A new approach for solving heat conduction under zero and non-zero initial conditions

Abstract

This paper provides a new approach for the analysis of transient heat diffusion arising from conduction. The diffusion is subject to zero and non-zero initial conditions in a two-dimensional domain, containing confined heterogeneous subdomains. This system can be subjected to a heat source. A new formulation is presented, in the frequency domain. It allows coupling between the boundary element method (BEM) and other methods (such as the method of fundamental solutions (MFS), the finite element method (FEM), the finite difference method (FDM), the meshless Petrov-Galerkin (MLGP) method, the virtual element method (VEM), and analytical formulations). The BEM is used for the homogeneous exterior domain and the other method is used to evaluate the solutions for the non-homogeneous confined subdomains, to overcome the specific limitations of each of these methods.