A new general analytical PBEM for solving three-dimensional transient nonlinear heat conduction problems with spatially-varying heat generation

Abstract

In this paper, a polygonal boundary element method (PBEM) is presented, to solve the transient nonlinear heat conduction problems with spatially variable heat generation and temperature-dependent thermal physical properties. A new general method is developed to analytically compute the domain integrals regarding arbitrary nonlinearly-varying thermal conductivity, specific heat, and density, by which the computations of numerous Gaussian points in the numerical method can be circumvented and the efficiency of the PBEM can be significantly improved. The finite difference scheme is employed to evaluate the transient term, and the Newton iterative method is used to search the exact solution of the nonlinear system equation. Four numerical examples are designed to examine the property of the proposed method. The results indicate that the proposed analytical PBEM can accurately solve the three-dimensional transient nonlinear heat conduction problems with heat generation.