Throughflow and Quadratic Drag Effects on Thermal Convection in a Rotating Porous Layer

A linear stability analysis is implemented to study thermal convective instability in a horizontal fluid-saturated rotating porous layer with throughflow in the vertical direction. The modified Forchheimer-extended Darcy equation that includes the time-derivative and Coriolis terms is employed as a momentum equation. The criterion for the occurrence of direct and Hopf bifurcations is obtained using the Galerkin method. It is shown that if a Hopf bifurcation is possible it always occurs at a lower value of the Darcy–Rayleigh number than the direct bifurcation. Increase in the throughflow strength and inertia parameter is to decrease the domain of Prandtl number up to which Hopf bifurcation is limited but opposite is the trend with increasing Taylor number. The effect of rotation is found to be stabilizing the system, in general. However, in the presence of both rotation and Forchheimer drag a small amount of vertical throughflow as well as inertia parameter show some destabilizing effect on the onset of direct bifurcation; a result of contrast noticed when they are acting in isolation. The existing results in the literature are obtained as limiting cases from the present study