Lattice Boltzmann Method Applied to the Analysis of Transient Conduction-Radiation Problems in a Cylindrical Medium

Abstract

The lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a 1-D concentric cylindrical participating medium. The finite-volume method (FVM) is used to obtain the radiative information. To study the effectiveness of the LBM-FVM combination to conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite-difference method (FDM) in which the FVM is used to compute radiative information. The effects of different parameters, such as the conduction-radiation parameter, the scattering albedo, the extinction coefficient, and the radius ratio on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. LBM-FVM results are also compared with those obtained by the FDM-FVM combination. In all cases, excellent agreement has been obtained.

Notes

β = 1.0, ω = 0.0, N = 0.1, r ₁ = 1.0, r ₂ = 2.0, T ₁/T ₂ = 0.1, and ϵ ₁ = ϵ ₂ = 1.0.

β = 1.0, r ₁/r ₂ = 0.5, and ϵ ₁ = ϵ ₂ = 1.0.