Abstract
A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD) viscosity saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic-body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that, in case of a 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; Darcy number, Da; and MFD viscosity parameter, δ; on the subcritical instability region has also been analyzed.
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