The heat transfer problem for inhomogeneous materials in photoacoustic applications and spectral parameter power series

摘要

A method for studying the one-dimensional heat transfer process within an inhomogeneous spatially bounded medium in the presence of an external heat source is presented. It is based on a recently introduced technique for solving problems related to Sturm-Liouville equations that consists in the representation of solutions in the form of a spectral parameter power series. We consider a heat transfer model linked to photoacoustic and show that the introduced method, besides its relative simplicity and analytical nature, offers an efficient numerical algorithm as well as a convenient way to work separately with different physically meaningful components of the temperature distribution function. Detailed explanations and numerical examples are given.