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