The solution of direct and inverse transient heat conduction problems with layered materials using exponential basis functions

Abstract

In this paper we present an extension of the formulation given in (EABE, 37 (2013) 868–883) to direct and inverse heat conduction problems in layered materials. Expressing the numerical solution as a series of exponential basis functions (EBFs) defined in space and time, is the main idea of the presented method. We shall show that the use of the EBFs provides a versatile tool for the solution of a variety of problems such as the classical heat diffusion with internal heat sources and the inverse problems in layered media with perfect and imperfect contacts. To this end, we choose a proper set of EBFs satisfying the governing differential equation and interface conditions. Then a collocation technique is employed to satisfy both initial and boundary conditions. The proposed formulation can also be easily extended to the solution of non-Fourier heat conduction problems or the analysis of thermal wave propagation. The capability of the presented method is investigated in the solution of some direct and inverse heat conduction problems including a boundary identification problem and backward heat conduction problems. Issues pertaining to short time solution and penetration time, in inverse heat conduction problems, are addressed in the problems solved.