Discrete Ordinate Methods for Radiative Heat Transfer in Isotropically and Anisotropically Scattering Media

TLDR: In this paper, the authors focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropic scattering media and demonstrate that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth-order solution using Gauss quadratures.

Abstract: The objective of this note is to focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropically scattering media. In particular, one dimension is chosen only for simplicity, since exact solutions are available for benchmarking the discrete ordinate method. One-dimensional radiative heat transfer has been analyzed in many previous investigations and has been extensively reviewed by Viskanta. The development of the discrete ordinate method has been described in detail by Chandrasekhar and Lathrop. The discrete ordinate method using Gauss quadrature has been compared with approximate solutions. In the cases previously analyzed solutions were obtained using ordinate sets that were larger than necessary. This note demonstrates that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth order solution using Gauss quadrature.