Title

Development of an efficient solution method for solving the radiative transfer equation

Abstract

The radiative heat transfer equation in a participating medium is a Fredholm integral equation of the second kind whose kernels are formally singular at the position where the incident radiation is to be determined. A general method is developed to remove this singularity by capitalizing on the mutual interactions between the source function and the exponential integral appearing in the kernel. The method is based on an interpolation of the unknown source functions, and the analytical integration of the resulting product in the integrand (source function expansion multiplied by the known exponential integral). As such, the method is considered semi-analytical. The method is superior to traditional solution techniques which employ quadratures approximating both the unknown and known functions appearing in the integrand, and which consequently, have numerical difficulties in addressing singularities. The general approach is presented in detail for one-dimensional problems, and extensions to two-dimensional enclosures are also given. One and two-dimensional numerical examples are considered, comparing our predictions to benchmark work. The method is shown to be computationally efficient and highly accurate. In comparison with traditional quadrature based techniques, our method readily handles the singularity of the exponential integral of first order at zero, converges rapidly under grid refinement, and provides superior prediction for radiative heat transfer. The technique is shown to be valid for a wide range of values of the scattering albedo and optical thickness. The proposed technique could be applied to a wide range of conservation problems which lend themselves to an integral formulation.

Publication Date

12-1-1996

Publication Title

American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD

Volume

332

Number of Pages

109-117

Document Type

Article

Personal Identifier

scopus

Socpus ID

0030397407 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0030397407

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