
0.98010
0.98367
0.98661
0.98903
0.99101
0.99263<.3?3?<
0.9950s
0.99818
0.99933
0.9997s
0.9999 r
0.99999
r.0000
1.0000
1.0000
1.0000
t.:.:ll rlt:.i
L-. a
E,il-: IL,j
t' :!it-_
{,.iB.i&::i
.J
liin Performance:The fin perfonnance inay be evaluated by one or
More of the folloil,ing parameters,
a)Fin Efficiencv:
4.f =4y ay
ir::
t..iemox lrAf9bWhere;
Q f =Fin heat fransfer rate (Watt), take from tzbl,e 3.4 l
A f = Surface area of the fin i.,
The efficiency and surface area of several common fin geometrics are l.r
surnmarized in Table 3.5 ,, ,
Table 3.5 Efficiencv of common finS-t"ieht Fim *.t rgrt*
*:P L+ at tI?: 2(w+*) 'Lr : cotected length
=Lrrz E frp rhtS.t"tgnt ft,A1:P L"P:2wL"=[L2 +(t/2f lttz
Circular Fin (annutar fin)
Af =2r(r!"-r? )A" = tr({lf\* t,rg/:f2"=12*(t/2)Ap = 4"t *8,* *rLo 9z
A _ tanh ffiL",, i
-tJ ffiL"
or use Figure 3. I
I
?tf + useFigures-i,Tl-
I i-.i
Pin Fins "" Q^rUn
Af=nDL,n
L":L+(D/a)
4f * useFigurc?o
l/o a(,
tctrth ntL
IlI
I
a-'i.
I
i
ffiL"
bQ
['',f,
f,I
f'rhE&
l"'"i
,t '
|..^,t:1r.1i.t
itit
r:?!-:iF,,3
i
riF-r
L:;
fi ';T
i
$,
d
ft-,i
I;E
L:i
r..]hiEt-
;.-
r"lFJk*,')
f-lL,
f;.,
Lii-
tI.i'', .-
1:tit
l-it. ,r,
I
E':!:,'lljii
^l^L'
Real fins (convection heat traFor real fins the frn efficien cy, rl f ,may be obtained from the following charts;
fitz g71plo1ttz
Figure 3,1 Efficiency of straight fins (reelangular, triangular and parabolic profiles)
r00o$fr
BO
1f;tzg4aer\atz
Figure 3.2 Efiiciency of annular fins of rectangrlar profiles
,,1
W*,,
Lc= L + tlz
,o'EIbr+t*l
*
Lc= LAu= I1l2
= 12* ttZ=L*tl?=L&
+
l;,
-g--
*
f, f = -If----={.from thabase withont fin
For single fin
€.f =4",6h 07
th: Vr*4rxt.o+Ab:AtxTltXhoxN
At= Ab+Af
4t: Ttr **tr- ar)
rII
Qno,fin
x n,]ru
i
Fi
(i*l
Hr
Wherc: .4o,6 is the fin eross*ectional area at the base
Ar,6 = Wt !-or siraight fins,(rectaryIrlar fin)
A",b = 2r r1t For amruiar firL ffid equal n D2 / 4 forpin fin
8l =Fit heat transfer rate
For multi fins:
i:::.;
[r:;
f:i.li
L _.*l
G.tl' -'-+ tYa o__4MAA/ le
%
l:r.'lI,J
i:ll.':
:-_}.i
4J
l:r.i.
1=
hi
-d
PI,.1
Jr;CY:
^lL-Irlllt,,al FixllF lr
_,: IrES
:ffi
f',:t5
r! -aiF-fta;
r.r.it.:lF'.-,t:
f':B
f't-[.
fi{iF.
rTE:g,,
('f->E:-r
[ii[,iitn-j
(:Fe
L.it
t.:E':F";
0.05 0.1
Po=*(2L)'
' Ternperatue For Lrfurite P[aLe of Tluckness 2L
And Diurensionless I{eat Flow
Wirh Strclden Cirange of Srtrface Tetnperatltt'e
Onelirnensiql - Transien! - Iufinite Ptatq (Slab\
1i
i.Irr&E
II
I
1'=
[-...:F-!:;
lri.
[-;B:.'.:
f?l::li:
oA'
Eo..
t\a
oE-xE,
C}!,Ct
ELo
(EEEE'
oD5E'o,ELECt
oEt,CL
-t
=
exIoooN
=e8oEoF
eo
o6t!.6lt
d Ell \)a
N
doN
===
l: r.l
ft:
Q ts h( n d - r 6s a N -=UU;'3: ;H4EHE EEEgEE E.tt t o oo o o o o oo o c 6H IF-_ rlr
E 6."1N-U
tsl 'r
c.lo
qqacn---E----E------:loocjdaJJ
i'li'r-"ll.,.-
iii
I
0)
A
/1
l
-:_i
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li-,\
o6N_
N/II
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0 Tr,. - T-
0, To,r -7, " -
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0.6
0.?
I
0.9
0.8
0.1
0.6
0.5
0.4
0.3
o.2
0.1
I 20 30 50 100
kli;T = Ti
1'emperature distribution in a plane rvali of thiekness 2 l,
t0-2 l0-r I
It'oT-u. tOk'
Intcnta]energ},chaxgeaSafinctionoftirneforaplane\\,allofthickness 2L
tor l0{
ffi
-7^
-58;:3 ;E5.43H E^QEqi i q-sr-s - o co o o c-lsrlr
^ . !1, -d HIF
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I?:]
fi:l
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ono
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or
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='ElC'
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l
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€Y)o 'c;
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il:,,!::.1
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0.8
0.7
0.(r
().5
4.4
0.3
v./
o.',
0
I
0.9
0.8
0.0r 0.02
k
: Ternperature distributi"r'#L infinite cylinder of radius ro
to-5
oo.
0.7
0.6
0.5
0.4
o,3
-0,2
0.t
0to-ll o-2lo-j
If crit = Bi2 Fo
' Irrtc,ural er)erlr5r change as a luncion of timc for rut inhtrite c5r[l1t6.t nt
radrus l'o
t\-r8o
;;:l,t\
i':l
{'ti\a+i
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r6!oNi q gq q q-, o oo e o
stlr-ltlr
r--'1r.,-
I,.trl'lt*,
- r hs 6 do icj i e;
q q e-----F-----=---d; E E
:1:'r-..'!s'-
0.20.t
0
, rli
ffiFr&,.t
ctf.k5
ft$iE:4.7?,:
**.:U ^1"E, '/
EBJDIL/
B?i"4
F laE;"E ,:-
2gn--E-i:-cha^
! li-l. i-li E-:iv
=,f7-:sliE*vr
UrS*5rgi plE+.-.CJ
e-uEd- <jgl Ct
iEi*:_*(."'
a"Eqto&:\'B} J,s:E
ffilE#ts@=
'.-<(":l:laniga
E1E._E, lu-;
€i-]F-;
E*
6'lISrL,'
f-ltr!*
*x:Ii?q;,j
f..*righ'-,
*i2-
A T,.o- T'od-=--
0, Ti,r -T-
0.t
00.G r 0.02
I
0.9
0.6
0.7
0,6
0.5
(r.4
0.3
0.2
0.1
0I 0-5
0.5t2k
hrn
Tcmperahre ciistribut-ion in a sphere of radius r.,
l0-? l0-r
,rtr = Biz Fo
function of time [o': a spi)ere of radius r..Inlenral enerry chutge as a
t
FA
r00r05!10t 15r20
t?5l]0i35lc0145
i 50 4.760160 6.18.rt?0 7.920t80 r0.0Jt90 17.-55
15.5519.0E23.2021,9833.48
19.7846.9455.0564.r914.45
8S.92I i2.9146.r186.7210.5
! ,at-luarl t0-1(mJlkgl
*/3-'
t157 8.49l50l 8.66t3C0 B.8lI t36 9.00100? 9. I 8
890 e.3 5
191 9.527 t8 9.706s r 9.8?594 10.0
544 10.250r t0.4461 10.6430 10,?400 10.9
3'14 I l.l351 ll.3330' I 1.4
3)l tl,6294 I t,8
719 12.0265 12.2?.52 12,424t 12.6210' t2.8
?20 13.0? il 13.2201 I1.1195 I 3.sl8B t3,7
r8t 13.9t 69 14,2159 14.6r49 l 5.01.1 I I 5,3
l14 I 5.7127 16.0r2r r6,Jll6 t6.7n r I7.lr07 t 7.5103 t 7.999 18.396 18.893' 19.3
90 I9,8
tPr)y (Pr\e
r2.96 0.9710.92 0.969.29 0.96?.99 0.966,95 0.96
6.09 0.965.39 0.964.80 0.964.30 0.96j.89 0.95
3.54 0.953.23 0.957.91 0.9s2.74 0.9J2.53 0,96-i:16
o.e62.20 0.962,06 0.96r.94 0.951.83 0.97
1.73 0.97r.64 0.98r .56 0.99L49 0.99t.{2 r,00
" r.l5 r.0lt -3 l t.02I .26 1.03t.zt 1.04l. I 8 1.05
I . 14 r.0?1.07 1.09t^02 l.l20.97 r, ! 50.94 t. r8
0.91 t.220.88 1.250.86 r.280.8s t.l I
0.84 r.l50.85 t.390.85 t,430.86 t.4 ?0.88 t.530.90 t.60
0.94 r.70
i,i.i.;::
Saturated Water aud Steamr
f--.
t.:4
l,.;
B
F-,i[]:'[:,
0.015
t0t520
25il0
3s'6045
JO55606510
)58085909s
0.006u2 0.!00020.0087 r9 0. r00010.0t721 0.100030.01?04 0. t00t00.0233? 0. 100I I0.01 r 66 0. r 00300.04242 0.100440.0s622 0.100600.073?5 0.100190.09582 0:10C99
0.1233 0,r0120, l5l{ 0.l0ts0.r992 0.t01?0.250r 0.t0200.3 l l6 0. r02l0.3855 ' 0.t0260.4?36 0. r0z90.5780 0.10320.?0r r 0,1036c.84$3 0.1040
{.210 1.864.2M 1.864. r 93 1.864.186 1.874.183 r.87
4.r81 '1.88
"fiT19 l.8s4.118 l.884.1?9 1.894. 18 r 1.89
4.182 1,904.183 r.904.tE5 r.9r4. 188 1 .924.19r r.93
4. 194 I .944-198 r.954.203 r.964.208 t.914,2t3 t.99
4.2r94.2264.2334.2404,248
1.264.214.28.4,294.30
4.3 24.354.384.424.46
4.514.564.634.704.18
4.874.985. l05,245.42
5,65
569 16.3578 16,7587 l?.1595 17,5503 r 1.9
6l l 18,3618 18.75ZS 19. I
632 19,5638 19.9
643 20.4648 20.8653 2t,2658 21.6662 zz.9
666 22"56?0 22.9613 23.3676 23.8678 21.3
68 r .24.8683 25.1684 25.8686 26,368 7 26.8
2.321 0.10652.10t 0. r0703. rJ I 0. 10753,6t4 0.10804.t55 0,1085.
1.01325r.208t.4311.69 l!.985
0. lo440. r o480. l 0520.t056o.t0&
2.0 r
2.032.052.07?.09)t1z. 152. rBz.2l2,25
2.292.-'r$
2.492.6L2.76
2.9 t1.073.253.453.68
J.944,224.554.985.46
6.r8
68?68868868868?
21,321-828.128.829.4
0.lo9i0. r t020.tIi40. l l?80.i t42
0,r 1570.1 1730. I 1900,12090. r 229
0.125 Io.t2760.13020-1t320. I 166
0. r4G{0. l 4990, I 5390.18944.2725
0.3t7
Ttc values lur saturatecl v/E[cr can be used with good accuracy above sBturation pressurc' Thc valocs lorsaturated srqam cen bc used ,with only rnodcrare accuracy bclow saturation prcssurc :( temPeraturcs
BJeatcr than 20O "C.
68? 30.068a 3 l.l68 I J1.6616 34, I61 | 35.7
665 37.5651 3e,4648 4 1.5
639 43.9528 46.5
6t6 49.5603 S2.8s89 56.6s14 5t.0558 65,0
54 t 72,0
L'.'tb."-:
la,j'f-:,1tii
II
2002t0220230240
250260210280290
300320340160370
3?4,15 221.2
l,',f,,-
kr k,
1s-o(kW/m KI
Pr
t7520022stJ0275
300325350375400
450500550600550
fse':BraE..,
tr.i
L;
Ffr:.E(s;
6is-ip,:
[;
B
;9"r, &-.:
ffi.B
iff'8:.!E:(&f
#",T_-{:,
f-;*-:fi- r
&i
ffiu
ffi
E€aFiE
B
r0=1G/*!k
l0-tlkW/m Kl
at I 8impv
IE/'.ti lo-t,r'Al
iri*,
7m7s0800850900
950r0001050r t00r 150
1200r 2501300r3 501400
t5001600l?001800
i reoo
20002100220023002400
2500260021W28002900
3000
cP cv
]k/kc Kl- |
r.0023 0.? I 52 1.401r .0025 0,7 I 54 1.40 It.002? 0.7 I 56 1.40 t
I .003 I a.1 160 l.{0 t1.0038 0,7167 t.401
r .0049 0.7 178 't,400r .0063 0.7 192 I ..100l.oo82 0.171t 1.398l.ot06 0.?1t5 1.3e7r.0135 0.1264 1.30s
t,0206 0.733s I.391r,0295 0.1424 L38?1.0398 0.1521 1,38i'1.051 I 0.?640 1.376r.0629 0.7758 I.l?0l,0750 0,7879 L364r.08?0 0.7999 1.3 s9r.0987 0.BII6 l.l54l.t l0r 0.8?30 1..349
r,1209 0.8338 1.344
t.llr3 0.8142 1.140l. 141! 0.8540 !.336L 1502 0.863 t !.J331.r589 0,8718 1.129I.1670 0.8''99 t.J26
L r?46 0,887s l. j23t.l8l7 0.8946 1.3211.r884 0.9013 1.319r.r946 0.9075 1.3 I6t.2005 0.9134 l,J l4
1,2112 0,9241 l.3llr.2207 0,93 36 1.3081.2293 0.9422 I.305r.2370 0.9499 1.302t.2440 0.9569 r.300
1.2505 0.9614 1,298r.2564 0,9693.1.296t.26 l9 0.9148 I .2951.2669 0.9798 1,293t.27r1 0.9846 1.192
t.2162 0.9891 I.2901.2803 0.9932 1.289I.2843 0.9972 L288r.zBB I r,0010 1.287L29 !6 r.0045 1,296
t.2949 r.0078 !.285
2.0 r I 0,586t.?6 5 0.'I5 3
1.s69 0.9351.4i2 1.1321.284 1.3{3
t.t'17 1.568r.086 1.8071.009 2.0s60.9413 2-3t70.8824 2.591
0.7844 3.1680.7060 3.7820.6418 4.4390.5883 5.1280.5430 5-853
0.s043 6.&10.4?06 7.399 I
0.44t2. 8.2140.4 153 9.0610.t922 9.936
0.3716 10.830.3530 I l,?60.3362 12.720.i209 13.700.3069 14.70
a.294t t5.730.?824 16.170.2? 15 17.85,0.2615 18.940.252r 20.06
0.2353 - 72J60.2206 ' 24.140.2076 27.100. r 961 29.120,r858 32.34
0.{ 7650.16810.16040, I 5350. l4? I
0.14120.13580.r3070.r2610.r217
0.1 177
fl!{:t.,
6.1
SiiEY
frllIl
Thc vslues for cr can atso be used with reasonable (tcctricy tor CO' N,-and O.r'
The values of Urc rfrermodil;i; propcrtics ." ^"J f "" in. l6 and. i? are those rt zero ptfttYj:'-l:
valucs for thc gases Br€ quit; oacurut" ouer a urid. ron'g". of prcssure. bur (hosc for the vapours incrcase
appreciablY with prcssure.The UanspOn prqPenies U and t for air are accursle ovcr a wide range Of pressutct gxccpt at ruch low
pressures thar $s mcan fice path of thc *of""uies i. compeiaUte to (he distance betwecfl the solid surfaces
containiog thc gas.
Al kigh.temperatures (>1500 K for air) dissociation becorrcs appreciable urd-Prcs6ure.is a signi$cant
varinble lor both g"r., *i vspoufr: the viues on pp. 16 and 11 apply only to. undisscciated ststes'
r'lt. i
i:-f,
Dry Air at Low Pressure
1,182r.329l.46?1.599r.725
r.8461.9527.O152.rBl2.286
2.4852.6702.8493.01?3.r783.1321.4823.6241.'!533,897
4.0264,t534.7764,395'4.511
4,6264-136{.8464.9525.05 7
5.2645.4515.6465.8296.008
1.5931.8092.0202.22',12.428
7.6242.816
-
3.0033.1863.36s
3.7104.0414.3514.66t4.954
s.2765.5095.1146.0306.276
6.5206.1546.985'1.2;09'1.421
7.6407,8498.0s4p 1<1
8.450
8.8319.1999'5549,899
10.233
=:
0.1440.7350.?28o,720o.7 t30,7070.70 r0.5970,692 .
0.688
0.6840.6800-6800.5800.682
0.6840,6870.6900.6930,696
o,6990.7020.7040.7070.109
0.?l I0.? l30,7 I50.? l70.719
0.7220;1240.1260.1780.730
:
=
t
_,)
-.tF
Ain Sharns University
Faculty of Engtneering
MANF' 475: Flea t Transfer
t{qw Inginq.qrin g Prbgrarns
Manufaeruring Department
Dr.. GamitW,.Younan
FT
t**L-
Yr+.r= k#prun S.w*;
$-$*w *,\ffir*-)l
r._,*1 f.i,n.gj[H5
Correlatisrr E q ua{ioms f$ i Fgtcd$ Cqny$ctipm
.t={qi-f,,C-q*y:qtliptl,, $grr Eor$psE+te:g+t .FIowJ
&f,er&+Brblu irfor_v (l{e*S 5*lt)s}
Local.I*itrssslf }itu",rtbe!.0 Nur= 0,33? ]*.o"-'2 F""*.-,.. ... (_1t
j
Arreragie l*|usselt Nuwber, gurT th€6$ e"*oro t #., ,. :", ,..(X)
p.i/orff p-f,1"\\,'i.re re Re*:i t " .-)., P"=
-'pr
S.nd Nu" e
i.li pu*trr'ertias in Eq.{1) anrl (2) ale el,aluar*d at E'r&r: t?T.-
t1-.3'or fgrtulq*rt florv (Re" > g* t {}s}
j-,ocal Nussslt ariorber , Nur: 0.SZg R**ffi*F..ffi,. . ,,'..,.(3)
r!.yar?gs Flu$s*Xl',*uinb*i", Hu1= 0JB$? $de1a#.P, .-.(4)
^ 4.54 XoHy =E
Orn=#
AII i'l.ni*l prgrtrryrriex in Ecg.(3] a*di.41ere etra]uareqi arEl,rxes: ryG- Cfoes Flsrtl afier a singlfi cylindgr:
Averagc Lrlus.selr irufl',.hei', I\u1; : C.]l.e'i,F,,t*"..-, .(5)
v*Ii$,fbr 8,4,< ff*$ < d.*Hf/
&,ff
k
#**.tdi -i-'"
Irtl
.."*+iIt---t*i
-wlrer* g.":1*I={1 . p-:u ILCP""".1 \. E jrrrr K
tt^xAnd- Fitr, : :f
- t6'*
ou*xWhere Reu = ft, i
ttcp,PaTft.o
A:rd Nuu =?
All propcrties are evaluated at Tm6 :ry and C and n for equation (5)
Reo = 0.4--*--- 4--..---- 40----- .{000------- 40,000--:--. 40,000
C : 0.989 0.911 0.683 0.193 0.0266
n,: $.303 0.38s 0.466 0.618 0.80s
D- For Flow over-Electric.].lz,ire :
Average Nusselt number for flow over
An electric wire has dianreter d, is
Nua: 1,11 b Rt/'.Proj' t't'zs
p.u.d u.CaWhereRc6= ,Pr:--itrKh.d
&.1: l= TK
All properties are evaluati:d at Tmrl -Tj!:2
And values of b and n are evaluated as :
Rea : 4t|------* 48{}{i- :--?,. 4,{}.SSS**---. 4sr{}Sil
J-,T
L4To
l: {- I.:
b: 0u615 il;174
r r $.466 {i.6I8
E-FIow across R.anks of tubes :
Average Nusselt number for in-line
8.S24
{}.8S5
nJife
*lp*
And staggered arrangemcnts is : in Lne JubeT"'l
iFNtt4= C:Reoa6,P1'Q''. , ll
,o''o*e p".w
Where Re6=p,:.u,d
. Pr: &cP.Kvts r*SO*.s
dze P
h.d& Nu6: -;
All properties are evaluated tt Tm6= Tn's+T*
exci;pt for p," at T,v and the values of C in
cq.(7) arc determined from the next table :
-_=f-
I i In Line Arrangernents i Stuggercd Arrangementsl_---__1_-=*_1_ r __-_,__---_ *|._."-- __l- r__-.-*:I I I I : r r*--l--*._i i
*I-w'
+-l"e b*nK i
l r,,o i *,^ '!
,rs i ,o i ,; i-;r- l ,;; tt ;; i-;; i -; :
,--i-lll-!.r--;i ,.r, i r.*r* l n.*ro i u.*ro i n*r, l ug' l o.r, i o.rr, ! n*,r ii ,2, i n.*r* i n.*sn i o.*ro i n*r, I ug' I o.r, i o.*r, ! n*,, I
i i ,--
{ \/}!,/\, , w.oov j \r.t)JJ
l.rt.rtt l.u-r", ,, w.o/., I \r,otz
Ii-----r--__ I-"-___j _ | --_j
_l --i I __;I i " t i I I I - --T----li z.o i o.ot: i o.ors i oe:r i oorz i o.oao i o.oos I o.ola I o.orr illlir----r----i"--i-'--'-rit-- - 'i, -*l - l__ - i i-"---
*-l- ---i -_* -i --- -iI :.0 i0.42i lo.+zt lo.soo 10.s04 io.sss lo.s+q io.soo io.soo ii_jli--.1-l--"1"-i-'-1""""ir___r_ *f_*_____i ffi- j.
"*1,,,o As"rc/f^N Y! --i,*r bwre ad N"Jit*llobe nu*fu
flF.
F-rk-E;
fnE.E
L}
{1ui.f,!
f:
E3
f'.'t(:E
f)E-*
H
F]
&i
8,.
Eii&r=j
rl*-k
gis.-lFltg::'
,trR,E ,i
I,1
F};bls.
E
HE.
f?F,.$'lTJ
E:*FJ'E#
s'iIrtL..;'
[;tl
Eii"{&c
!.tE.E_ -it;#
*/8"*
ll- ror flgw,inside Ductsrl]steqlel.nl-otry I :
h,DNu =: f(*,e.Pr).K where }du: avcrage Nusselt number : T
Re= p'U'D
o Pt'= ry attd D: Equivalellt diameter:--T' k
K= C.orrcction factor
And all fluid propedies are evaluatcd at Tmr = Tt+To
2
AJutly- Developed Laminar F low : ( Re < 2300 )
Nu = l,s6 ( Re. Fr)1/'1l}/L1"*tt*/!r*)o'tu
where re.nr.f =tc o^q8 <P"{/drc"L*
and pr* is evaluated at T*
B- Fuliy De-lleloped Turbulcnt flow ( Re > 2300 )
i- Nu = 0.023 Re0'8 Prn for S.6 < Fr <ltl$
Where n=0.4 for heating ( To>Ti)
n=fr.3 for cooling ('Ir<Ti)zr
ii- Nu = t}.$2? r.qo'. I""t. (,rrlF *)u''o
Where p is evaluated at watl temperattue T*
C- Entrancq Region (Turbule&iqyL
I{u:0.036 Roo-8PrI/3 ( D/[-)o'oss
wherel{}<l.tott
4.&g
. ,:]A*-l -
-A-li,rbu-le...t $Lout
-/o*,l
Ain Shams UniversityFaculty of Engineering
MATL4BO: Heat Transfer
Nu=f(G,,P,)=f(Ra)
Where G, =Grashof numbergp(Ts-T@) Lcg
y2
And R'= Rayleigh number= G,rp.9$ (Ts-ra)tc1
Flow Condition Rr c d
Laminar 10o -r 10e 0,59 7/4
Turbulent 10'+ 10" 0.10 1/3
Qo.,,.=Arh[Tr-T-] tWl
L. = characteristic Ieng(h =L (platJorcytinOer l-reight)
New Engineering ProgramsMaterials DepartmentSpring 2009
' a-'i
L,
f:,lt
ti
f'a
l
i.
d.y
wherc f:Vorumetric thermar expansion coefficient =*.#f o=.onr,rn,
1.. Characteristii t-enSttr.
y: Kinematic viscosity = L 6,61
a: Thermal diffr- k ',sivity = p 6rt^'/s1
All fluid properties are evaluated at mean film temp. t^, =72
I-ForVertical plates and long cylinders;
N,=C[G.'P,Jd =C lR"Jd
where c and d are constants and evaruated from the next table
.'l ;
"iJ.t+' .I:;-r..*Y'+- -Sl i-zv/
+\Y- -
| 'l t -tI- ',: r1 | f i-',tiut.oz- )?-l! i
1 ...1i S
l{r;$\ c;,iT,r*:..1 \ r;. \.J
,!t,.,/,r /,/ai<.
flxFti
Er_
&t
FT
EE,
g-is-;ts
&.f
F,JlF;{
&;
f''s
E.L.
G1EiB
B&:
*a
E',
*;g, -.
*-.
f.r:'rE: }
ElE:;R.G-.j
f,iB+H
GTEJ
E
t'1E
t-,
E:i;F--{ts
g.F6.frrL--,:
p1E:&;
F:.*
U
gfs::k;
-8,o-.
2:For Horizontal CYlinders:
Nr=C[G,i P,]d =C IR"]d
Where C and d are constants and evaluated from the next
table
Flow Condition R. c d
Laminar 104 + 10e 0.53
Turbulent 1Oe + 10t' 0.13 L/3
L. : Equal the outside.diameter of cylinder = Do
3-Horizontal Plates:
Nr=C[G,*P,]c =C IR"]d
Where C and d are constants and evaluated from the next table
L.: characteristic length ='!w= ii ro, all shapes
r*),\
J
)t6'\
,^, (1'
n?'\ 4',':<'<r?
Plate 0rientation Steam Pattern c d
a)Hot surface facing uP:
1-Laminar Flow
loscRu<107
2-Turbulent Flow
1o7<Rn<1010
tt --
-'* h./i''><fi{,'L
| \:.\is\+.:s\ \\l)TF"*
f;;.trror^-/
0.54
0.15
1'
a
1
3
B)Hot surface facing down:
Laminar flow1o5.Rn<1010
.r-/ ' I'lp -/ /t/,.--:_r'
J\l\?\<<- 0.27 1
a
*"R l*
4-Eor Enclo-sed Spaces:
A) Horirontalspace or cavity Heated from upward:
hbNr- =fr'!
l*: Characteristic length in this case =b
All properties are eva{uated at Tm where r^=!2
Qsonr. =&h[Tr-Tz]
,\ = upper plate surface area.
B) Horizontal space or cavity heated from down:
hb ' .,,N,= T =0.195 Gr^"
For 10acG,6<4+10s
hb i,iNr= T =0,068 G.a"'
For G,p 4*1.0s
where u,o=Nff-
And all properties are evaluated at T,=EI3
And O.o*. = A,h[T:-Tz] where A, : Lower plate surface area.
C!.Verlkal space or cavity:
N,s = 19 =1 for G,.6 <zooo
Nur = 0.18 G.1/a1!;'rts for 2*10acG,r<2*Xos
Nvu = 0.065 g,,'(i)''ln for 2*10s<G.s<L.L*107
All properties are evaluated at T,n =L
'!77'u',i \e"6.t/
T/,6ata.r ;r.ofu2/ Y< 7-
H4t..'
s"r/ti
'Xrd
IIi
iL:
iI
-2I
b
t.
ii.
iii.
l.'ib:,lG
t'..i:t::
[.ii
1i;
f,-.1
t::;I :i'
-+,/o(Yrh,aJT
t*:
I
-tzllt,
F.tlt --
*9L*Ir&i
f:f,[,
f-: Simplified Emoirical Relatlon for Fre_e ConvectionE[;
ru
Ei
F'Flgti- i,
&.
E.::
H
Fr&-i
,i.&,&,
&''
tlif;-:&.;R
L;
$,3E:J&,e
HEJ
EE
Ei"ffr":1.[.J
c?
EJ
€rrEI*a:
f,-:N,;
E-
s,+
&J
eTlc. -d
&-HIE
Nusselt Equation; Nr=C[Gr-P,ld =C R.d
where N,=T , G,= ry},=+,andr."[email protected]
Anda -*, T =L ,and"P = *-Ylp=consr.=(1/T.i) (ForGases)
All propertie: are evaluated at roean film temperatore a.#= ,no
Oconv.=A, h AT where AT=Ts-T-
Geometry CharacteristicLength
tFlow type
Ra
Constants For Atmospheric Air h
lw/m2.t<J
c d
Vertical plate
or
Cylinders
Height
L
Laminar flow104 to 1oe
Turbulentflowtoe to lorr
0.59
0.10
1/4
713
h = 1.42 (atlt)'/o
h = 1.3 (AT),/3
Horizontal
cylinder
outsidediameter
Dn
Laminar flow104 to roe
Turbulentflow1oe to to12
0.s3
0.13
114
113
h = 1.32 (AT/Do)l/o
h = 1.24 (ar)'/'
Horizontalplates:
A-l-lot surface
facing up
B-Hot surface
facine down
L=As/P
Laminar flow10s to 107
Turbulentflowto7 to 1o.Io
Larninar
1os to loro
0.45
0.15
0.27
7/4
L/3
u4
h = 1.32 (AT/t )"'
h = 1.53 (Atltil
h = 0.59 (bl/L.Po
i.,0
-'2.3-Chapter 12 x ftorliotion: Proce.s.scs o.nd Properties
T.trit.r 12.1 Blackboclv Radiation I'unctiort.s
AT(prm 'K) F(o - ^l
It,t(L,7UoT;(pm . K'sr)-r
Ir,(r\, fJIr.a(A-"', 7)
.,i,
rrI,, .
Nt..
f.".
L='
200
400
600
0.000000
0.000000
0.000000
0,0000r6
0.00032r0.002134
0.007790
0.019?18
0,039341
0.066?28
0.10088s0.1402_56
0.183 120
0.3r8r020.361?3s
0.40360?
0.4433820.480877
0.si 60i40.548796
0.s79280
0.60?s59
a.$37410.6s89?0
0.680360
0.?0r0460.720 t 58
0.?378r8
0.i541400.769234
0.783199
0.796r290.808r090.819217
0.82952'1
0.839r02
c.848005
0.856288
0.874508
0.890029
0.375034 x l0-2?
0.490335 X t0-'30.tMM6 x l0-80.99r 126 x r0-?
0.118505 x t0-sa.523921X l0-5o.t344ll x 10-4
0.2491-?0
0.37s568
0.493432
0..589649 x 10-4
0.658856o.701292
0.000000
0.000000
0.0000)4
0.00r3720.016406
0.0725340, t86082
0.344904
0.519949
0.683123
0.8r6329
0.91215.<
0.97089 r
I::800
i.000i,2001.400
r.600
1,800
2.000
2.200
2.400
2.600
2.800 0.22'789't A.720239 0.997i23-r;8119............,- '- -- ,-0r5ftid8
*","-, .0:ri23,i.q'x!q-;a;,,ii"'.;''--'u-Tp@
3.000 0.273232 A:720254 x l0-4 0.99?143
3.200
3,400
3.600
3,800
4.000
4.200
4,400.
4.600
1,800
5.000
5,200
5.400
.5.600
.s,800
6,000
6,200
6.+00
6,600
6.800
7.000
7.200
7,400
?.500
7,800
8.00c
8..r00
9.0\r)0
0.7059',74
0.6813440.650396
0.615?25 x r0-{o..s78064
0.540394
0.503253
0.46'7343
0.4.33 r 09
0.400813
0.370580 x i0-40.342445
a3163',76
o.29nu0.2'70t21
0.249't23 x I0-4
0.230985
0.213786
0.r980080. l 83534
a.170256 X t0-{0.1s8073
0. r.4689 r
0. r3662 r
0.127!&50-106772 X t0-{0.901463 x l0-s
a.w3i3c.943551
0.900429
0.85i73?0.80029i0.?48 r 39
0.696?20
0.64',1004
0.s99610
0.554898
0.513043
0.4740920.438002
0.40/,6'71
0.37396.5
0_34577-
0.3 r 9783
a.295973
0.2741280.2s4090
0.235?08
0.218841
0.203360
0.i89r 43
0. I ?6079
0.t478t90.1 2480r
;f
f'I{-
ri
i
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tr1E:F,i
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E
s.:E]{1{rt,
$ttE;E:1
H
I2.3 e Blackbody Radiari,on
T.tnlr I2.l Continued
XT(pm'K)
I^.r(I, I)loTs(,r.lm'K 'sr)-l
I,r,a(tr,I)
I,r,r(l-,*,7JFqo - r)
j!: '
tE,g
-,
9,500
10,000
l'0,500
I1,000. i1,500
12,000
13,000
14,000
i5,00016.000
18,000
20,00025,@0
30,000
40,000
50,000
75,000
100,000
0.90308s
0.914199
0.923710
0.931890
0.93e959
0.94.s098
0.955139
0.962898
0.969981
0.973814
0.980860
0.985602
0.992215
0.99s340
a.997967
0.998953
0.999713
0.999905
0.765338
0.653279 x I0-5
0.560522
0.48332I0.418'.125
0.364394 x lo-sa.27945',1
0.21764t0.171866 x 10-s
0.137429
0.908240 x 10-6
0,623310
a.,64140.140469 x 10-6
0.473891 x l0-'?
0.20t605
0.1r859? x I0-80.t35152
0.1 05955
0.09M420.07?600
0.066913
0.0579?0
0.050448
0.038689
0.030131
0.023794
0.0190260.012574
0,008629
0.003828
0.00r945
0.000656
0.000279
0.000058
0.000019
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