Penetrative Convection in a Fluid Overlying a Highly Porous Material

Summary This article examines the linear and nonlinear stability analyses of penetrative convection in a two-layer system in which a layer of fluid overlies and saturates a highly porous material, with an internal heat source/sink. A two-layer approach is adopted, in which the flow within the porous medium is governed by the Darcy–Brinkman equations, while the Stokes equations describe the flow in the overlying fluid layer. The lower boundary of the porous medium is maintained at a constant temperature, whereas the upper boundary of the fluid layer is held at a higher constant temperature. Internal and quadratic temperature-dependent density takes place in both layers and allows the model to describe penetrative convection. A normal mode approach is employed for the linear analysis, and the energy method is employed for the nonlinear analysis. The comparison between linear and nonlinear theories gives the region of subcritical instability, and within a certain regime, the region of subcritical instability exists. It is found that a heat source/sink in the fluid layer and porous layer has a destabilizing effect on the porous layer and on the fluid, respectively. Also, the ratio of thermal diffusivity parameters, porosity, and Darcy number has a destabilizing effect. Furthermore, it can be seen that the temperature of the upper surface has a stabilizing effect, and the system exhibits greater instability when the internal heat sink of the porous layer is higher compared to that of the fluid layer.