Development of a thermal lattice Boltzmann method to simulate heat transfer problems with variable thermal conductivity

In this study, a modified thermal lattice Boltzmann method is developed to model heat transfer problems with variable thermal conductivity. The Chapman-Enskog analysis is employed to mathematically derive the transient energy equation. The variation of the thermal conductivity has been considered by adding an extra term to the equilibrium function. The present model is validated against 1-D and 2-D heat conduction problems under steady and transient conditions. The nonlinearity due to variation of thermal conductivity in a combined radiation-conduction heat transfer problem has been studied in a 2-D rectangular enclosure. Good agreement with available data is obtained. Finally, it is shown that the present model is capable of simulating the effect of high nonlinearity in the heat transfer equation in presence of a heat generation source. This has been accomplished by employing a multi relaxation time scheme to model a natural convection current in a 2-D cavity.