Application of the lattice Boltzmann method and the discrete ordinates method for solving transient conduction and radiation heat transfer problems

This article deals with the use of the discrete ordinates method (DOM) to compute radiative information about an energy equation for a combined-mode heat transfer problem to be solved using the lattice Boltzmann method (LBM). For this study, transient conduction and radiation heat transfer in 1-D planar and 2-D rectangular geometries have been considered. To study the performance of the LBM-DOM combination, the energy equations of the two problems have also been solved using the finite-difference method (FDM) in which the radiative information has also been provided using the DOM. For the performance study of the two combinations of methods, i.e., the LBM-DOM and the FDM-DOM, results have been analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter, and the boundary emissivity. The results of the LBM-DOM combination have been found to be in excellent agreement with the FDM-DOM combination. The numbers of iterations and CPU times in the two combination methods have been found to be comparable.