Onset of Darcy-Convection in a Magnetic-Fluid-Saturated Porous Medium Subject to Temperature Modulation of the Boundaries

Abstract

In the present article, we study the effect of temperature modulation on the onset of thermal convection in an electrically conducting-fluid-saturated porous medium, which is heated from below and cooled from above. The porous medium is confined between two horizontal walls, and subjected to a vertical magnetic field. The temperature gradient between the walls of the porous medium consists of a steady part and a time dependent part, which is oscillatory. Performing the linear stability analysis, the combined effect of magnetic field and temperature modulation on the stability of flow through porous medium has been investigated using Perturbation procedure. The correction in the value of the critical Darcy Rayleigh number is calculated as function of amplitude and frequency of modulation, Darcy Chandrasekhar number, thermal Prandtl number, magnetic Prandtl number and the Vadasz number Va. The influences of the magnetic field and the Vadasz number have been studied. Further, it is found that the effect of temperature modulation on the onset of convection is to advance or delay the convection, depending on the proper tuning of the frequency of modulation.