Transient buoyant convection in a porous-medium enclosure by sudden imposition of gravity

Abstract

Transient buoyant convection in a rectangular cavity, filled with a fluid-saturated porous medium, is considered. The Brinkman-extended Darcy flow model is adopted. The vertical side walls are at two different temperatures, and the horizontal end walls are thermally insulated. At the initial state, the fluid is motionless and under zero gravity, and the conduction-controlled, horizontally linear temperature profile prevails. At t = 0, the gravity g = go is imposed on the system, and the flow is initiated. An order-of-magnitude analysis is performed. Numerical solutions are secured over broad ranges of nondimensional parameters. Similar to the pure-fluid model of Kim and Hyun (2003), due to the presence of the preexisting cavity-scale horizontal temperature gradient, bulk flows occur in much of the interior core at early times. As time approaches the steady state, the initial horizontally linear temperature profile decays, and cavity-scale bulk flows weaken. Considerations are focused on the influence of the porous medium on the transient flow. When epsilon(-1/2) Ra-1/2 Da is relatively high, the Darcy-term effect is meager, and transient behavior of the present porous system recovers that of the pure-fluid model. As C 112 Ra-1/2 Da is decreased, the Darcy-term effect becomes significant over the bulk flow period and for the steady state. Detailed evolutionary flow patterns are illustrated in various parameter spaces.