Proposing a Numerical Solution for the 3D Heat Conduction Equation

Mansour Al Qubeissi

doi:10.1109/AMS.2012.10

Proposing a Numerical Solution for the 3D Heat Conduction Equation

Mansour Al Qubeissi

School of Mechanical, Aerospace and Automotive Engineering

Research output: Contribution to conference › Paper › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages	144-149
DOIs	https://doi.org/10.1109/AMS.2012.10
Publication status	Published - 2012
Event	Sixth Asia International Conference on Mathematical Modelling and Computer Simulation - Bali, Indonesia Duration: 29 May 2012 → 31 May 2012

Conference

Conference	Sixth Asia International Conference on Mathematical Modelling and Computer Simulation
Country	Indonesia
Period	29/05/12 → 31/05/12

Bibliographical note

© 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Keywords

3D heat conduction equation

Access to Document

10.1109/AMS.2012.10

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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. ",

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