A Distributed Transfer Function Method for Heat Conduction Problems in Multilayer Composites

Abstract

A new analytical solution method is developed for problems of conduction heat transfer in one-dimensional multilayer composite bodies. In this method, the original governing equations are first cast in a spatial state form in the Laplace transform domain; the solution of the state equation is then obtained in terms of distributed transfer functions. With a new residue formula, inverse Laplace transform of the s-domain solution yields exact transient temperature and heat flux. Exact steady-state solutions are also obtained with the transfer function formulation. The proposed method is numerically efficient as it only requires simple operations of two-by-two matrices.

This work was a result of the author's previous projects partially sponsored by the U.S. Army Research Office and NASA's Jet Propulsion Laboratory. The author would like to thank Professor S. S. Sadhal for discussions on the subject.