The Diffusion Equation for an N-Layered Cylinder

In this section, we present a solution of the DE for a N-layered cylinder. This extends the findings of Ch. 11, where only a two-layered cylinder was considered. Contrary to Ch. 11, the method used to implement the solutions is based on transformed domains. The reason for this choice is given by the fact that the eigenfunction method (Ch. 11) shows an increase of complexity in its implementation when used with a high number of layers. In fact, for a three-layered cylinder, the solution requires us to consider seven combinations of eigenvalues in the different layers. This means that the implementation of the method for an arbitrary number of layers becomes prohibitively complicated. For this reason, we have opted for the transformed domains approach to solve the DE in a cylinder with an arbitrary number of layers. The DE is solved for an N-layered finite cylinder (see Fig. 12.1). Solutions are given in the steady-state, frequency, and time domains.