Solution of the Isotropic Heat Equation Using the Finite Volume Monte Carlo Method

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, University of Bojnord, Bojnord, North Khorasan, Iran

2 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract

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 used for the solution of the isotropic heat equation due to two intrinsic capabilities 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 is a statistical approach based on the physical simulation of the problem capable to solve heat equation with any degree of complexity. First, a simple problem was investigated for validation of the method by comparing results with the analytical solution. Second, the prediction performance of the finite volume Monte Carlo 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 computational fluid dynamics 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.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 1 (Special Issue)
April 2021
Pages 467-482

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