Exact Solution of Radiative Transfer Equation for Three-Dimensional Rectangular, Linearly Scattering Medium

Abstract

Three-dimensional radiative integral transfer equations for a cubic absorbing, emitting, and anisotropically scattering homogeneous medium are solved. To remove existing singularities of the radiative integral transfer equations, the surface and volume integrals arising from the application of the subtraction of the singularity technique are analytically treated to ensure highly accurate solutions and to reduce the computational time. The resulting system of linear equations from the integral equations of the incident energy and the net partial heat fluxes are solved iteratively. Three benchmark problems for a cold participating medium, subjected to externally diffuse radiation loads in various combinations, are considered. The solutions for the incident energy and the net partial radiative heat fluxes are given in tabular and/or graphical form for scattering albedos of ! 0 0:01, 0.5, and 1.

Multi-hp adaptive discontinuous Galerkin methods for simplified P approximations of 3D radiative transfer in non-gray media

“…Modelling and simulation of radiative transfer are for decades a vast research area in mathematics and engineering, see [24,1,2] and the references therein. The main focus in these studies is on the analytical and numerical resolutions of the boundary layers due to temperature gradients.…”

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

“…Li et al [20] adopted the Galerkin boundary element method to discretize the thermal radiation problem without scattering. Altac [3], [4] used a singularity removal method to calculate the surface and volume integrals from the RITEs model.…”