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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.

Effect of rotation on double-diffusive convection in a magnetized ferrofluid with internal angular momentum saturating a porous medium

Sunil, Mahajan A.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 4

1059-1078

This paper deals with the theoretical investigation of the effect of rotation in a magnetized ferrofluid with internal angular momentum, heated and soluted from below saturating a porous medium and subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been employed to study the onset of convection. The influence of various parameters on the onset of stationary convection such as rotation, medium permeability, solute gradient, magnetization and internal angular momentum parameters (i.e., coupling parameter, spin diffusion parameter and heat conduction parameter) has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferrofluid with internal angular momentum saturating a porous medium heated from below in the absence of rotation, coupling between vorticity and spin, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the rotation, coupling between vorticity and spin, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.