Solution of radiative heat transfer problems with the discrete transfer method applied to triangular meshes

• Published in: Journal of computational and applied mathematics Vol. 168; no. 1-2; pp. 179 - 190
• Main Authors: Feldheim, Véronique, Lybaert, Paul
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2004; Elsevier
• Subjects: Discrete transfer method; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat transfer; Heat transfer in inhomogeneous media, in porous media, and through interfaces; Mathematical analysis; Mathematics; Partial differential equations; Physics; Radiative heat transfer; Ray effect; Sciences and techniques of general use; Triangular meshes; 35K05; Discrete transfer method; 80A20; Triangular meshes; Radiative heat transfer; Ray effect; Source terms; Numerical analysis; Applied mathematics; Gray medium; Benchmarks; Triangular finite element; Absorbing media; Radiative transfer; Heat transfer; Cylinders
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2003.05.016

The present communication deals with the solution of the radiative transfer equation in a gray absorbing media. The solution is performed on unstructured triangular meshes using the discrete transfer method (DTM). The application of the DTM to triangular meshes is detailed and discussed. The developed code is validated with benchmark cases and applied to pure radiative problem (with and without evaluation of the source term). The approach shows very good performances for the wall heat transfer evaluation. The discrete transfer method also presents a particular ray effect. This effect is clearly brought up with the study of radiative equilibrium between eccentric cylinders: wiggles can appear in the temperature field. To reduce this ray effect, the use of a great amount of rays is required to get a smooth (i.e. wiggle free) solution, in the case of pure radiative problems. The solution of coupled conductive–radiative problems or convective–radiative heat transfer necessitates less rays to obtain a converged solution.