Analysis of two- and three-dimensional transient heat conduction problems including moving point heat sources using the method of fundamental solutions

In this research, an effective formulation based on the method of fundamental solutions is presented for analyzing the two- and three-dimensional transient heat conduction problems including moving point heat sources. This is a new formulation and has not been presented yet. The path of motion and the intensity of the moving point heat source are arbitrary functions of time and the number of moving point heat sources is unlimited. Solution of the problem is considered as a linear combination of time-dependent fundamental solutions and a particular solution involving the effect of the moving point heat source. The particular solution is presented as a time and space-dependent integral and is obtained without using any internal cells or points and without any time transformation. Numerical examples show the efficiency and accuracy of the proposed method in comparison with the finite element method. In the finite element modeling of the moving point heat source, it is necessary to use a fine mesh in the path of the moving point heat source that increases the cost of the preprocessing step. Compared to the finite element method, the proposed method is very simple and gives very good results even with a small number of source points. For example, in the second solved example, the average relative difference percentage between the results of the proposed method with 218 source points and the finite element method with 7268 nodes is 0.65%.