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

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

5 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
Title of host publication	2012 Sixth Asia Modelling Symposium
Publisher	IEEE
Pages	144-149
Number of pages	6
ISBN (Print)	978-1-4673-1957-7
DOIs	https://doi.org/10.1109/AMS.2012.10
Publication status	Published - 19 Jul 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/Territory	Indonesia
Period	29/05/12 → 31/05/12

Keywords

3D heat conduction equation

Access to Document

10.1109/AMS.2012.10

Cite this

@inproceedings{9360fb413d2649f5b991f133f0b215a7,

title = "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. ",

keywords = "3D heat conduction equation",

author = "{Al Qubeissi}, Mansour",

year = "2012",

month = jul,

day = "19",

doi = "10.1109/AMS.2012.10",

language = "English",

isbn = "978-1-4673-1957-7",

pages = "144--149",

booktitle = "2012 Sixth Asia Modelling Symposium",

publisher = "IEEE",

address = "United States",

note = "Sixth Asia International Conference on Mathematical Modelling and Computer Simulation ; Conference date: 29-05-2012 Through 31-05-2012",

}

TY - GEN

T1 - Proposing a Numerical Solution for the 3D Heat Conduction Equation

AU - Al Qubeissi, Mansour

PY - 2012/7/19

Y1 - 2012/7/19

N2 - 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.

AB - 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.

KW - 3D heat conduction equation

U2 - 10.1109/AMS.2012.10

DO - 10.1109/AMS.2012.10

M3 - Conference proceeding

SN - 978-1-4673-1957-7

SP - 144

EP - 149

BT - 2012 Sixth Asia Modelling Symposium

PB - IEEE

T2 - Sixth Asia International Conference on Mathematical Modelling and Computer Simulation

Y2 - 29 May 2012 through 31 May 2012

ER -

Proposing a Numerical Solution for the 3D Heat Conduction Equation

Abstract

Conference

Keywords

Access to Document

Fingerprint

Cite this