2-d problem with Neumann boundary conditions

Let us replace the Dirichlet boundary conditions (221) by the following simple Neumann boundary conditions:

$$\frac{\partial T(x,0,t)}{\partial y} = \frac{\partial T(x,L,t)}{\partial y} = 0.$$ (228)

The method of solution outlined in the previous section is unaffected, except that the Fourier-sine transforms are replaced by Fourier-cosine transforms--see Sects. 5.8 and 5.9.