Analysis of two-dimensional nonlinear transient heat conduction in anisotropic solids by boundary element method using homotopy and dual reciprocity

This paper is concerned with an application of the homotopy boundary element method originally proposed by Liao and Chwang to the analysis of nonlinear transient heat conduction in anisotropic solids. Usually, domain integrals arise in the boundary integral equation of this formulation. Some ideas are needed to keep the boundary-only feature of BEM. In this paper, the resulting domain integrals are transformed into boundary integrals by the dual reciprocity method using a new set of radial basis functions. The mathematical formulations of this approach for two-dimensional problems are presented in detail. Two schemes are discussed in this paper: the "isotropic" scheme, in which the state before mapping is considered as steady-state heat conduction in isotropic solids; and the "anisotropic" scheme, where the state before mapping is considered as steady-state heat conduction in anisotropic solids. The proposed solution is applied to some typical examples, and the accuracy and other numerical properties of the proposed BEM are demonstrated through discussions of the results obtained.