Convective heat transfer in porous and overlying fluid layers heated from below

The onset of convection when a porous layer underlying a fluid layer is heated from below has been numerically investigated. In order to validate the interface boundary conditions along with the numerical scheme, the present study has focused on the critical Rayleigh number and the corresponding number of cells. In addition, the effects of the Rayleigh number, aspect ratio and thickness ratio on supercritical convection in the composite layer have been investigated. The results show that the number of cells at the critical Rayleigh number (Ra-pc) is in good agreement with the previous report based on the linear stability theory. The abrupt change in convective flow patterns accurately verifies the precipitous drop of Ra-pc with the increasing the depth ratio (d) and the rapid change of the wave number (a(p)) near d = 0.12. As Ra-p increases, the cell size changes for all depth ratios (d = 1.0, 0.5, 0.2, 0.1 and 0). In particular, heat transfer rate changes dramatically due to the effects of the aspect ratio and the corresponding number of cells when d = 0.1.