Quiz_3_Solution - Michigan State University DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE CHE 210 Modeling and Analysis of Transport

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Michigan State University DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE CHE 210: Modeling and Analysis of Transport Phenomena Fall 2007 Quiz 3: Solution 1. (20 pts.) Oxygen is stored in a spherical well-insulated container surrounded by a thick evacuated annular jacket filled with particulate insulation. The radius of the container is r 0 and the outer radius of the insulation jacket is r 1 . The temperatures at r 0 and r 1 are T 0 and T 1 , respectively, with T 0 < T 1 . The thermal conductivity is constant and, for the purposes of this analysis, you may assume that the spherical container itself has negligible thickness. a. (17 pts.) Use a shell balance to derive the equation for the temperature distribution across the insulation. b. (3 pts.) Derive an expression for the steady-state rate of heat transfer from the atmosphere to the insulation . Solution : a. The shell balance gives: () ( ) 22 44 0 rr r rq ππ = Dividing by Δ r and taking the limit as r Æ 0, we get 2 11 0 0 0; Boundary conditions: at ; at r d r q TT rrTT rr dr == = = = We integrate this equation once to get: rq C q r C =⇒= Noting that q = – k(dT/dr) , we get: 111 2 r CCC qd T d r T C rk r k r = +
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This note was uploaded on 05/21/2008 for the course CHE 210 taught by Professor Robertofoli during the Fall '07 term at Michigan State University.

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Quiz_3_Solution - Michigan State University DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE CHE 210 Modeling and Analysis of Transport

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