The lattice Boltzmann equation for natural convection in a two-dimensional cavity with a partially heated wall

Abstract

The lattice Boltzmann equation method in two dimensions was used to analyse natural convective flows. The method was validated with experiments in an open cavity with one of the vertical walls divided into two parts, the lower part conductive, the upper part and all the other walls adiabatic. An upward thermal boundary layer formed near the conductive wall. This layer gave way to a wall plume. The numerical results compared well with experiments in the laminar ($Ra\,{=}\,2.0\,{\times}\,10^9$) and transition ($Ra\,{=}\,4.9\,{\times}\,10^9$) regimes. The behaviour of the starting plume was numerically studied for Rayleigh numbers Ra from $10^6$ to $4.9\times 10^9$. The wall plume grows in three stages: in the first with constant acceleration, in the second with constant ascending velocity and in the third with negative acceleration due to the presence of the top boundary layer. The acceleration of the first stage and the velocity of the second both scale with the Rayleigh number.