Lattice Boltzmann method simulation of natural convection heat transfer in horizontal annulus

The lattice Boltzmann method is employed to simulate the stability and transitions of natural convection in a horizontal annulus with the Prandtl number varying from 0.1 to 0.7 and the Rayleigh number ranging from 103 to 5.0 × 105. Different flow patterns including steady upward flow, oscillatory upward flow, steady downward flow, and oscillatory downward flow are found for different values of the parameters. The flow pattern is very complex when the Rayleigh number is large. The critical Rayleigh number increases with the increase of the Prandtl number and with the decrease of the aspect ratio.