THE BRINKMAN MODEL FOR NATURAL-CONVECTION IN A POROUS LAYER - EFFECTSOF NONUNIFORM THERMAL-GRADIENT

The effects of nonlinear temperature distribution on stability and nat ural convection in a horizontal porous layer, with heating from below, are investigated using the Brinkman model. The horizontal boundaries are either rigid/rigid, rigid/stress-free, or stress-free/stress-free. Constant-flux thermal boundary conditions are considered for which th e onset of convection is known to correspond to a vanishingly small wa venumber. An analytical solution for the flow and heat transfer variab les, based on a parallel flow assumption, is obtained in terms of the Darcy-Rayleigh number, R, and the Darcy number, Da. The critical Rayle igh number for the onset of convection arising from sudden heating or cooling at the boundaries is also predicted. Various basic temperature profiles are considered. Closed form solutions are obtained from whic h results for a viscous fluid (Da --> infinity) and the Darcy porous m edium (Da --> 0) emerge from the present analysis as limiting cases.