Diffusion in composite layers with automatic solution of the eigenvalue problem

Abstract

The analytical treatment of transient heat conduction problems for one-dimensional multilayered composites by the orthogonal expansion technique requires the solution of a corresponding eigenvalue problem if this analytical solution is to be implemented for practical purposes. Such an eigenvalue problem is not of the conventional Sturm-Liouville type because of the discontinuities of the coefficient functions. Its solution with conventional techniques is not guaranteed from missing eigenvalues in the course of the computation. An analytical solution of one transient heat conduction problem in one-dimensional multilayered slabs, cylinders and spheres is presented, which implements a safe algorithm for the automatic computation of the eigenvalues and the eigenfunctions of the resulting Sturm-Liouville type system.