Double Diffusive Convection in a Rotating Porous Layer with Temperature Modulation on the Boundaries

Linear stability analysis is performed to find the effect of temperature modulation on the onset of double diffusive convection in a rotating horizontal layer of a fluid-saturated porous medium using Darcy-Lapwood-Brinkman's model. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The combined effect of rotation, permeability, and temperature modulation on the onset of double diffusive convection in a porous medium has been investigated using Galerkin method. The value of the critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Prandtl number, Taylor number, Darcy number, diffusivity ratio, and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. Furthermore, it is found that both rotation and the porous medium have stabilizing influences on the system. The effect of other parameters on the stability of the system is also discussed.