Coriolis effect on thermal convection in a couple-stress fluid-saturated rotating rigid porous layer

Abstract

Both linear and weakly nonlinear stability analyses are performed to study thermal convection in a rotating couple-stress fluid-saturated rigid porous layer. In the case of linear stability analysis, conditions for the occurrence of possible bifurcations are obtained. It is shown that Hopf bifurcation is possible due to Coriolis force, and it occurs at a lower value of the Rayleigh number at which the simple bifurcation occurs. In contrast to the nonrotating case, it is found that the couple-stress parameter plays a dual role in deciding the stability characteristics of the system, depending on the strength of rotation. Nonlinear stability analysis is carried out by constructing a set of coupled nonlinear ordinary differential equations using truncated representation of Fourier series. Sub-critical finite amplitude steady motions occur depending on the choice of physical parameters but at higher rotation rates oscillatory convection is found to be the preferred mode of instability. Besides, the stability of steady bifurcating equilibrium solution is discussed using modified perturbation theory. Heat transfer is calculated in terms of Nusselt number. Also, the transient behavior of the Nusselt number is investigated by solving the nonlinear differential equations numerically using the Runge-Kutta-Gill method. It is noted that increase in the value of Taylor number and the couple-stress parameter is to dampen the oscillations of Nusselt number and thereby to decrease the heat transfer.

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

“…Following the same procedure, the equation of motion for couple-stress fluid through porous media can be obtained from Eq. (3) and with the inclusion of inertial effect the equation reads as [17,18] …”

“…Gaikwad et al [16] have investigated linear and nonlinear double diffusive convection by considering both Soret and Dufour effects in a layer of couple-stress liquid. Recently, Shivakumara [17] has discussed the effect of various nonuniform basic temperature gradients on the onset of convection in a layer of couple stress fluid-saturated porous layer, while Shivakumara et al [18] have analyzed the effect of Coriolis force on both linear and weakly nonlinear thermal convection in a couple stress fluid-saturated rotating rigid porous layer.…”

On oscillatory rotating convection of a couple‐stress fluid with helical force

“…Hsu et al 20 investigated the effects of couple stress and surface roughness on the non‐Newtonian fluid. The nonlinear stability results for couple‐stress fluids were obtained by Sunil et al 21 Shivakumara et al 22,23 discussed the nonlinear instability theory of a couple stress fluid. The problem of thermal instability of a couple‐stress fluid in a porous layer with the effect of an internal heat source was studied by Gaikwad and Kouser 24 .…”

Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

“…The effect of rotation on double diffusive convection in a magnetized ferrofluid with an internal angular momentum was studied by Sunil et al [15]. The effect of Coriolis force on thermal convection in a couple stress fluid saturated rotating rigid porous layer was studied by Shivakumara et al [16]. Paras Ram et al [17][18] discussed the ferrofluid flow with magnetic field dependent viscosity due to a rotating disk with and without a porous medium.…”