A lattice Boltzmann model for the conjugate heat transfer

Abstract

Conjugate heat transfer problems are of great importance in many applications, while the available lattice Boltzmann (LB) models have some limitations in the study of such problems with the heterogeneous media. In this paper, we develop a new LB model for the conjugate heat transfer problems where the evolution equation with a modified equilibrium distribution function and a source term is considered. Through the Chapman–Enksog analysis, the macroscopic temperature equation can be recovered correctly. In order to test the accuracy, efficiency and stability of this LB model, some simple but nontrivial benchmark problems, including the planar thermal Poiseuille flow with two immiscible fluids, the conjugate heat transfer between a stratified heterogeneous medium with variable thermophysical properties, the steady and unsteady-state planer thermal flows with the two immiscible fluids, the steady-state conjugate heat transfer problem with a vertical interface, and the natural convection in a square cavity filled with circular and square rods, are studied. It is found that the results obtained from the present LB model are in good agreement with the analytic solutions or some previous works. In addition, it is also demonstrated that the developed LB model has a second-order convergence rate in space, and is more stable than some previous LB models. Finally, it should be noted that in our work, there is no special treatment to the interface, and the continuity conditions at the interface can be satisfied automatically.