The Method of Fundamental Solutions for Two- and Three-Dimensional Transient Heat Conduction Problems Involving Point and Curved Line Heat Sources

The objective of this paper is to formulate the method of fundamental solutions (MFS) for solving transient heat conduction problems involving concentrated heat sources with time- and space-dependent intensities. The heat sources can be concentrated on points or arbitrary curved paths. In the proposed MFS formulation, a linear combination of time-dependent fundamental solutions and particular solutions is considered for approximating the solution. The particular solutions are expressed as time- and space-dependent integrals, which are computed effectively without considering any internal points or internal cells and without using any kind of time transformation. Several 2D and 3D numerical examples are analyzed. The finite element method (FEM) with a fine mesh and with a small size time step is used to find an accurate reference solution. In comparison to the FEM solution, the proposed MFS formulation achieves accurate results with a small number of source points and a large size time step.