Rayleigh-Benard convection subject to time dependent wall temperature/gravity in a fluid-saturated anisotropic porous medium

Abstract

The effect of time-periodic temperature/gravity modulation at the onset of convection in a Boussinesq fluid-saturated anisotropic porous medium is investigated by making a linear stability analysis. Brinkman flow model with effective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature/gravity modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of the modulation, viscosity ratio, anisotropy parameter and porous parameter. We have shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature and to advance convection by gravity modulation. It is also shown that the small anisotropy parameter has a strong influence on the stability of the system. The effect of viscosity ratio, anisotropy parameter, the porous parameter and the Prandtl number is discussed.