Radial integration BEM for solving transient nonlinear heat conduction with temperature-dependent conductivity

In this paper, a new and simple boundary-domain integral equation is presented for solving transient nonlinear heat conduction problems with temperature-dependent conductivity of materials. The boundary-domain integral equation is formulated for transient nonlinear heat conduction problems by using the fundamental solution for the corresponding steady linear heat conduction problems, which results in the appearance of domain integrals. The arising domain integrals are converted into equivalent boundary integrals using the radial integration method (RIM) by expressing the temperature as a series of radial basis functions. This treatment results in a pure boundary element algorithm and requires no internal cells to evaluate the domain integrals. Based on the finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. To solve the final system of algebraic equations, the Newton-Raphson iterative method is applied. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method.