A mathematical method for solving mixed problems in multislab radiative transfer

Abstract

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

On Increasing the Efficiency of a Discrete Ordinates Radiative Transfer Method With Periodic Relations

“…22). From this condition (de Abreu, 2003;de Abreu, 2004a), the coefficients g r,m , r = 1:R, m = 1:N, can be found to be given by: from 1 to N) are found to satisfy the system of N linear algebraic equations…”

On Increasing the Efficiency of a Discrete Ordinates Radiative Transfer Method With Periodic Relations

“…22). From this condition (de Abreu, 2003;de Abreu, 2004a), the coefficients g r,m , r = 1:R, m = 1:N, can be found to be given by:…”

“…A two-component method for solving both conservative and non-conservative discrete ordinates (S N ) radiative heat transfer problems defined on a multislab domain irradiated from one side with a beam of radiation has been recently developed by the author (de Abreu, 2003;de Abreu, 2004a). The beam is allowed to be composed of a monodirectional (singular) stream and of a continuous (regular) distribution in angle.…”

“…Solution to the uncollided problem is fairly easily obtained but, solution to the diffusive problem is not usually so. Then, a standard S N approximation (Lewis and Miller Jr., 1993) has been considered to the diffusive problem, which has been solved with an improved spectral nodal method free from spatial truncation error (de Abreu, 2003;de Abreu, 2004a). In addition, the slabgeometry equivalence between S N and spherical harmonics (P N ) formulations (Duderstadt and Martin, 1979) has been used to generate an angularly continuous approximation to the solution of the diffusive problem.…”