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

The stability of a Boussinesq fluid-saturated horizontal porous layer, heat ed from below, is examined for the case of a time-dependent buoyancy force generated by gravity modulation. The Brinkman-Forchheimer flow model with e ffective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. A method based on small amplitude o f the modulation is used to compute the critical values of the Rayleigh num ber and wave number. The shift in the critical Rayleigh number is calculate d as a function of frequency of the modulation, Prandtl number, porous para meter, and the ratio of the effective viscosity to the viscosity of the flu id. It is found that the low-frequency g jitter can have a significant effe ct on the stability of the system. It is also found that the effect of grav ity modulation is used to stabilize the system in case of a porous medium, far a large Prandtl number. The effect of the ratio of the effective viscos ity to the viscosity of the fluid is also shown. Finally, an asymptotic ana lysis is presented for small and large frequencies.