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1 International Journal of Applied Mechanics and Engineering

1 2011

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Thermoconvective magnetized ferrofluid with internal angular momentum: a nonlinear stability analysis

Sunil, Mahajan A.

International Journal of Applied Mechanics and Engineering

2011

Vol. 16, no 2

557-580

The generalized energy method is developed to study the nonlinear stability analysis for a magnetized ferrofluid layer heated from below with intrinsic rotation of the particles, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic body force, inertia forces 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 the linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, 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, coupling parameter N1, and spin diffusion parameter N3, on the subcritical instability region has also been analyzed. It is shown that with the increase of the magnetic parameter (M3) 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 the nonlinear energy stability analysis as well as in the linear instability analysis.