Ain Shams UniversityFaculty of Engineering

MANF475: Heat Transfer

New Engineering Programs

Manufacturing DepartmentProf. Dr. Gamil W. Younan

Time allowed:75 minutes Maximum Mark= 25 Marks

Mid-Term Examination November 2012

Question One [8 Marksl:

Air at temperature of 20"C and 1 atmosphere enters a rectangular duct having adimensions of 2.5 m long, 150mm depth and 250mm width. The mean surfacetemperature of the duct wall is maintained at 100'C. lf the air mass flow rate is 12.5kg/min, calculate the heat transfer rate and the air exit temperature.

Question Two 18 Marksl:A very long metal rod 0.5m in diameter is placed in an oven for heat treatment. Thegases in oven are at temperature of 600oC with convective coefficient of 160 Wm2.K. Ifthe initial temperature of the rod is 40oC, determine the amount of time that the rodmust remain in the oven to ensure that the rod surface temperature reaches to 400oC.Also determine the minimum temperature through the rod at this time and the amountof heat energy transferred to the rod through that time in kJ per meter tength. Take forrod material k=40 Wmake and c =1.85x10-s m2/s.

Question Three [12 Marksl:A new process for heat treatment of special material is to be evaluated. The material ismade as short cylinder (Disc) of 40mm diameter and 60mm tength is equilibriumcondition at initialtemperature of 450oC in a furnace. lt is suddenly removed from thefurnace and subjected to a two steps cooling process as foilows:Step l: Cooling in strearn air at temperature of 20oC with convective coefficient h=40

W/m2.xfor a period time T1 untilthe center temperature reaches to a certain value ofT 1o,o,r1 =300oC.

Step ll: After the disc reaches to the temperature in step l, then it subjected in a large

oil bath for another period time of Tz=3 minutes, where the temperature and convectivecoefficient of oil bath are 30oc and 400 wfm2.K, respectively. calculate:i-The time required t1 for step I of the cooling process to be completed.

li-The midpoint temperature T 1qo,tz) of the disc after the period time T2 .

iii-The temperature at center of the circular surface, T (l,o,.z) afterthe period time T2.v-The total heat energy transferred through the both steps in kJ.

[Take for disc materia I p =32OO Kg/ m3, k=20 W / m. K and C=1 kJ/KS. K].

N4t4{.15r!*q*rufu_4 dn"F,r"fsr,"**.* Ao rr.{a{*E *,r/o4 Z*t Z

&Xf- &*1dt

t I spa#'J3 rP&8

/.ff.7{* * 13 *?€/./FFx a.zfvat{

4,2.t*

' l*b,ne tp,v

&rtI

I!d

g

-"6

t-t-g E#

,/)t yz{p?

f-2

fuHc* rua*€ xo,B/€wag Z{".?f*o,t# d6?'!&i r "'}

p- -- -P,J"Dv* (fftr-ff-tp,:tx{-u*:r€;"t.. / F#€x6 "*

dH

* td lrr d.,rir,i.,." U/*o"!&** * /

Nru *c.e,.?3 @r

*E^.: o,{

r *.o,33 {r*lX*uo{uft# '

€ *.*2 3 /{3e t#} {a,rES ry" L*.6,&/'P

€ , f'/,u # * G€-a .? ,{Iy#:= * ty. F r*rt*,f fr ADff d a.ftrtf *#dt

q* - ,4:{ {K*rx{; .qzNa.r€x.?,{}*1{F(ro**ge)2ffK{ *r*#.@: fi*w/q{.

"or}

ay

a."zd d*nr *wip(ry-";; **{,ffi*Q.}

ry //,f*Ea*3.2b iL/., W ""2-n

r#*as# /aM Y. 327 c*b se*x# a.ss,n*./*rx ar*d **

Err** Y* /tn\, -&.*, V fir1-'ff G, ,,h , ,H.- '" sr3o r

Fx*y,*noroO* # sl,-r ;,1 Yr 3o+-2f 3 = 3o3 l<

# * lo*"gxrf %.n-"atu*

lyqd^G&/*-* Ir//v?p6s

Ho r.f€ - U

Sl rt{wg

*aso{*e *#- /rab/exr & *s*# #"r #w** sse_r**.ys .bu-su#- J

fla54<sre,lt /@

tr aB*"# Arts,,#",4

L*y"{ys{a$,,u/6o x 0,,2%**,,e{?*,/ /.r*ed !'-.t foi

"{sf dd,*f

*,w

=E=.-''#-,r ff,* t, ax'€f *r kw€d, f3, #rk/\Ja,t# W,y:q- T4,*% #:*-,W-

j._.: ;- -_*:.'-"*-_.--_.

, -'to fr",ri - "T ' r,' -'(oa*ffi'*

*q.:*s -,'K Xfrfi **;;;F : -rr;

'{ c4ooZvs77

Id*\

2r" *qf

#""* X = o.3rgU, sl- -

z^-r "(r) t^ tn7 t@vrJ s td

-{*

* l{ft nd#r E

"rc'dW*

@,

t-r* **arci-,'>'a 44, M*Tf ** utf*rtkr$*ag ""?R."./-

% 7

l\t/t r\r--.* 'ko-Yl!{o

{wl'w''"eSaP

' grr,n!A^* tqyl$l{+f/" E

Fp*, t/ea/-($*,./ nl lTtnofra;fivd.il 4 B;, /.--*fu,.;f -/'*

.t1 ,o- td-P'/ r /^i'-%*4r 6/ *,-axa{;!* o,,#*f f€{y_ySo*eid ,;;: #r.'r,(y)r6*rr

fu**, G,*;*rf+trg r#;;*-/ ** 7= f,o # * ^* lo -a w*%"U f*o;

ir s{9";o.€*x3*{fuqT{A'i )4o

lgxfi>/ /23,6$xd-#M,"L*

@ 4 Lf

atr' {t

t) *rt#f x/0J

q1*-e

-#* 4o a{*, ff

7&M"l,ffffi

YW, Y c"*rft,rr* ),#ior"t

/u nF)q t{ * r. }r.d /- ;

%, '--r"'{t*t---- El- .2-P%et'7 ,/'p 4 , 'r-' er'€2**Yfi{zA} €raf*

zreLl*.?"

JT fr * 6 I4,ett #.s #t* fc#*ri, eor{'#Zos

s'u€ *,.* u,, +&*/rn"*y*e*{ ). EF**f j

dt &€rqo-ft;---+- W4Fff"ia *

-{.- {2,XA? X/A )1

r t , z4{o7

C

_R,tro 3oo ^ ? o**--*.-_--1__*J *L* a*t{S

#€s **.*s&-a€ {r SXrvte-E^ {,q'a s ;*3-r ---+- V*, , P {iffp .- f :. !.-'-Ii Y

l.\ lzix66le rod 6

9fr€'iix,ts

*# {Z# &r- * €.,5y3l?4.$"

?-"*,*€ * tut,*y#<,{*f t.*ru? #;F;--f 0,,u. ,;,::*i ,, +Ru rutu,? '* t* 4*cx+{ntf,3# u - T,* F _****-_**" g*,

n,t'- D n

--+!' izi n-_. ,/) / /I { ffip i' A t.r xp /* r { ${: #r*; i-;*f i ,y' t, "-F"€Fr:*

t, -1r" 4u-si'' T** 4 ;:s !l r+.* fc V -:-.

#w?

! *-*r&rh'o

ar r/ ,fu sn

-/ttfi 3"*n

# 3. d, @s Sr,r, *o l*,/* o,s $ r 4 *f, cA* t* t'*f,l\ #*

ArE{t

f^wtrtl ,&o-tf{fi ?t rrtr k n 'Ytu---, /() l?

p/*

{ToJx y't, ";/ {s /3.,*65 A ,A yl67 ---* X # '/9Tl-'6

n -. /q - 6.{

e'- - . .rF odg.r; #0,{*P*r, dur' ,,ibu " WX$- { _ 3t }*t

e# €

-f71*rr*" r '/v.r ".o= 8uxA12 # @.06't e4 /ifnh W

?' \ -' -s

s o,a/ {3oo-3*} *Sff * WZ *

ti

"{6 rfst e1 Sxd*"** * 13 { **.rr Fr**e$*,' &r' -{*p*- e*.:

Tr?ns*T z. d

*,*-E P o.1"4 3

'/r' * lro €=* -S#r *3

*** *"*qx:'u**r,-,fft3 so 6/ 4 2o

Y e*-:

* *.€ t-*---F

&.),'4 g l*

ry'bur#

' / (/tofr)TI

ir--i, tfr.nF)| '{nQ t'i J!-*- +!**

**t

.*rl\I/l €

i{7orn;l**e eJ *r**rn ry/{,t,r,,fiyr S*r}*ce * %.,o,q , 7? fl*u6;c!i#-"r

Fooo, #zrs/uf-.rt*r/c(;f =/6Fl0l ",j,

oap"xt*i=p 8-L f.o*F-o,,& ra!6.k zl -{E $* 1oIZ:*-*f

fi,,u* m *o,or_J6,a^W

? !\---/r' / -' v

*lo*ap V*y)% ,r,' '*F #*;-{X^l/)-o { W*.= {o"{xaxd}{p'/a} va"a46

W,o,e s 0,*#€{S** *S*J *3# * W 7 L).<<*-.

{B: V **-{rnnd* & vfu */ea/^ &r,ffH,ko*r}u,** e{ #+**@ Aore* "d s#P :urr..u fdg;x,ff*v_l*r.

vv

+r !&{PT/a, ,rLF r: * = f r."T F, [, _ f*--_-r-**J l*qs I u

( t&q o-Zr)-u-/3. :- "'' " ,1*rr M{rlo.rrirora;l rt*}fi*}'

g 3,{,/'fr*V 2; SE&ls.vtuurl*te-a &; * #,*e{ .J {* ;.X{f?tr