A Dual Reciprocity Boundary Element Method Applied to the Steady-State Heat Conduction Problem in Temperature-Dependent Materials.

Abstract

This paper presents the dual reciprocity boundary element method (DRBEM) for solving the steady-state heat conduction problem of temperature-dependent materials. The integral equation formulation uses the fundamental solution of the Laplace equation for homogeneous materials, and due to this fact a domain integral arises in the boundary integral equation. In this paper, this domain integral is transformed into a boundary integral based on the dual reciprocity introducing a new set of radial basis functions. An iterative solution procedure is used because material constant is temperature-dependent and hence nonlinear. The details of the proposed DRBEM are presented, and a computer code is developed for two-dimensional problems. Through comparison of the results obtained by the computer code with the exact ones, the usefulness of the proposed DRBEM is demonstrated.