Heat Conduction in a slab with Nonhomogeneous Boundary Conditions

Example 7.7. Heat Conduction in a slab with Nonhomogeneous Boundary Conditions 

Consider heat conduction in a rectangle with a nonhomogeneous boundary condition at x = l.[l] 

The separation of variables method cannot be directly applied because of the nonhomogeneous boundary condition at x = 1. To take care of this nonhomogeneity the following transformation is introduced  

Substituting the transformation equation (7.35) into the governing equation (7.34) we get  

equation (7.39) can be solved using separation of variables method with the homogeneous boundary conditions (equation (7.37)) as in Example 7.1 as  

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