Combined effect of thermal modulation and rotation on the onset of stationary convection in a porous layer

Abstract

The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Darcy-Rayleigh number and wavenumber. The shift in critical Darcy-Rayleigh number is calculated as a function of frequency of modulation, Taylor number, and Darcy-Prandtl number. It is established that the convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase modulation. The effect of Taylor number and Darcy-Prandtl number on the stability of the system is also discussed. We found that by proper tuning of modulation frequency, Taylor number, and Darcy-Prandtl number it is possible to advance or delay the onset of convection. © Springer Science+Business Media, Inc. 2007.