A mathematical method for solving mixed problems in multislab radiative transfer

• Autor(a) principal: Abreu,M. P. de
• Data de Publicação: 2005
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782005000400006
• topic: Radiative transfer; multislab problems; mixed beams; conservative scattering; discrete ordinates

In this article, we describe a mathematical method for solving both conservative and non-conservative radiative heat transfer problems defined on a multislab domain, which is irradiated from one side with a beam of radiation. We assume here that the incident beam may have a monodirectional (singular) component and a continuously distributed (regular) component in angle. The key to the method is a Chandrasekhar decomposition of the (mathematical) multislab problem into an uncollided transport problem with singular boundary conditions and a diffusive transport problem with regular boundary conditions. Solution to the uncollided problem is straightforward, but solution to the diffusive problem is not so. For then we make use of a recently developed discrete ordinates method to get an angularly continuous approximation to the solution of the diffusive problem. We suitably compose uncollided and diffuse solutions, and the task of generating an approximate solution to the original multislab radiative transfer problem is complete. We illustrate the accuracy of the proposed method with numerical results for a test problem in shortwave atmospheric radiation, and we conclude this article with a discussion.