Group_Exercise_01_Solution

Group_Exercise_01_Solution - Michigan State University...

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Michigan State University DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE CHE 210: Modeling and Analysis of Transport Phenomena Fall, 2006 In-Class Exercise on Shell Balances : Solutions 1. Liquefied oxygen is stored in a spherical container vented to the atmosphere. The container is well-insulated, with 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 The thermal conductivity of the insulation varies linear with temperature from k 0 at T 0 to k 1 at T 1 . For the purposes of this analysis, you may assume that the spherical container itself has negligible thickness. a. Draw and label a diagram for this problem. b. Starting with a shell balance, derive the temperature profile within the insulation. c. What is the steady-state rate of heat transfer through the walls of the container? d. Using the parameters below, estimate the rate of evaporation of liquid oxygen from a spherical container 6ft in diameter covered with a 1-ft-thick annular jacket: Temperature at inner surface of insulation: – 183 o C Temperature at outer surface of insulation: 0 o C Boiling point of O 2 : – 183 o C Heat of vaporization of O 2 : 1636 cal/g-mol Thermal conductivity of insulation at 0 o C: 9.0x10 -4 Btu/hr-ft- o F Thermal conductivity of insulation at – 183 o C: 7.2x10 -4 Btu/hr-ft- o F Solution : b. The general balance is rate of energy in at rate of energy in at 0 rr r −+ Δ = Mathematically, () 22 44 0 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 =⇒= In general, q = – k(dT/dr) . For this problem, k
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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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Group_Exercise_01_Solution - Michigan State University...

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