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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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X04306108 |
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| _version_ | 1850222177091059712 |
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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. |
| format | Article |
| id | doaj-art-6e8cb575a8df4e28a033d4e6d56fde46 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| 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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