Thermoconvective magnetized ferrofluid with internal angular momentum saturating a porous medium: A nonlinear stability analysis

The generalized energy method is developed to study the nonlinear stability analysis for a magnetized ferrofluid layer with intrinsic rotation of particles, heated from below saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body force and body couple on a fluid element. By introducing a suitable generalized energy functional, we perform a nonlinear energy stability (conditional) analysis. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter M3, medium permeability Da, coupling parameter N1, and spin diffusion parameter N3′, on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter (M3) and Darcy number (Da), the subcritical instability region between the two theories decreases quickly while with the increase of N1 and N3′, the subcritical instability region between the two theories increases. We also demonstrate coupling between the buoyancy and magnetic forces in nonlinear energy stability analysis as well as in linear instability analysis.