Boundary elements for non‐linear heat conduction problems

Abstract

Abstract Boundary element formulations employing time‐independent fundamental solutions are becoming popular for treating transient problems described by parabolic or hyperbolic partial differential equations. This paper describes the extension of one such formulation, named the dual reciprocity boundary element method, to non‐linear transient heat conduction problems with temperature‐dependent material parameters and boundary conditions of the radiative type. The original non‐linear diffusion equation is solved in a transform space, where it appears in a pseudo‐linear form, since it contains a modified time variable which is itself a function of position. The problem is solved by using an iterative algorithm of the Newton‐Raphson type.