A multi-relaxation-time lattice Boltzmann model for axisymmetric convection with both isotropic and anisotropic diffusions is proposed.
Chapman–Enskog analysis demonstrates that the macro cylindrical energy equation can be recovered.
Numerical results predicted by the present LB model show good agreement with the existing studies.
Natural convection in a vertical annulus with anisotropic thermal diffusion at different Rayleigh numbers are numerically investigated using the present LB model.
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.