Slab with Nonhomogeneous Flux Boundary Conditions

Example 7.9. Diffusion in a Slab with Nonhomogeneous Flux Boundary Conditions 

Consider diffusion in a rectangle with a nonhomogeneous boundary condition at X = 1 x[4] 

The technique illustrated in section 7.1.5 cannot be directly applied for this problem because w(x) cannot be solved to satisfy the two flux boundary conditions at x = 0 and x = 1. To take care of the non-homogeneity the following transformation is introduced 

Substituting the transformation (equation (7.48)) into the governing equation (7.47) we get 

The left hand side of equation (7.54) is a function of time alone and the right hand side is a function of x alone. Hence, both sides should be equal to a constant k. 

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