Thermoconvective instability of paramagnetic fluids in a uniform magnetic field

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Abstract
The effect of a uniform oblique magnetic field on a laterally unbounded insulating paramagnetic fluid layer heated from below is studied using a linear stability analysis of the Navier–Stokes equations supplemented by Maxwell’s equations and the appropriate magnetic body force. Two-dimensional rolls in an arbitrary vertical plane are considered. Longitudinal rolls with axes parallel to the horizontal component of the field are the rolls most unstable to convection. The corresponding critical Rayleigh number and critical wavelength for the onset of such rolls are less than the well-known Rayleigh–Bénard values in the absence of magnetic fields. Vertical fields maximize these deviations, which vanish for horizontal fields. Horizontal fields increase the critical Rayleigh number and the critical wavelength for all rolls except longitudinal rolls. These effects should be observable in careful experiments at high fields.

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