Exponential basis functions in solution of time - dependent heat equation in axially layered materials

In this paper we present a novel method based on using Exponential Basis Functions (EBFs) to solve heat conduction problem in axially layered materials. In the first step, we have considered each layer of material as a separate element. Then the solution in each element was approximated by a summation of EBFs satisfying the differential equation of transient heat conduction problem. The unknown coefficients of the series solution were related to initial condition and Dirichlet side conditions of each layer employing a discrete transformation technique. Finally, the general solution of material was completed by satisfying the continuity conditions between adjacent layers in a manner similar to conventional finite element method. In this hybrid method, a collocation scheme was used for satisfying the time dependent boundary conditions as well as the initial conditions. The capability of the presented technique was investigated in the solution of some benchmark problems.