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Engineering and Tech / Introduction to Heat Transfer 6 / Chapter 3 / Problem 3.9

Introduction to Heat Transfer | 6th Edition | ISBN: 9780470501962 | Authors: Theodore L. Bergman

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A nuclear fuel element of thickness 2L is covered with a

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QUESTION:

A nuclear fuel element of thickness 2L is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate q . is removed by a fluid at T, which adjoins one surface and is characterized by a convection coefficient h. The other surface is well insulated, and the fuel and steel have thermal conductivities of k and ks, respectively. (a) Obtain an equation for the temperature distribution T(x) in the nuclear fuel. Express your results in terms of q . , k, L, b, ks, h, and T. (b) Sketch the temperature distribution T(x) for the entire system

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QUESTION:

A nuclear fuel element of thickness 2L is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate q . is removed by a fluid at T, which adjoins one surface and is characterized by a convection coefficient h. The other surface is well insulated, and the fuel and steel have thermal conductivities of k and ks, respectively. (a) Obtain an equation for the temperature distribution T(x) in the nuclear fuel. Express your results in terms of q . , k, L, b, ks, h, and T. (b) Sketch the temperature distribution T(x) for the entire system

ANSWER:

spanning from x = 0 to x = 2L.

(a) The governing equation for the fuel element is:

?/?x(k ?T/?x) = q/L

The solution of this equation with appropriate boundary conditions, the heat s

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