Explanation Case (a) In this case, the temperature distribution is linear; therefore, there is no energy generation takes place. The expression for the heat equation is given as, d d x ( d T d x ) = 1 α d T d t At x = 0 , there is no heat flux due to no slope on temperature distribution. The expression for the initial condition for the initial temperature is given as, T ( x , 0 ) = T 0 At x = L , there is no change in surface temperature with time, so surface temperature remains constant. The expression for the surface temperature is given as, T ( L , t ) = T s Case (b) In this case, the temperature distribution is parabolic not linear, therefore, there is energy or heat generation takes place. The expression for the heat equation is given as, d d x ( d T d x ) + q ˙ k = 1 α d T d t In this case, initial temperature is constant for x = L and for x = 0 , it is same as the surface temperature. The expression for temperature is given as, T ( x , 0 ) = T 0 T ( L , t ) = T 0 Case (c) In this case, the temperature distribution is linear; therefore, there is no energy generation takes place. The expression for the heat equation is given as, d d x ( d T d x ) = 1 α d T d t At x = 0 , the initial temperature and boundary conditions are same

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ISBN: 9780470501962

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

Publisher: Wiley, John & Sons, Incorporated

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Chapter 2 Solutions

Introduction to Heat Transfer

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The heat diffusion equation.

Solution Summary: The author explains the heat diffusion equation. In this case, the temperature distribution is linear; therefore, there is no energy generation.

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Chapter 2 Solutions