Chebyshev Collocation Spectral Methods for Coupled Radiation and Conduction in a Concentric Spherical Participating Medium

Abstract

The Chebyshev collocation spectral method for coupled radiative and conductive heat transfer in concentric spherical participating medium is introduced and formulated. The angular dependence of the problem is discretized by conventional discrete ordinates method, and the space dependence is expressed by Chebyshev polynomial and discretized by collocation spectral method. Due to the exponential convergence of the spectral methods, very high accuracy can be obtained even using a small resolution (i.e., number of collocation points) for present problems. Comparisons between the solutions from Chebyshev collocation spectral–discrete ordinates method (SP-DOM) with available numerical or exact solutions in references indicate that the SP-DOM for the combination of radiation and conduction in concentric spherical participating medium is accurate and efficient.