The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

Abstract

AbstractThis article deals with the implementation of the lattice Boltzmann method (LBM) in conjunction with the finite volume method (FVM) for the solution of conduction–radiation problems with heat flux and temperature boundary conditions. Problems in 1‐D planar and 2‐D rectangular geometries have been considered. The radiating–conducting participating medium is absorbing, emitting and scattering. In the 1‐D planar geometry, the south boundary is subjected to constant heat flux, while in the 2‐D geometry the south and/or the north boundary is at constant heat flux condition. The remaining boundaries are at prescribed temperatures. The energy equation is solved using the LBM and the radiative information for the same is computed using the FVM. In the direct method, by prescribing temperatures at the boundaries, the temperature profile and heat flux are calculated. The computed heat flux values are imposed at the boundaries to establish the correctness of the numerical code in the inverse method. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction–radiation parameter, the boundary emissivity and the total heat flux and boundary temperatures are studied on the distributions of temperature, radiative and conductive heat fluxes. The results of the LBM in conjunction with the FVM have been found to compare very well with those available in the literature. Copyright © 2008 John Wiley & Sons, Ltd.