Journal of Applied Mathematics

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

Naji Qatanani and Monika Schulz

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2004, Number 4 (2004), 311-330.

Dates
First available in Project Euclid: 8 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.jam/1099924167

Digital Object Identifier
doi:10.1155/S1110757X04306108

Mathematical Reviews number (MathSciNet)
MR2100258

Zentralblatt MATH identifier
1079.65117

Subjects
Primary: 45B05: Fredholm integral equations 65R20
Secondary: 65F10 65N38

Citation

Qatanani, Naji; Schulz, Monika. The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries. J. Appl. Math. 2004 (2004), no. 4, 311--330. doi:10.1155/S1110757X04306108. https://projecteuclid.org/euclid.jam/1099924167


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