Radial integration boundary element method for nonlinear heat conduction problems with temperature-dependent conductivity

Abstract In this paper, a new and simple boundary-domain integral equation is presented to solve nonlinear heat conduction problems with temperature-dependent conductivity of materials. The boundary-domain integral equation is formulated for nonlinear heat conduction problems by using the fundamental solutions for the corresponding linear heat conduction problems, which results in the appearance of a domain integral due to the variation of the heat conductivity with temperature. The arising domain integral is converted into an equivalent boundary integral using the radial integration method (RIM) by expressing the temperature as a series of basis functions. This treatment results in a pure boundary element algorithm and requires no internal cells to evaluate the domain integral. To solve the final system of algebraic equations formed by discretizing the boundary of the problem into boundary elements, the Newton–Raphson iterative method is applied. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method.