Lattice Boltzmann Method Applied to Variable Thermal Conductivity Conduction and Radiation Problems

In the present article, application of the lattice Boltzmann method has been extended to solve the energy equation of a problem involving temperature dependent thermal conductivity. To validate the formulation, transient heat conduction in a planar medium with and without temperature dependent thermal conductivity was analyzed. Next, a problem involving transient conduction and radiation in a participating medium was considered. To compare with the performance of the lattice Boltzmann method, the energy equation was also solved using the finite difference method. The discrete ordinates method was used to compute the radiative information in both methods. After benchmarking the results against those available in the literature, temperature and heat flux results in the two methods were compared for different parameters. The results of the two methods were found to compare very well.