Lattice Boltzmann simulations of axisymmetric natural convection with anisotropic thermal diffusion

Abstract

In this article, a multi-relaxation-time lattice Boltzmann model for axisymmetric flow and heat transfer is presented. The main advantage of the present LB model is that it is able to simulate flow and heat transfer with anisotropic thermal diffusions. Also, by incorporating the radial coordinate into the temperature distribution function, only one simple source term is needed in the present LB model and thus the simplicity of the LB is well kept. Chapman–Enskog analysis demonstrates that the macro cylindrical energy equation can be exactly recovered. Numerical results obtained by the present LB model show good agreement with the existing studies. Natural convection in a vertical annulus with anisotropic thermal diffusion coefficient at different Rayleigh numbers are numerically investigated using the present LB model. It is found that as the thermal diffusion coefficient increases, the average Nusselt number decreases while the maximum axial velocity at the mid-height of the cylinder increases, which implies that both the diffusion and convection increases, and the diffusion triumphs over convection as thermal diffusion coefficient gets larger. What’s more, flow and heat transfer is more sensitive to the radial thermal diffusion coefficient as the radial thermal diffusion coefficient itself is relatively small. Also, the diffusion coefficient in the radial direction exerts much more influence on the flow and heat transfer than that in the axial direction in the present physical model.