Natural convection in porous media under non-Darcian and non-uniform permeability conditions

The first part of this work discusses the three effects for natural convection from a heated vertical plate embedded in a porous medium and some recent results are presented. The second part considers another class of problems involving non-uniform permeability. Many past studies have been conducted on the onset of natural convection with heating from below and cellular convection in rectangular enclosures with heating from either the vertical and/or horizontal boundaries. In a fluid-saturated porous medium, the onset of natural convection when heated from below is of considerable interests because of its connection with the modelling of geothermal fields. An excellent summary of this problem was provided by Cheng. Most studies assume the porous medium to be homogeneous. In real situations, especially for geothermal systems, inhomogeneities, particularly layering, are common