aer205_t1_2007_solutions

# 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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