A nonlinear stability analysis in a double-diffusive magnetized ferrofluid layer saturating a porous medium

A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer heated and soluted from below, saturating a porous medium in the stress-free boundary case. A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that subcritical instabilities may exist but, in the case of non-ferrofluid, the 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 the magnetic parameter, M3, solute gradient, Sf, and Darcy number, Da, on the subcritical instability region has also been analysed. It is shown that with an increase of the magnetic parameter and Darcy number the subcritical instability region between the two theories decreases quickly, while with an increase in solute gradient the subcritical region expands. We also demonstrate coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis