Finite analytic numerical method for transient heat diffusion in layered composite materials

The finite analytic (FA) method, which has been recently developed and used in fluid flow and heat transfer problems, is presented and extended to the solution of the problem of transient heat conduction in a one-dimensional multilayered composite slab. The basic idea of the FA method is to incorporate a local analytic solution of the governing equation in the numerical solution of the boundary-value problem. In this study, the local analytic solutions are obtained by the standard integral-transformation technique and the associated eigenvalue problem is solved by the Galerkin method. Some numerical examples are computed to demonstrate the applicability of the FA method in dealing with heat diffusion in a composite material. It is shown that the FA method is accurate and provides reductions in computational costs.