Effect of Temperature Modulation on the onset of Darcy Convection in a Rotating Porous Medium

In this article, we study the effect of temperature modulation on the onset of thermal instability in a horizontal layer of a fluid-saturated porous medium heated from below and subjected to constant rotation. An extended Darcy model, which includes the time derivative term, has been considered, and a time-dependent periodic temperature field is applied to modulate the surfaces' temperature. A perturbation procedure based on the small amplitude of imposed temperature modulation is used to study the combined effect of rotation, permeability, and temperature modulation on the stability of flow through a porous medium. The correction in the critical Darcy Rayleigh number is calculated as a function of amplitude and frequency of modulation, the Darcy Taylor number, and the Vadasz number. It is found that both rotation and permeability suppress the onset of thermal instability. Furthermore, we find that temperature modulation can advance or delay the onset of convection.