A general analytical PBEM for solving three-dimensional transient inhomogeneous heat conduction problems with spatially varying heat generation

In the present work, a polygonal boundary element method (PBEM) for solving transient inhomogeneous heat conduction problems with spatially-varying heat generation is developed for the first time. A new general analytical method is proposed and employed in the present PBEM, by which the radial integrals associated with arbitrary spatially-varying density, specific heat, and thermal conductivity can be analytically computed, and the efficiency of the PBEM for solving the transient inhomogeneous problems can be significantly improved. The transient term is dealt with by a finite difference scheme. Three examples are designed to investigate the performance of the proposed method, and the results show that the present method could accurately and efficiently solve transient heat conduction problems with arbitrarily-varying thermal physical properties.