Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures

The S_n discrete-ordinates method is used to find numerical solutions in a two-dimensional rectangular enclosure with a gray absorbing, emitting, and isotropically scattering medium. Results are obtained for the S₂, S₄, and S₆ approximations that correspond to 4, 12, and 24 flux approximations, respectively, and are compared with exact solutions, numerical Hottel’s zone results, P3 differential approximations, and an approximation method developed by Modest. The S₂ approximation solutions were found to be applicable only for several specific cases and are not recommended for general use. The S₄ and S₆ solutions compare favorably with other methods and can be used to predict radiant intensity and surface heat transfer rate for various surface and optical conditions.