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.
Accepted Version (Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.