The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries

This paper gives very significant and up-to-date analytical and numerical results to the three-dimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral op...

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Main Authors: Naji Qatanani, Monika Schulz
Format: Article
Language:English
Published: Wiley 2004-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/S1110757X04306108
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author Naji Qatanani
Monika Schulz
author_facet Naji Qatanani
Monika Schulz
author_sort Naji Qatanani
collection DOAJ
description This paper gives very significant and up-to-date analytical and numerical results to the three-dimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral operator of the radiosity equation have been thoroughly investigated and presented. The application of the Banach fixed point theorem proves the existence and the uniqueness of the solution of the radiosity equation. For a nonconvex enclosure geometries, the visibility function must be taken into account. For the numerical treatment of the radiosity equation, we use the boundary element method based on the Galerkin discretization scheme. As a numerical example, we implement the conjugate gradient algorithm with preconditioning to compute the outgoing flux for a three-dimensional nonconvex geometry. This has turned out to be the most efficient method to solve this type of problems.
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record_format Article
series Journal of Applied Mathematics
spelling doaj-art-6e8cb575a8df4e28a033d4e6d56fde462025-08-20T02:06:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422004-01-012004431133010.1155/S1110757X04306108The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometriesNaji Qatanani0Monika Schulz1College of Science and Technology, Al-Quds University, Abu Dis, P.O. Box 20002, Jerusalem, Palestinian AuthorityInstitute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, Stuttgart 70569, GermanyThis paper gives very significant and up-to-date analytical and numerical results to the three-dimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral operator of the radiosity equation have been thoroughly investigated and presented. The application of the Banach fixed point theorem proves the existence and the uniqueness of the solution of the radiosity equation. For a nonconvex enclosure geometries, the visibility function must be taken into account. For the numerical treatment of the radiosity equation, we use the boundary element method based on the Galerkin discretization scheme. As a numerical example, we implement the conjugate gradient algorithm with preconditioning to compute the outgoing flux for a three-dimensional nonconvex geometry. This has turned out to be the most efficient method to solve this type of problems.http://dx.doi.org/10.1155/S1110757X04306108
spellingShingle Naji Qatanani
Monika Schulz
The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
Journal of Applied Mathematics
title The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
title_full The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
title_fullStr The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
title_full_unstemmed The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
title_short The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries
title_sort heat radiation problem three dimensional analysis for arbitrary enclosure geometries
url http://dx.doi.org/10.1155/S1110757X04306108
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