RIBEM for 2D and 3D nonlinear heat conduction with temperature dependent conductivity

In this paper, a new and effective radial integration boundary element method (RIBEM) is presented to solve nonlinear heat conduction with temperature dependent thermal conductivity of materials. Boundary-domain integral equation is formulated for nonlinear heat conduction by utilizing the fundamental solutions for the corresponding linear heat conduction, which contains a domain-integral due to the temperature dependence of the thermal conductivity of the materials. Two different approaches based on the radial basis functions are implemented to approximate the unknowns appearing in domain integrals. The arising domain-integral is converted into the equivalent boundary integrals using the radial integration method (RIM), resulting in a pure boundary element analysis algorithm. Newton−Raphson iterative method is applied to solve the final system of algebraic equations after the discretization. Numerical examples are presented to demonstrate the accuracy and the efficiency of the present method.