Convection in a Box of Porous Material Saturated with Fluid

Abstract

The true critical Rayleigh number for the onset of a convective flow of a fluid in a rectangular box of porous material heated from below is found for various box geometries. The preferred cellular mode of the motion at Rayleigh numbers just above the critical is determined. In contrast with the established results for the similar problem in a continuous fluid, the roll (a cell with only two nonzero velocity components) is not the only cellular mode and the roll axis direction is such that there is the greatest degree of “squareness” in the cross section of each roll. The invalidity of a frequently used form of Darcy's law and the present form of the energy method for the stability of flows in which fluid crosses the boundaries is discussed.