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t 1,,,"t {u-*"ui.i 7
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't4o n*^at r,L ,*rh'{ ;,, A^*/ * L** b*0,^*
I 1.5 2 n-l n n+'7
Frcune 5.4- l. Unsteady-state conduction in a slab.
C,uJ*,y*L51r,"{ wVnml h,fb4
*"{- 4,{*a(*,
t)
a
Tn+l
I Wrh,lr" ' Ter,,ytarxre r,\l ev rc,^t t)n*
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(.'t+*E l ) te F* * J;\{"r"r* >,1bti'' *'-'t/*
?adilia4- .^4 k*r/o+gt**
*# jto*i'. . "*$ l, *hL:^" af V, &"" "AL'1'l.aufLr4h 1I
rln-t * .sln",.-__"945-
sr,,pltfr"l x,l.;k *Ar{ F ", tC . ML=z , il-,'-l^ =
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I > . (s*/z*t7"n rtL do $n*,f-a;-
, *4t trldiLr rk ,,r{" qrl, +1,,N*-{ % IF*,I brJ*,nn
6o 4l**t in Yo 4 l,*ot *ttAtJ"-rr ,t - * f.r ,
*ilJ =. ,il
-kA - (-T *'t \L^lA) ti-' i -rr is I
t;lu
fat* r{ W* ftiu*nafta1i2n(Aax,L)(?l_:t _T )jt tttat ll.eS y! 1.vi1
flo,vtron1,g rn, at+rL I I
. .-L
f4= tdx)Ja{
i.',+iq [t Nt ;l; r (&t- lzif t',;1'
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rznl
h Jr*il,^tt- L"-trry m"/*r*, , ,
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'\' t'1* *^h
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f,,r +o tr*t- N v^L,u t tJ = L'// A ) , [** r'Lt,;i"nw(!rtirt ]n t/.s '#-I,*( *st"t *qW \nrzl , ,f
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A tl'
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H+LA,V
='"-FrNfl
il
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I"rr/U,tx -* A )
+ ) Hew t: v"!L ;^hi;/. b"*rl,o,g *e'r,vfz+ariwtz
F"r l4=z ,rr{, 1f^tul in*ewnei , f ,1n = ( T t|" ,,..__- t i_lr.
W *oLrfi(t, c4kh n = J. .-p +, *,,{ t ,'t,tlt -r" w,.nle.l u*|,*r|in +, * rwvl unt* ctv,u [a,ul {"r**d * i,r<",r,{
UoF-
EXAMPLE 5.4-1. Unsteady-State Conduction and the SchmidtNumerical Method
A slab of material 1.00 m thick is at a uniform temperature of 100"c. The frontsurface is suddenly exposed to a constant environmental temperature of 0.c.The convective resistance is zero (h: oo). The back surface of the slab is insu-lated. The thermal diffusivity a : 2.00 x 10-s m2l$. Using five slices each 0.20 mthick and the schmidt numerical method with M = 2.0, calculate the temperatureprofile at r : 6000 s. use the special procedure for the flrst time increment.
solution: Figure 5.4-2 shows the temperature profile at r : 0 and the environ-mental temperature of ro : 0'c with five slices used. For the Schmidt method,M :2. Substituting into Eq. (5.4-3) with a:2.00 x t0 5 and A-x : 0.20 andsolving for Ar,
+
M :2: g:d - Qzl)'zotat tz.oo x ro-llr a/:1000s (5'4-3)
6a| 5;;6 t i:'.t ir,ta?. r*n1.SI
F""t"rl -:f\ n t lt , - t-'r .r\ rtf' (:"
(\t'n:.ttr-r fuif -h{L. :l; =(-'" n'T')/, Fn--, , ol' T -T *ou," I i^rilL 'p,/f,rn,.,Jn
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t=3Lt
5.
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b.4;L, ,-< t'..5
h,tefyb-,lt.ii,*C1lu'{t+-:
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fhtL 4 Lr,t ;" ,rn\tL "( ktt "at
.= f^fr- 4 luat ruc*r.r'(r.+i*n
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to"cln M L aL rzlntr. >/^
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b*W f,s-l , W *,,t ,*/,/ \ /*d{"
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fur,f{,"*nJ'1*3vt! ,4,Fto <-f ,o,rtu.ns ,,J. J**s. erlqnr- hn'wtid F'1" fU;"*r ,( f**-r;*s ,rrs [,rt tt i.ert ;s freie"rr(
Ayy*;*,v A*rr,n 4 pL.e + fu"* i ;s ,.^,(,*,,.nrwfir*'
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= ^?f:,'q*fl/x -#H;r*'
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