Modelling of non-steady heat transfer in a non-homogeneous spherical domain using a combined variant of the boundary element method

The combined boundary element method (the BEM using discretization in time) is applied to the numerical simulation of non-steady thermal diffusion in the multi-layer spherical domain. The fundamental solution is found on the basis of considerations concerning 3D problems for object oriented in Cartesian coordinate system. Next, the weighted residual method criterion for the energy equation written in spherical coordinate system is applied in order to determine the boundary equations in the case of single layer. The continuity conditions given on the contact surfaces between the layers allow one to construct the system of boundary equations for the whole domain considered. In the final part of the paper examples of computations are presented.