Effect of gravity modulation on the onset of convection in a porous layer

Abstract

The stability of a Boussinesq fluid-saturated horizontal porous layer, heated from below, is examined for the case of a time-dependent buoyancy force generated by gravity modulation. The Brinkman-Forchheimer flow model with effective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. A method based on small amplitude of the modulation is used to compute the critical values of the Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of the modulation, Prandtl number, porous parameter, and the ratio of the effective viscosity to the viscosity of the fluid. It is found that the low-frequency g jitter can have a significant effect on the stability of the system. It is also found that the effect of gravity modulation is used to stabilize the system in case of a porous medium, for a large Prandtl number. The effect of the ratio of the effective viscosity to the viscosity of the fluid is also shown. Finally, an asymptotic analysis is presented for small and large frequencies. Copyright © 1998 by Marcel Dekker, Inc.