A Comparison of the Discrete Ordinates Method and Finite Volume Method for Radiative Heat Transfer Analysis

The time-dependent equation of radiative transfer is solved for a participating medium housed in an axisymmetric cylindrical enclosure by both the discrete-ordinates method and the finite volume method. Many heat transfer processes, including absorption of renewable and sustainable solar energy in a solar receiving tube for use in power plants, can be modeled in a cylindrical enclosure. Steady-state and transient heat flux profiles are generated for both purely absorbing and absorbing-scattering media using both solution methods. The effect of changes in scattering albedo and optical thickness is investigated. A basic modeling of a solar energy receiving tube is presented, and the volumetric radiative absorbed energy rate at the radial centerline is calculated to determine the amount of absorbed energy that can be transferred to a working fluid in a solar reactor. Comparisons of both computational time and committed memory usage for each method are presented. In general, heat fluxes predicted by the FVM with 288 directions tend to slightly underpredict those determined using the DOM S₁₆ quadrature. The FVM requires more committed memory and has longer convergence times than the DOM due to the inherent differences in angular quadrature.