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A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid
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| Zeitschriftentitel: | Zeitschrift für Naturforschung A |
|---|---|
| Personen und Körperschaften: | , |
| In: | Zeitschrift für Naturforschung A, 63, 2008, 12, S. 797-807 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Walter de Gruyter GmbH
|
| Schlagwörter: |
| author_facet |
Mahajan, Sunil Mahajan, Amit Mahajan, Sunil Mahajan, Amit |
|---|---|
| author |
Mahajan, Sunil Mahajan, Amit |
| spellingShingle |
Mahajan, Sunil Mahajan, Amit Zeitschrift für Naturforschung A A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid Physical and Theoretical Chemistry General Physics and Astronomy Mathematical Physics |
| author_sort |
mahajan, sunil |
| spelling |
Mahajan, Sunil Mahajan, Amit 1865-7109 0932-0784 Walter de Gruyter GmbH Physical and Theoretical Chemistry General Physics and Astronomy Mathematical Physics http://dx.doi.org/10.1515/zna-2008-1207 <jats:p>A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. 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. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M<jats:sub>3</jats:sub>, and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.</jats:p> A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid Zeitschrift für Naturforschung A |
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| title |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_unstemmed |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_full |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_fullStr |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_full_unstemmed |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_short |
A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_sort |
a nonlinear stability analysis of a double-diffusive magnetized ferrofluid |
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Physical and Theoretical Chemistry General Physics and Astronomy Mathematical Physics |
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http://dx.doi.org/10.1515/zna-2008-1207 |
| publishDate |
2008 |
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797-807 |
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<jats:p>A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. 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. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M<jats:sub>3</jats:sub>, and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.</jats:p> |
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| description | <jats:p>A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. 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. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M<jats:sub>3</jats:sub>, and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.</jats:p> |
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| spelling | Mahajan, Sunil Mahajan, Amit 1865-7109 0932-0784 Walter de Gruyter GmbH Physical and Theoretical Chemistry General Physics and Astronomy Mathematical Physics http://dx.doi.org/10.1515/zna-2008-1207 <jats:p>A nonlinear (energy) stability analysis is performed for a magnetized ferrofluid layer, heated and soluted from below, with stress-free boundaries. 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. For ferrofluids we find that the existence of subcritical instabilities is possible, however, it is noted that, in case of a nonferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of the magnetic parameters, this coincidence is immediately lost. The effects of the magnetic parameter, M<jats:sub>3</jats:sub>, and the solute gradient, S1, on the subcritical instability region have also been analyzed. It is shown that with the increase of the magnetic parameter the subcritical instability region between the two theories decreases quickly, while with the increase of the solute gradient the subcritical region expands. We also demonstrate the coupling between the buoyancy and magnetic forces in the nonlinear energy stability analysis.</jats:p> A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid Zeitschrift für Naturforschung A |
| spellingShingle | Mahajan, Sunil, Mahajan, Amit, Zeitschrift für Naturforschung A, A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid, Physical and Theoretical Chemistry, General Physics and Astronomy, Mathematical Physics |
| title | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_full | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_fullStr | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_full_unstemmed | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_short | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| title_sort | a nonlinear stability analysis of a double-diffusive magnetized ferrofluid |
| title_unstemmed | A Nonlinear Stability Analysis of a Double-Diffusive Magnetized Ferrofluid |
| topic | Physical and Theoretical Chemistry, General Physics and Astronomy, Mathematical Physics |
| url | http://dx.doi.org/10.1515/zna-2008-1207 |