The usage of the Lattice Boltzmann Method (LBM) in heat transfer problems has gained a momentum and this method has also been applied to solve energy equations of problems dealing with conduction, convection and /or radiation heat transfer.
The relaxation time in the LBM depends on the thermal/momentum diffusivity, the lattice size and the time step. If either of them is not a constant, the relaxation time becomes a variable one. In heat transfer applications so far, the LBM with a variable relaxation time owing to non-uniform lattice sizes have not been studied.
To enhance the computational efficiency of the LBM, in the present work, a variable relaxation time LBM was used to analyze transient conduction and radiation heat transfer in a 1-D planer absorbing, emitting and scattering medium. The relaxation time was made variable by considering non-uniform lattices/control volumes. The radiative information of the energy equation was computed using the finite volume method. Temperature results for various parameters like the scattering albedo, the conduction radiation parameter and the emissivity were analyzed for both constant and variable relaxation time LBM. Variable relaxation time LBM was also found to provide accurate results and for the same number of lattices/control volumes, computationally it was found faster.