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

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.