Heat Transfer by Holman Solution

Chapter 2 2-l i-F

T -To

r?00_30

=# 1830

ffi

Et**#),",

Ax = 0.238m 2-2 AssumeLinear variation:k =

he+ pf1

-frlq_r, -,r| 11 + := #1, *,r, :"!,:'^T^:J= '

Q_=95oC, 4=62"C, Tt=35"C,Ar=ti.OiS

,b, - zs+ rrr,]= - 35+ fn(o.oaoozs,12 6)(rBly4 = 0.0063W 1223

lz

2-12

ku=W-5.35x10-5 0.003 = 0.0181 0.166 0.06 RFi = 1.579 0.039

RA, =

*=#=313# 2-13

#

R-"c -

= 0'721 ozx o'5778t

Rr f = - . . , . #

.s9 - = 7' 'J(o.o3gxo.577g)

&=# = 1.082 5 (0.05) (0.577gJ Rr= *=0.5

& =+=e.r43

q _72 -ZO

A-E--r'ru u -*=0.0996

h,.ft,

In

2-r4 0.004 Rr=+= = 0.0025 T6

=+=+=0.00833 &veralt U

I2O

1 4 ' = & , -- 0 ' . 0 0 2 5 = 0 . 3 A%veralt $veralt 0.00833 A4r=(0.3X60)-tgoc

lb

Chapter 2

2-r5 Ice at OoC p - ggg.gkel ^3 V - (0.25)(0.4X1 .0)= g.I m3 m:100 kg q - (100X330 x 103)= 3.3x107J + (z)(0.4xr.0)+ (2x0.25x1 4 - Q)(0-25)(0-4) .0)= 1.5mz A0- (2X0-35X0.5)+ (2X0.5X1.1)+ (2X0.35X1 .l) = z.zz^2 A m - 1 . 8 6^ 2 0.05 rr Ax . l'){ ^ = = - - 0 . E i 4 6 - Vr kA (o.o33xl.g6)

&-

'1- = 0 . 0 4 5

nAo R 0.9596 0 _ 3 . 3 x 1 0 7_ 2 5 - 0 LT LT 0.9596 Lr - 1.135 x 106sec - 3 1 5h r - 13days 2-16 q (noins.) - hA(Tw- T*) = (25)gn)(0.5)2 e20- 15)= gz47w l S m W , '-'fbam m.oC

q-W-

h4trrazeo-L) r;

rg

(0.018x1 20- 40)_ _ ls) (zs)rc2(40 05- rt rg - 0.5023m thk=rc-r;=O.OZ3m Q (w I ins) - (ZS)(42X0.5023)2(+O- 15)= 1982W 2-L1

q-+nrc{a1ril

m'oc

T- h

=

ll

k-zo4+=

-

o3z 034

-5 n7W

14

Chapter2 2-18 ot I-n_

AT

& t u , , , =arcQOa) #--& =9.752xr0-3 I

__l

. s-- @ m= 4-0 6 'p\ n --3

&vv'!r' onuqC T-_

-7 .9 5 g

hA

-1.592 (ZO)(4,n)(0.0,2

- 9 Q.4 A 11 \W I/ = 0 . 0 0 97 5 +7 .9 5 8l .S + 9Z

2-lg di - 2.90 in.

do - 3.50 in. k - 43

ln(3.5f2.9)

m.oC

= 9.96 xl0-4

&teet Rin, =

W

(zrc)(43X1) ln(5.5f3.5)(2n)(0.06X1)

1.lggg

I - -l- =0.2278 &onu vvr., h4 (10)zr(5.5X0.0254) Ro, - I .427

q-

LT -R

250_20 1.427

w m

7-r8 kA- 0. 166 3t5-4

@=@ 0.166

kf :0.0485 4 -38

m'oc

-T34E -

0.7283(3 15- 4) = 0.0828(4- 38) 4 -296.7oC

L6

Chapter2

2-21 Qr = -k4nr2

dT dr

- -k4ttf' dr n,f'o ry. +dr r' J4 (r r)

a,l;-rt)l - - 4 r c k ( T o - T i ) \t

qr =-+ryn$o ,4) [ v - a )r i \b

I

(t-r) r/ &n_\r4rck 2a2 r;=Q.5mm-5xlOam k r sx 1 0 - 4+ 2 x l O a - J x l O a ;=5

k - (7xlo-4xt2o)= o.og4 w q(barewire) = x(a.ootxtzuff4r,,li40)- I 3s.7Wm = (135.7)(0.25)

4(insulated) 400- 40 q-

= 33.93Wm

In(bfsxto-oF

33.93

@+ffi ffiT-----

By iteration:rc = 135mm - 1345mm thickness 2-23

(1)(r2)

- 6.16x l0-2 4.=(30)rc(2.067) Rp

4

ln(Z.37512.067) - 8 . 1 8 8x l 0 - 4 2rc(27) ln(3.37512.37 5) 2.432 2n(0.An)

(1x12)

&= 2n(3.375) - 5 . 6 5 9 x 1 0 - l

IG

Chapter2

2-24 dl kao{ro:rD -(To-L) q, = -k4nr2 = k4nroz dr i._a Tt-T*

q-T

'

I ll -orn\i-

ll,

hl-@,

I

Take& =o dro Resultis:,n=ZL "h

2a5 (2)= 35I I kg Mn at 90Vofull= (0.9x970)ft(0.8)2

a t Z o C l hqr = r y = 8 1 7 4 W

3600 = + z(0.8)(2) = 9.048m2 A 2rc(O.8)2 Fiberglass boardswith k = 40 mWm.oC (40x l0-3x9.048x80-20) =2.66x l0-3 m Ax _ 8174 2-26 .torImlength , = ln(9.1/8) = 4.363x lOa

R(pipe) ffif

ln(27'U9'l)= 0.3474 R(ins(l))2n(o.5) R(ins(2))-ln(35'U27'l)= 0.8246

zn(o.25)

R(tot)=1.172 LT zsO-2O=t96.2 Y 4= *= m Lr72 2A1 Fiberglass ft = 0.038 k =0.154 Asbestos brick

-, , --

k=0.69

Lx =1.2 cm x 2 Ar = 8.0cm Ax=l0.0cm

=o'684 h*(%#*r*0.,r**d* # |

t1

h=15

W m.oC

*2

Chapter2

2-28

R:1 k Fiberglass Urethane Mineral Wool CalciumSilicate

KR 0.046 0 .019 0.091

21.74 55.6 I 1.0

0.058

I7.z

2-29 M

\ 1000"c rz:4oooC Ti - 55"C mw km-9o m.oc

mW kr = 42 m.oC

h = tL 5a ' re

Y ^2.oc

T* =40oC

g = -h(r? g - 40) - \ - J - T*) ' @ / = (15X55 ' u , - 225 \^"/\u" A

q _ t. (1000- 400)

i=o^T q _k, (4oo- 55) A

'nr'

LxF

^2

Lxm-0.24m LxF:0-0644 m

r6

Chapter2

2-30 Uniformly distributedheat sources n

d'T,q -+--0 dx" k

T=Tt

at x--L

T=Tz. at x=+L

.)

qxT | -= *c1x*c2

2k .

? t

n

qLT 1'12=k- - - C 1 L + c 2

rz: L 2 k +*cl L+c2 T - + U 3 - * Z' y + T ) : Txt * T t + \ ' 2k\ 2L 2 2-3r ry=2.5 ry:3.5 r y =6 . 5 ln(ry|ry)-ln(3-512.5) = a.2433 R, r_ 0.22(2n) 0.22(2rc) R r _ l n ( r yl r) _ 1 .6 4 2 L

0.46(2n)

Rw*=

1 ^ 1= =0 .0 408 hA (60)n(2X0.065)

R - r . 9 2 6 2" c ' m

w

/.' -

L

LLT R

(20)(400- 15) -, .Of}?

\I/

r.9262

lcl

2-32

r- &)l q-q*U+P(

4*{=Q k

dx' T=T* at x=IL Generalsolution

tw4;

r-r*=c,[,"{ W"l *c2['"1 From boundaryconditions 1 cr= cz=O

T-T*=

cos W.

}-ffi k:43;

rr:0.015; t2:0.04; To:250oC; T*:35"C) h:43

L = 0.025 L": O.0255 rzc= 0.0405 r z J n : 2.7 tz 1,"3211r/kAor)t: o'825 Fig.2-12 8r: 0.59

= s 0Ew - 3sx0.3e) - o.ots'x250 - -...J": (ffKF(o,ffios2 2-34 MW q- m = -0 . 3 0 - r s a m e a s h a l f o f w a l l 1 5 c m t h i c k w i t h c o n v e c t i o n o n e a c h s i d e .

1o6xo.o6o)2 =25.7oc

at -(o.3ox To-T*=e=6 hA(T,-T-) qI^A,=

(o.lo = 31.6oc "-196)(o.0o0) T, -T* = --y15--

= To= T-" = 93+ 25]t+ 31'6 150'3oC

(o -**."*t#r-*l**

_**--..

*

,rqcuilr!!]irr#rrrarFrFttif,rufilttltiltrililrilrl'|F;lrFrilrll

ulurrt!

t!tlfllitltlttitl

l'

iit:tttttl[itf,ll

Chapter2

2-35 tQo /

Is

T; X+

dzr - -qoe-*

ex = eoe-ax

E:T

T -cl * czx-+e-crx ' atk

Boundaryconditions: (l) T=Tt at x=0 (2) T=hat x=L

c1-Ti..fr T - T,+ ge- *r, o2k'

c2-ro-r'-hQ-e-"1) - r, -

hQ L

- e-oL)x *$

e-ax

atk-

zl

Chapter2

2a6

l*-L4 qQ € y ray flux QO

Ti*

1'*" q - qor-o*

4=-Qo

E-

k"

o.-ax

- +e-o* T -ct * c2x e a"k

Boundaryconditions: (l)

atx=L

+-0(adiabatic) drc

(2)

at x=0 T=Tr Qo L) e -\* ozk

ln^ 3 t

-L

AK

T - r i + g - q a ' - o L x* - + e - o * oTk

ak

oTk

7z

Chapter2

2-37

T-T*=ctcos W.*czsin W. T:Tt

at x-tL

;

c2-0

-'fr ATI \11 -Tw+{ -/.A+l -r*) c1=m =hA(rt-L) l*-r

ve equatron:

2-38 fuAL:hPL(T*- T*) - 20) (35.3x 106X0.02 '2 - (4000X4X0.02t(r, T w: 7 5 .1 6o C 2-39

4*

E-k-

dI =+sin(ax)+cr

4ocos(ax) -o

T=T*at x-XL

dx

. ' . c l- 0

Tw - a*: cos(aL) + c2 a'k q -zk#|,= -zk A

=

L

#[-

ak

." T-+cos(ax)+ c1x*cz a'k . T - T* - Q9:[cos(ax)- cos(at)] a "k -

= sin(aL)J Tsin(al)

7,,

Chapter2 2-40

k - 0 . 01 2 4

W

cm. oC

-1.24 W m.oc

p = l . 5 x t 0 - 3C l - c m

(r.sx to-'{i) = {.5x lo-3

R-

q - I2R= (50)'(4.sx 1o-')= I 1.25w q-

+=#

-3.7s#

r--*x2+ctx*cz

L_ 1.5cm=0.015m T-300at x=-0.015 T - 100at x- +{.015 - 0.015) 300 - 100= cl(-0.015 \= 4667

(-9.25x to6xo.ot5)2_ (6667X_0.01 5)+ c2 (2X1.24) atx -0 T=cz=540.zoc 300 _

c2 = 540-2

2-4I /ra.ozsf'|t",no _40)=r 1.2w q=\hPt(Ato=LT J 2-13 IO=150oC L=15oC

h=20+ . o C m'

t=l.35cm

Z=6.0mm /=1.5mm

k=2ro w

m.oC

+ 0.75= 6.?5mm l=6.0 =2.025cm Qe= rtr L, =1.35+ 0.675 Lc= L*

D"'=1.5A 11

= 1.012x l0-5 m2 A^ = t(r2"- rr) = (0.0015)(0.00675)

-lt'' =0.0s38 ,zrz( h )t" =(0.0067$3,r1 zo -c x ro-))l lkt^ ) L(zroxr.or2

Tlf=97Vo FromFig.2-ll - n\go - T*)= 3.86w = 2hn(r2"2 emax = 3.75W q = (0.97)(3.86)

7t

Chapt* 2 2-74 L c= 2 3 + l = 2 4 m m

1tt2=o',7r7

-4 )t" = 0.o24\3nl -T ,trz( "

.uri>to.ol,49J L(l4xo

\ft,A, )

4f =o'77 - 23)= 192Wm Q= 4yA0s = (o.77)(2s)(O.024)(2)(220 2-75 Lc=3+0.1=3.1cm rr= 1.5

D c = I . 5 + 3 . 14=. 6 c m

%-=3.M7 11

6, -4 =(0.031)3/2[,--, ,r,r( ,, f''' =o.tt " [e1, ))t" L(5sx0.002x0.031)l

4,r= 0.58 - O.OtS2l000 - 20)= 37.4gw e = qlA,s = (0.58X68X2n)lO.Oa62 2-76 4 = total efficiency A/ = surfaceareaof all fins 4f = ftnefficiency A = total heattransferareaincluding fins andexposedtube or other surface. 7O= basetemp L = environmenttemp = Qact h(A- Ay)Qo ?i) + rUAyhQs- T*) {idear= lxAQo-L)

- A- 4 ! Arqr=r-{tr - er) a, - ' =P A A' eiua 2-77 Io = 4ffi

/ = 6.4mm

k=r6.3

n^= -\z 4+\=8x10-5m2 p.r,r(-n )t" = o.s1s

L=2.5 cm

L = 93oC

)

4,r= 0.85 - 93)= 437w q = (0.85)(28X1X2X0.025)(460

trl

h=28

Chapter2

2-7E 6 = 200oC T* =93oC k =204

Lc= 12.9mm

h=r.03xr0-5 m2

r = 0.8mm

L=12.5mm ft = I l0

D,c=2.54

t:,r(Lo,+)" =0.335

t = 1.25cm b =2.O3 11

er =0.87

1'0 = 105.3 0.0095 - 0.8)(10-3)= 0.0719m2 Tubesurfacearea= (t05.3)z(0.025x9.5 Tubeheattransfer= (l10X0.0719)(20O-93)= 846.6W No. of Fins =

-!l- = 1o.aT(2)z(1 - o.onsz)e00- 93)= 31.46* 10Xo.o2542

fin = 3312W Totalfin heattransfer= (31.46)(105.3) Totalheattransfer=846.6+3312= 4159W 2-79 rt=l.0cm T* =93oC

Z=5mm k = 43

fu-=1.62s

= 1.56x10-5m2 A, = (0.0025X0.m625)

11

t=2.5mm h=25 Lc = 5+1.25= 6.25mm

TO=26O"C e,c=1.625cm

-rll2

(

h )r/2 == Q . t2 25 _l = $.095 . Lrt''l .006: 25531 ,) t^4 ^ ) (4 3Xl .5 6 x l 0)-s)J \ 2 -0 q = ( 0 -e7)(2sx 2)t, 6225" .a12 )n(l0.01, X260 - 93li:) = =4 . 17 1w 2-80 k-43 (

Lrt''l

t -- . 1 -.L

lcm

h )r/2 := $ . .723

^-) \ lrA* q=(0-

7sx20x 2)( x0..tsx00

=20 fu=

Lcc ' 1 5rcfim L

.'l5 41 f = o).1 1 5) = 8 i3: 3 W I m derprh

1d

4f :97To

Chapter2 2-gl | =1.6rrm

r y = 1 . 2c5m

T* =20"C

h=60-,W ,X36 t2c=2.0& 2c =2.58cm rI

/ ,r 3 l i l l - l n )l/2 L \k4")

= 0.18

!-n

L=12.5 mm

To=zWoC

w kk--220o44, *

Lr=L3,3ilrm

=),.rzgxlO-sm2 u= (0.0016)(0.0133)

ef = 95Vo

- 0.0n52x200- 20)= 32.g4w q - (0.95).rc|)?)n(0.025g2 2-83 tx+ft,

A-2r=;

y=i.=;

-M --hP - -l^ # dx(rr*) # . *(*A#)*] -hP(r-r*)=Q e - T - T * ^+) +( dr\ dx) ktx A20 . kt de

,

iw+;;-hPe=s Aze de hpL ^

f-*-

dx'

dx

kt

2-94 f! = 0.05 ry,= 0.2 = L, 0.1+0.001- 0,101 t2'c4

L-0. 15 r2c= 0.201

ry

1,3tz(*)'''

l2

= (0.rorf /2 =2.388 [ (170)(0.101X0.002)

4f = 0.16 q = eyhAilo= (0.16)(60)n(0.20f- 0.05')(Z)(lZ0- 23)= 222 W 2-95 k=16

h= 40

- )5f|0(' T^ -1, --/v \r'

T* - gOoc

P=(4X0.0125)=0.05 m A=(O.Ol2r2=1.565x104m2 = (4oX0.05Xt6Xl.56s q = ffieo x to4)l1t21zso-90)= n.3l w h1

Chaptcr2 2-86 t =2.lmm L =1 7 mm h =7 5 L = 30oC Lc =17 + 1.05= 18.05mm 4,, = (0.0021X0.0180 5) = 3.79x l0-5 m2 -

""t,(Llt" \kA, )

k= 164

?b= l( ) ( ) "C

=(0.ols0t3,rl$=0.?66

LeUX3.79xl0q = (O.94}(75X2X0.01 805X100- 30) = r7 8.2 w

4! =e4Eo

r.r

2-87 Lc = 0.0574ft

rzc= 2.688in. = 9.931in2= 5.97xl}4 4 =(0.125X0.688)

b=t.34 4

= as2s

,,trz(Llt" "

\kAn)

ft2

4f =87%

-100) = 2hrQ2"2- rr2'11+5o ' h=r591+!g emax 'hr 4=(0.87xsel)=514 +q 2-88 Calculateheatlost (not temp.at tip) d = 1.5mm k =L9 L=12 mm h=500 Useinsulatedtip solution

To= 45oC

T- =20oC

5 L c = L + 4 , =1 2 +0 .3 7 5 =1 2 .3 7mm 4

*=(np1r"=f tsooloto.oor.sl lt'' =264.s \ta)

L(1e)z(0.001sX4)J

mL"= (0.01237 s)Qe., = 3.278 q = ^lffi0yrrnh(tnL) =

r

- 2o)tanh( = 0.177w 3.27s) [s00)z(0.0015X1e)a(0.oots{;)]t",0,

For 11= 200

mL, = 2.073

= 0.969 tanh(mLr)

o1 =('\t/2(0. \ I 77{0'969) '\0.997 = o.togw \500/

Forh-1500

ar =f

)

mLr=J,677

15oo)t/2(0. r'o = w ' \ 0 . 9 9 7) ) 0.307 \ r 77r(

\500/

tanh(mLr)=1.0

2-89 k:204; T-:2OoC; To= 70"C L = 2 5 nw t h= 13.2; d:2 mm; N = 225pins : I I .38 m : I(r3.2X4y(204)(0.002\7tn L : 0.025+ 0.002/4:0.0255 q/pin = (hPkA)t" 0otanh(rnl") : [( 13.2)n(0.002)(204\n(0. 00I )2]trz(70 - 20)tanhKI I .3SX0.0255)l : O.lO29W pin fin = 23.1'5W total: (225)(0.1029)

At

2-94

k--2M;N:8;

To= lOOoCi T* = 30oC;h: 15;L= 0.02;t = 0.002

P = (2)(0.15+ 0.002): 0.304 : 0.0003 4: (0.002X0.15) :8.632 m : [(15)(0.304y(2s4)(0.0003)]t2 L : 0 . 0 2 + 0 .0 0 1:0 .0 2 1 q/fin: (hPkA)t" 0otanh(ml") 02I )l : [( l 5X0.304X204X0. 0003)]t/2(I 00 - 30) tanh[(8.632x0. :6.62 Wfin Total: (8X6.62): 53W

2-9L : 0.04864 SurfaceareafromProb.2'90 = (8X0.304)(0'02 - 0'01251= 0.00565 tuea percircularfin = (2)r(0.03252 Numberof circularfins:0.04865/0.0565:8.6 Roundoffto 9 fins r r : 0 . 0 1 2 5) tz=0 .0 3 2 5 ;L = 0 .0 2+0.001: 0.021 rz"= 0.0335; rzJn-- 2.68 tz 1"321trlkA-)t : o'1273 r11:0.98 For 9 fins;

-30x2) - 0.01251(100 q = (e)(0.e8)((ls)r(0.033s2 = 56.2W

+v

Chapter2

2-92 Q = c r € -^ +c2 e +^ 0-100-20=80 at x=0 e- 35-20=I5 at x=0.06

m=W {a

8 0= e * c 2 15 = ct€-*(0'06)+ c2e+m(0'06) -kfcp-n(0'06) ed * c2e+m(0'06)(+r)l- h(Is)

I nne.az)(4)1'''

(1) (2) (3) (4)

,-n:t-l

L k(0.02)' J

4 Equations,4 unknownS,cL, c2, m, h. Solve, and then evaluateq from Eq. (2-37) or (2-36) using Lc 2-93

L- 2.5cm

t - 1 . 5m m

k = 50

W m. oC

7b= 200oC L, = 0.025+ 0.00075 = 0.02575 emax= Q)(500X0.02595X20020)- 4635Wm 3.863x 10-5 Am=(0,0015X0.02575)-rl (,^ \ ^,^f 5OC

L,3rzt Lc +l ln+",

| =(o.azsl8y3rzl # loT)J L(50x3.863x

T* = 20oC

h-500

=2.L

4f = 0'36 q - (0.36)(4635)= 1669w 2-94 L r = 3.57cm t-L.4mm [-3.5cm -20) = hAilo= (500X2X0.0357X150 - 4641w/m emax ( 2h " l l 2 t12 = 4.068 =l *LI r'

L

\M*)

tanh(mLr) _ 0 .246 rlf = mL,

Qact- (A.246)(4641) 1140 Wm

4r

k: 55

Chapter2

2-95 k=43 T* =2OoC (,{/2

ft=100 t =2 mm

=r.74

L,t''l+l "

4=2.5cm rz=]$cm lc = 5.1cm 4c =7.51cm

b-=3

L=5cm

=0.27

ef ,r \.&4.) q = 11 5t2 - o.ozszxt50- 20) )(2)n(0.07 r2hn(r2"2 rr2)0o= (0.27X100 =l10.6W 2-96 rZ=3.5cm L=2cm /=1mm =2.05 L, cm r2c=3.55cm

{=l.5cm k=2ffi /

,

1l/2

Lrt'tl +l " te{. )

=o.4l

ft=80

fu-= 2.37 4,r= o.8l ,r

- 20)(0.s1)= 75.9W q = ggn(0.03552- 0.0152X2X200 2-97 h=SO

k=20

=3r.62 ^ =(!!\'/2 - f tsolzto.orxlllt'' \fr,A/ [ (20)z(0.01)'I = 6.324 *7 = (O.2)(31.62)

e^L =557.8 e-^L =0.00179 ew =2362 e-^ =O.A423 2 0 = 3 O = 5 0 0r 0 z= 1 0 0 - 2 0 = 8 0 Usingsolutionfrom Prob2-61 - (30)(557.8)l+(23.62X30X0.00179) - 801 (0.0423X80 /, s(.x=10 cm)= 0001?9L5?f -704.46- 1888.33 -557.8 = 4.650C T-2A+4.65=24.65oC

4+

Chapter2 2-98 k =386 L = 0.6cm t = 0.625cm = f 0.3mm Lc = 0.6+ 0.015= 0.615cm =1.71 rzc=0.625+0.615

h= 55

8" = l'24 =zo 11 0.625 t' ' 1l/2

r

5t 1ll2 =(o.oo6l5ft2l-l Lcatzl =0.134 -----' +l " (e4, )' L(386X0.0061sX0.0003)l

4f =a'95 e = rl 7,.A0s = (0.95X55 )x (2)(0.01?tt2- O.N6ZS,Xt OO- 20)= 3.012 w 2-99 t =2 cm /

,

L,t''l+l "

L=17 cm 11/2

=0.e3

k = 43

l c = 1 8c m

h=23

4r=o.il

\kil) - 25)= 1sg6Wm = (0.64X2X23X0.18)(230 q 2-100 L=Scm /

,

Lc=Scm

f=4mm

k=23

h=20

1l/2

=r.042 4f =0.68 4=nyfuos Lrtrzl+l " \k4) A = (2X0.0 022 + 0.0s2yrrz= 0.10008 ;ft - 40)= 217.8IV/m q = (0.68X20X0.10008X200

2-101 f=1.0mm 4=l.27cm L=l.27cm Lc=l.32cm h , c= 2 . 5 9c m

h= 56

k=204

, t' t z ( . = 4 l t " = o , 2 r g \kA^ )

D'-=2.04 4r =0.93 4 -o.otz72x56)(125 - 30)= 15.84w q = (0.93X2)n(0.02592

+5

rz=2.54cm

Chapter2

2-102 t =2 mm

rt=2.0cm

h=?.0

=!0.2 cm rzc

Lc= 8'1cm

rz= 10'0cm L = 8 cm

.,U2

1

tt''lhJ

k=r7

=r'eo

tlf =0'19

b=5.L 11

-0.02\(2)(135- 15)= 28'7W q = (0.19x20)n(0.t022 2-103 L=2.5cm /=l.lmm /

.

n

r.]t2l uc [m'

il/2

|

=2.32

k=55

h=500

L"=2'555cm

4f =0.33

)

-20) = q = (0.33X'Q.OZSSSX500X125 885flm

2-t04 f = 1.0mm h=25 /

,

1l/2

Lltzl'l 4 Vq)

rzc=2'55cm 12=25 cm rt=l'25cm Lc=l3 cm L= 1'25cm k =?-O4

=0.?A9 4l=0.9t

- 30)= 4'94W -0'01252X100 q = (0.gt)(2)Q5)tt(0.02s52 2-105 d=lcm T* =2O

L=5 cm

h=20

k=0j8

Z 6= 1 8 0

d Lc= L+t= t+O'25= 5'25cm

(ry\''=m=fryT =ror.3 \*a,/

J L(o.zs)z(o.ol):

nLc = (101.3)(0.0525)= 5'317 = 1'0 tanh(5.317)

t"o- 2ox1'0)

=tryl" mL,) 06tunhl q=(hpt.o)u2 =0.993W

4G

Chapter2

2-106

A=lxlcm2

z=8cm

L.=g.5cm^=lryrl'' =31.62 Lt1,AJ

mI+ =2.6g8

r7,=6nh(YLr\ =0.369 "m4 - 50) = l4.ll W 4 = (0.369)(45X0.085)(4X0.01X300 2-107 /=l.Omm T* =25"C

\=l.25cm h=120

L c = 0 . a 1 2 +0 .0 0 0 5 =0 .0 1 2 5

L=l2mm k =386 12"= z.O r zc=O.AZ5

TO=2 750C '

11

=1.25x l0-5 4- = (0.0125X0.0O1) /

,

1l/2

-._f rno =(0.0125)3t21 rzv - 1| l l 2 =0.22 Lcat2l+l ' \e4. ) Ltgs0ltr.25xl0-))J =o'93 4f - o.otzsz)(z)(zts - 2s)= 82.12w q = (0.93X r20)n(0.02s2

z-roo k=17 /

h=47 ,

1l/2

Z=5cm

t=2.5cm

L"t''l +l "

= 0.657

4.r= 0.8

2-109 t = 1.5cm

L=2 cm

12=3.5cm

ft = 80

k = 204

Lc= 2.o5cm

2 c = 2 .3 7

e f =0 .7 g

Lr=6.25cm

\lA^ ) = -20)=376 Wlm q (0.8X47)(2)(0.0625X10o

rl

/ = I mm

Llt" ,rtrz( \tA- )

- 0.0$2x200 -20)='74W q - (0.79)(90x2)z(0.03552

41

kc =3.55cm = 0.0,

Chapter2

2-110 rL=l'5cm

rz=4'5cm

k-204

L, = 3'05cm

4c = 4'55 cm

h-50

l-1'0mm

%-3 4,

4f=0'6

y-3tz( uc l-1" = 0.78 V,e^l 5 0 - 7-6- -. 5 w I t--m ' oC o.o3ot3 (0.?8)z

(0.001x0.0305)

2-lll

l-1.0mm

L-zJcm

ry=1'0cm e,c=3.05cm

L, =2'A5cm

k-204

h-150 rzc3.05

ro = 150

ry

T* =20 150

u2

L,3rz(*)''' =(oozos) 204)(0.001x0.020

- 0.556

4f =o'75 - 20)= 76'3W - O.Ot2xts0 4 = (0.75x150x2)z(0.0:052 2-ll2 ks=kr=l'l

.

ttd' - ^5j A=T =)'u( x10a -2 =0'00|{ AT=300oC 4

t! =r.rx 1o{ m 2

kf = 0'035 Le = La = 7'5cm

--lf 1( ?o 'n'o" \. 4A o,f= ' re,e86 # +ks) LsLatto :o: J 1 = =0 .098?"C/W x 10--) (19,986X5'067 hrA

q=

resistance =!7.31w w/nocontact ffi

(17X5.067x10*)

=fi.zzBW ,,^LT - o2g.o6rylo-4x3oo) q=A;=T-

ar?

2 Chapter z-tj4

&^=#,=+=2.4sxlo-5& =+=o.88xtoa hrA = (2)(2.45x10-5)+0.88+104 = l'37 xloa Iqu ^nI . = #(8OX0.8Sxlo4) L =51.4=C ' 1.37x 102-115 L=0' 0125

ri =0 .0 !2 5

r = 1 x 1 0-3

rzc=0.0255

?=r.Y

/,1t2

,t,r[ -4 I'- = 0.322

Lc= 0' 0130

m2 Ar/'=(0.001X0.0130)=1'3x10-5 ] = 0.ssx toa

4I = o.86

To= 200oc

T- =20oC

I &,n=ffim=29e7 oclw

n" =l o' =

oqw =r.t?-o1

h"A 0o

= 43.72w

! 6 o +{t 0o =60.06 W o -= Rno

w/o contactresistance

7oReduction-6o'W--!?'72 x1oovs=27.2vo 60.06

2-116

l=o.qxloa

4=3oomw

4=o.5cm2

hc

Assurnefrn at27"C

q = (3ooxto-3)=

#(0.s)(10-4)

(r, -27)

Tt =T7'54"C

+9

CrEftr2 2-ll1 2L--Ncm=O.2m

ft=

L=50"C

- 5OX2) = 40,0fi)w|tt = 2td4u-L) = (a(X)XT, q