Effect of temperature modulation on the onset of stationary convection in a rotating sparsely packed porous layer

Abstract

The effect of temperature modulation on the onset of stationary convection in a Boussinesq fluid-saturated sparsely packed porous layer is investigated, when the porous layer is subjected to rotation about an axis parallel to the gravity vector. The linear stability analysis is used to study the effect of infinitesimal disturbances. The onset criterion is derived using perturbation expansion in powers of the small amplitude of the applied temperature field. The critical correction Rayleigh number is found to be a function of the frequency of modulation, the Taylor number, the Darcy number, the Prandtl number, and the viscosity ratio. The interaction of rotation and thermal modulation is studied. It is found that the rotation reinforces the effect of thermal modulation. The large-frequency symmetric modulation, asymmetric modulation, and bottom-wall temperature modulation stabilizes the system compared with the unmodulated system, while small-frequency symmetric modulation destabilizes it. The effect of the Darcy number, the Prandtl number, and the viscosity ratio on the stability of the system is also discussed. © 2007 NRC Canada.