Thermal modulation of Raleigh-Benard convection in a sparsely packed porous medium

The linear stability of thermal convection in a horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation using the Brinkman model with effective viscosity larger than the fluid viscosity The temperature field between the walls of the porous layer consists of two parts; a steady part and a time-dependent part that varies periodically. The combined effect of permeability and modulation of the walls' temperature on the stability of flow through a porous medium has been investigated using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of amplitude and frequency of modulation, porous parameter, viscosity ratio, and Prandtl number. It is found that the permeability has a stabilizing influence on the onset of thermal instability. Furthermore, it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls' temperature. The effects of other parameters are also discussed.