New interface integration BEM for solving multi-medium nonlinear heat transfer problems

In this paper, a new single interface integral equation method is established for solving non-linear multi-medium heat transfer problems with temperature-dependent thermal conductivity. At first, the boundary-domain integral equation for nonlinear heat transfer in single medium is established based on the fundamental solution of Laplace equation. Then, based on the variation feature of the material properties, a new single integral equation for material nonlinear multi-medium is established according to the degeneration rule from a domain integral to an interface integral. Next, the final system equations are solved by Newton-Raphson iterative method after the discretization. Comparing with conventional multi-domain boundary element method, the presented method is more efficient in computational time, data preparing and program coding. Three numerical examples are given to demonstrate the correctness and robustness of the method presented in the paper.