A Nonlinear Stability Analysis for Thermoconvective Magnetized Ferrofluid Saturating a Porous Medium |
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Authors: | Sunil and Amit Mahajan |
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Institution: | (1) Department of Applied Sciences, National Institute of Technology, Hamirpur, H.P., 177 005, India |
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Abstract: | The generalized energy method is developed to study the nonlinear stability analysis for a magnetized ferrofluid layer heated
from below saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the
nonlinear terms caused by magnetic body force. 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 linear instability analysis, and thus indicates that the subcritical instabilities are possible.
However, it is noted that, in case of non-ferrofluid, 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 magnetic
parameter, M
3, and medium permeability, Da, on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter (M
3) and Darcy number (Da), the subcritical instability region between the two theories decreases quickly. We also demonstrate coupling between the
buoyancy and magnetic forces in nonlinear energy stability analysis as well as in linear instability analysis. |
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Keywords: | Magnetized ferrofluid Nonlinear stability Porous medium Magnetization Medium permeability |
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