%0 Journal Article
%A Sunil,
%A Sharma, Poonam
%A Mahajan, Amit
%D 2009
%I Begell House
%N 7
%P 667-682
%R 10.1615/JPorMedia.v12.i7.50
%T A Nonlinear Stability Analysis for Thermoconvective Magnetized Ferrofluid with Magnetic-Field-Dependent Viscosity Saturating a Porous Medium
%U http://dl.begellhouse.com/journals/49dcde6d4c0809db,73fc19a203a9e84e,455d5a7835aef6e4.html
%V 12
%X A nonlinear stability analysis of a magnetized ferrofluid with magnetic-field-dependent (MFD) viscosity heated from below, saturating a porous medium for the case of stress-free boundaries, is studied by a generalized energy method. 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. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of the linear one, thus indicating that subcritical instabilities are possible. It is also observed that a subcritical region of instability can be induced by a magnetic mechanism alone. However, the global nonlinear stability Rayleigh number is found to be exactly the same as that for linear instability in the case of a non-ferrofluid. For lower magnetic parameter values, this coincidence is immediately lost. The effect of the magnetic parameter (*M*_{3}), medium permeability (*D*_{a}), and MFD viscosity (δ) on the subcritical instability region has also been analyzed. It is shown that with the increase of the magnetic parameter (*M*_{3}) and Darcy number (*D*_{a}), the subcritical instability region obtained by the two theories decreases, whereas with the increase of MFD viscosity δ, the subcritical instability region expands.
%8 2009-07-01