A nonlinear stability analysis is performed to study the onset of convection in a fluid saturated porous layer subject to alternating direction of the centrifugal body force. By introducing a suitable energy functional, the analysis is carried out for the Darcy and the Brinkman models of flow through porous media. The nonlinear result is unconditional and its sharpest limit is determined and is compared with the corresponding linear limit. The failure of linear theory in describing the instability is established in a certain region of the parameter space where possible subcritical instabilities may arise. The stability boundaries are discussed graphically for various values of the Darcy number and comparison is made with the available known results.
A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection.
This paper deals with convective instability in a fluidsaturated, rotating porous layer subject to alternating direction of the centrifugal body force, when the layer fails to exhibit thermal equilibrium. The Darcy model is used to describe the flow, and a twofield model is used to take care of the energy exchange. The normal mode approach of the linear theory and the energy approach of the nonlinear theory are used to find the stability characteristics. Unconditional and sharp nonlinear thresholds are found. The study brings out the failure of the linear theory in describing the instability in most parts of the parameter space of interest where possible subcritical instabilities may arise. The stability boundaries are presented graphically and it is found that the interphase heat transfer coefficient has a significant effect in the thermal non-equilibrium regime.
a b s t r a c tThe energy method is employed to investigate the stability of a steady convective flow in a heat generating fluid arising due to the combined effect of buoyancy, shear and pressure gradient. By introducing a suitable generalized energy functional and using energy inequalities sufficient conditions for the existence of such a flow are found. An analysis through the variational principles is then made to find sharper limits for nonlinear stability. Comparisons are made with linear results in the literature and it is shown that the linear theory fails to capture the physics of the onset of secondary flow.
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