(a) Explanation Given: The nuclear fuel thickness is 2 L . The steel cladding thickness is b . The rate of heat generated in fuel is q ˙ . The thermal conductivity for fuel is k f . The thermal conductivity for clad is k c . The constant temperature is T ∞ . Formula used: The general heat equation is given as, d 2 T d x 2 + q ˙ k f = 0 Calculation: The assumptions made in the analysis are as follow, One dimension heat transfer. Steady-state condition. Uniform heat generation. All Constant properties. Negligible contact resistance between fuel and cladding. The general solution to the heat equationis given as, d 2 T d x 2 + q ˙ k f = 0 ...... (i) On double integration the above equation (i) is, T = − q ˙ 2 k f x 2 + C 1 x + C 2 ......(ii) The insulated wall at x = − ( L + b ) dictates that the heat flux at x = − L is zero (for an energy balance applied to a control volume about the wall, E i n = E O u t = 0 ). The value of T s 1 may be determined from the energy conservation requirement that E g = q c o n d = q c o n v , or on an unit area basis is, q ˙ ( 2 L ) = k s b ( T s 1 − T s 2 ) = h ( T s 2 − T ∞ ) T s 1 = q ˙ ( 2 L b ) k s + T s 2 T s 2 = q ˙ ( 2 L ) h + T ∞ T s 1 = q ˙ ( 2 L b ) k s + q ˙ ( 2 L ) h + T ∞ Substitute all the values in equation (iii) (b) To determine The sketch of temperature distribution for the entire system.

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Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Chapter 3, Problem 3.90P

(a)

To determine

The temperature distribution in the fuel.

(b)

To determine

The sketch of temperature distribution for the entire system.

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Chapter 3, Problem 3.89P

Chapter 3, Problem 3.91P

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Introduction to Heat Transfer

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The temperature distribution in the fuel.

Solution Summary: The author explains the assumptions made in the analysis: One dimension heat transfer. Steady-state condition. Uniform heat generation. Negligible contact resistance between fuel and cladding.

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The temperature distribution in the fuel.

The sketch of temperature distribution for the entire system.

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Chapter 3 Solutions