ABSTRACT
Heat conduction problems in heterogeneous media involve spatial variations of thermophysical properties in different forms, depending on the type of heterogeneity involved, such as large-scale variations, abrupt changes in laminated composites, and random variations due to local fluctuations of concentration in dispersed systems, and so on. This chapter provides a systematic derivation of the analytical solution of heat conduction problems in heterogeneous media, introducing a more general perspective of the integral transform method. The expressions provided by the integral balance approach can then be employed back into the solution of the eigenvalue problem, yielding a modified algebraic eigenvalue that provides the eigenvalues and the eigenvectors. The integral transform method described comes from the application of the integral transform method in the more general treatment presented in Mikhailov and OzisIk, Cotta. The chapter discusses the concept of a single domain formulation for heterogeneous multidomain problems.
