Proposing a Numerical Solution for the 3D Heat Conduction Equation

Abstract

The current paper presents a numerical technique in solving the 3D heat conduction equation. The Finite Volume method is used in the discretisation scheme. Gauss's theorem has also been employed for solving the integral parts of the general heat conduction equation in solving problems of steady and unsteady states. The proposed technique is applicable to unstructured (tetrahedral) elements for dealing with domains of complex geometries. The validation cases of the developed, FORTRAN based, heat conduction code in 1D, 2D and 3D representations have been reviewed with a grid independence check. Comparisons to the available exact solution and a commercial software solver are attached to the manuscript.