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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.244 SNIP: 0.434 CiteScore™: 0.7

ISSN Imprimir: 1940-2503
ISSN On-line: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2015014843
pages 353-371

HIGH-ORDER SPHERICAL HARMONICS METHOD FOR RADIATIVE TRANSFER IN SPHERICALLY SYMMETRIC PROBLEMS

Guillaume Lambou Ymeli
Laboratoire de Mecanique et de Modelisation des Systemes Physiques (L2MSP), Department of Physics/Faculty of Science, University of Dschang, Cameroon, P.O. Box 67 Dschang, Cameroon
Herve Thierry Kamdem Tagne
University of Dschang

RESUMO

A matrix formulation of the spherical harmonics method to predict radiative transfer in participating layer and layered media within spherical geometry is presented. This formulation combines forward finite-difference spatial discretization and the conjugate gradient squared methods to solve the resulting partial differential equations of radiative intensity moments. Henceforth, a high-order spherical harmonics solution has been obtained without difficulty. Comparisons with other methods are carried out for boundary radiative fluxes, transmittance, and reflectance associated with radiative heat transfer through homogeneous/inhomogeneous, isotropic/anisotropic participating spherical layer and layered media. The comparisons show excellent agreement between exact and very high-order spherical harmonics predictions. It was found that a high order of the PN approximation is necessary to produce accurate results at the inner boundary of hollow spherically symmetric media, while low- or moderate-order of the PN approximation is sufficient to obtained accurate results at the outer boundary of both hollow and solid spherically symmetric media.


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