Numerical solution of multi-dimensional transient nonlinear heat conduction problems with heat sources by an extended element differential method

In this paper, the element differential method is extended to solve a transient nonlinear heat conduction problem with a heat source and temperature-dependent thermophysical properties for the first time. The transient term is discretized by employing a finite difference scheme. An iterative methodology is developed to deal with the nonlinearity caused by temperature-dependent thermophysical properties. Examples of two-dimensional (2D) and three-dimensional (3D) problems are given to validate the present method for solving multi-dimensional transient nonlinear heat conduction problems. The results show that the present EDM provides a promising way that is effective and with high accuracy for solving multi-dimensional transient nonlinear heat conduction problems.