Solution of the Isotropic Heat Diffusion Equation using the Finite Volume Monte Carlo Method

The solution of the heat diffusion equation in most practical applications involving complex geometry, thermophysical properties, and boundary conditions is not simply possible and there are some limitations for available numerical solutions. In this research, the finite volume Monte Carlo method was proposed for the solution of the isotropic heat diffusion equation due to two intrinsic capability of the finite volume method; first, each cell is energy conserved and second, the grid transformation is not necessary for complex geometries. The Monte Carlo method as a statistical approach based on physical simulation of the problem capable to solve heat diffusion equation with any degree of complexity was utilized in three different problems. First, a simple problem was investigated for validation of the method by comparing results with the analytical solution. Second, the prediction performance of the proposed method was evaluated in a problem with complex geometry, varying properties, and boundary conditions. Finally, the performance of the finite volume Monte Carlo method was investigated in estimating the temperature distribution of a three-layer body with different thermal conductivities and convection boundary condition. In all of the considered test cases, the predicted results were in good agreement with analytical and CFD solutions. It was also indicated that for a relatively small number of particles, it is possible to achieve acceptable accuracy with a low computational cost.