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000000Clark Colton

000000Clark Colton - 10.302 Fall 2004 Exam 1 Wednesday...

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10.302 Fall 2004 Exam 1 Wednesday, October 13, 2004 Problem 1 (40 points) A very long composite cylinder consists of two concentric cylinders. See attached sketch. The inner cylinder of radius r 1 has no heat generation. The outer cylindrical shell, with inner radius r 1 and outer radius r 2 , is capable of being heated at a uniform volumetric heat generation rate of . The two cylinders are in intimate thermal contact. The outside of the cylindrical shell is immersed in a flowing fluid with temperature q & T far from the cylinder and heat transfer coefficient h. The thermal conductivity, heat capacity, and density of the inner cylinder are and ρ 1 1 k , c , 1 , respectively. The values of these three thermal properties for the cylindrical shell are 2 2 2 k ,c ,and ρ . Initially, the temperature of the entire composite cylinder, T i , is equal to the ambient temperature, T , and there is no heat generation = 0 in the outer cylindrical shell. At the heater is turned on and the outer cylindrical shell is heated at rate q .

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000000Clark Colton - 10.302 Fall 2004 Exam 1 Wednesday...

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