The effect of an external magnetic field on oscillatory instability of convective flows in a rectangular cavity

The present study is devoted to the problem of onset of oscillatory instabi lity in convective flow of an electrically conducting fluid under an extern ally imposed time-independent uniform magnetic field. Convection of a low-P randtl-number fluid in a laterally heated two-dimensional horizontal cavity is considered. Fixed values of the aspect ratio (length/height=4) and Pran dtl number (Pr=0.015), which are associated with the horizontal Bridgman cr ystal growth process and are commonly used for benchmarking purposes, are c onsidered. The effect of a uniform magnetic field with different magnitudes and orientations on the stability of the two distinct branches (with a sin gle-cell or a two-cell pattern) of the steady state flows is investigated. Stability diagrams showing the dependence of the critical Grashof number on the Hartmann number are presented. It is shown that a vertical magnetic fi eld provides the strongest stabilization effect, and also that multiplicity of steady states is suppressed by the electromagnetic effect, so that at a certain field level only the single-cell flows remain stable. An analysis of the most dangerous flow perturbations shows that starting with a certain value of the Hartmann number, single-cell flows are destabilized inside th in Hartmann boundary layers. This can lead to destabilization of the flow w ith an increase of the field magnitude, as is seen from the stability diagr ams obtained. Contrary to the expected monotonicity of the stabilization pr ocess with an increase of the field strength, the marginal stability curves show nonmonotonic behavior and may contain hysteresis loops. (C) 2001 Amer ican Institute of Physics.