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A Nonlinear Stability Analysis of a Rotating Double-Diffusive Magnetized Ferrofluid Saturating a Porous Medium

Volume 40, Issue 4, 2009, pp. 351-378
DOI: 10.1615/HeatTransRes.v40.i4.60
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Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
Poonam Sharma
Department of Applied Sciences, National Institute of Technology, Hamirpur, 177 005, India
Amit Mahajan
Department of Applied Sciences, National Institute of Technology, Hamirpur, 177 005, India; Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, N9B3P4, Canada

ABSTRACT

Thermal stability in a layer of a double-diffusive ferrofluid rotating about an axis orthogonal to the layer in the direction of gravity saturated by a porous medium for the stress-free boundaries is investigated by nonlinear analysis. A rigorous nonlinear stability result is derived by introducing a generalized energy functional. A comparison with the linear instability theory shows that there is a considerable difference between the critical values of magnetic thermal Rayleigh numbers and thus indicates the possibility of subcritical instabilities. However, it is noted that, in 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, solute gradient, Sf, Taylor number, TA1, and Darcy number, Da, on the sub-critical instability region have also been analyzed. We also demonstrate coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.

CITED BY

  1. Sharma Poonam, Mahajan Amit, Onset of Darcy–Brinkman double-diffusive convection in a magnetized ferrofluid layer using a thermal non-equilibrium model: a nonlinear stability analysis, Journal of Geophysics and Engineering, 7, 4, 2010. Crossref

  2. Pérez L.M., Bragard J., Laroze D., Martinez-Mardones J., Pleiner H., Thermal convection thresholds in a Oldroyd magnetic fluid, Journal of Magnetism and Magnetic Materials, 323, 6, 2011. Crossref

  3. Laroze D., Martinez-Mardones J., Pérez L.M., Rojas R.G., Stationary thermal convection in a viscoelastic ferrofluid, Journal of Magnetism and Magnetic Materials, 322, 21, 2010. Crossref

  4. Laroze D., Siddheshwar P.G., Pleiner H., Chaotic convection in a ferrofluid, Communications in Nonlinear Science and Numerical Simulation, 18, 9, 2013. Crossref

  5. Pérez L.M., Laroze D., Díaz P., Martinez-Mardones J., Mancini H.L., Rotating convection in a viscoelastic magnetic fluid, Journal of Magnetism and Magnetic Materials, 364, 2014. Crossref

  6. Nield Donald A., Bejan Adrian, Double-Diffusive Convection, in Convection in Porous Media, 2017. Crossref

  7. Nield Donald A., Bejan Adrian, Double-Diffusive Convection, in Convection in Porous Media, 2013. Crossref

  8. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2013. Crossref

  9. Choudhary Shalu, Sunil , Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium, Studia Geotechnica et Mechanica, 41, 1, 2019. Crossref

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