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Stability of convection in a horizontal channel subjected to a longitudinal temperature gradient. Part 2. Effect of a magnetic field

Published online by Cambridge University Press:  10 September 2009

D. V. LYUBIMOV ,
T. P. LYUBIMOVA ,
A. B. PERMINOV ,
D. HENRY  and
H. BEN HADID
D. V. LYUBIMOV
Affiliation:
Perm State University, 15 Bukirev Street, 614990 Perm, Russia
T. P. LYUBIMOVA
Affiliation:
Institute of Continuous Media Mechanics UB RAS, 1 Koroleva Street, 614013 Perm, Russia
A. B. PERMINOV
Affiliation:
Perm State Technical University, 29a Komsomolsky Prospect, 614000 Perm, Russia
D. HENRY
Affiliation:
Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR-CNRS 5509, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
H. BEN HADID*
Affiliation:
Université de Lyon, École Centrale de Lyon/Université Lyon 1/INSA de Lyon, Laboratoire de Mécanique des Fluides et d'Acoustique, UMR-CNRS 5509, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
*
†Email address for correspondence: [email protected]
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Abstract

The stabilization of buoyant flows by a magnetic field is an important matter for crystal growth applications. It is studied here when the cavity is an infinite channel with rectangular cross-section typical of horizontal Bridgman configurations and when the magnetic field is applied in the vertical and transverse directions. The steady basic flow solution is first calculated: the usual counter flow structure is modified by the magnetic field and evolves towards jets in the cross-section corners when the magnetic field is vertical and towards a more uniform structure in the transverse direction when the magnetic field is transverse. The stability results show a very good stabilization of the convective flows for a vertical magnetic field with exponential increases of the thresholds for any width of the channel and for various Prandtl numbers Pr. The results for a transverse magnetic field are more surprising as a destabilizing effect corresponding to an initial decrease of the thresholds is obtained at Pr=0 and for small channel widths. A kinetic energy budget at the thresholds reveals that the main destabilizing factor is connected to the vertical shear of the longitudinal basic flow and that it is the modifications affecting this shear energy which are mainly responsible for the variation of the thresholds when a magnetic field is applied.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 635 , 25 September 2009 , pp. 297 - 319
Copyright
Copyright © Cambridge University Press 2009

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