Heat Transfer with Nonhomogeneous Boundary Conditions

Example 7.13. Heat Transfer with Nonhomogeneous Boundary Conditions 

Consider the steady state heat transfer problem with nonhomogeneous boundary conditions in both x and y 

The final solution u = v + w satisfies nonhomogeneous boundary conditions at both y = 1 and x = 1. The solution for v was derived in Example 7.11. The solution for w can be obtained by interchanging x and y in the solution for w. The Maple output for this example is given below  

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Consider steady-state heat transfer in a rectangular cross section, with constant thermal conductivity. Design the four nonhomogeneous boundary conditions such that the final expression of the temperature distribution consists only of four terms and not an infinite series of terms. Write down this expression. (Hint Look at the solutions of Ex. 4.3 and Prob. 4.9.)... 

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