aer205_t1_2007_solutions - f,lfi.ns AER205F(2007)Midterm 1...

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f. (,lfi.ns AER205F (2007) Midterm 1 Problem 1 [25 Marks] Provide brief answersto each of the questions below. t5l (1a) There are two physical intelpretations of the quantity r"r. Explain each interpretation,and explain what the r and y directional indices refer to in the context of each interuretation. tsl (fb) Recall that in steady state one-dimensional conduction with no heat generation, the rate of heat conduction (J/s) in the x-direction is given by: q, : kA(+T) where k is the thermal conductivity, A and L are the cross-sectional area and thickness of the slab, respectively,ana Af is the temperaturedifference across the thickness of the slab. For the following composite structureof solid materials " 1" ,'2" and " 3", draw the equivalentelectric circuit diagram, and write an expression for the overall thermal resistance across the structure. 4_A X=Lr+LI R'- L 1\ t( _[ RJ "tt -, 1 Explanation of Interpretation Fry.s-- Pj^ w1+ ^ 'F str.r{z.cl d\ a 1,.i"4{^- (t..< 4 c+3 f i,.". t; "-* (&- ( X- 6*.- ) Ll "re rlr- fnrv,t'e^fu "^ flC-X jire.1r.r. i u WL:."L 1r.,6',^tt t"^ 'ct' ].wnt f *f, /)"". "( vr (8 * tz r8Y L &*1 tQ*t F,|) R, 0(.. -l -al l+ R. R*rt ' I Lr1(4,A, ,l -t
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Afi}{:fl5Ii {:#{J/i $.rtirjt*xrn I fr*hlrm l. s*ntinned l5l {f t} Th* tetrfr*?turLr pnrlil* in a fltxving llnid in {$ntn{l with a r*lid is shrrrvn in t}re gr*ph b*l*x'. ?]s iri t.he trrnp*r*ture at the r$lid sudirerr. ffi{t f; i* th* t*nr}:*ral$le in thri l.:ru}k lluid; b$th $ff cr}n$tiurt li*r tlris prohhrn" {a} In lhs graphxhtw*, add a rk*lch *f ;r tenrperxlurc Br*lile when flnw in th* {luid inr:r*,;xet. {h} Inilic*te ufi thr} ;;irilph tl}{} tr}r'rFsrilt$re grudie*ts thur rlatp rlir**tly {u {he c$n!*ctiv*r h*;rt trantl"er crl}icient, $. 1*r ihe t!e{) lir:w situirtilnr. {*} ffxpl*in h$w irlrrr$il$ed flrrr I*;lds !r.r;rn iucr*are iu lr. flowing fluid .r*lr/ sir'JL*- [v;) - k-4 M).;"1-r^) €*)', t^,FL 'rxvutJ "fl-.l {ltl) A thenrir:;rl sp*tie* ",{" is s*ltthlc in X {rt liquid), 1" {* r*li*} anrl Z {* liquid}. f;xpedmelts sil*w thllr nt qll* r:quilibrium c*nditi**. the c*ncr:ntrnti*n* tlf "A-' in X, Y *nd Z *r* {l ug/ml- I mg/rrl" anrl 3 mglml, r*spe*tively. ln the two ex1:eriments
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