Studies of convection in the horizontal Bridgman configuration
were performed to
investigate the flow structures and the nature of the convective regimes
in a rectangular
cavity filled with an electrically conducting liquid metal when it is
subjected to a
constant vertical magnetic field. Under some assumptions analytical
solutions were obtained for the central region and for the turning
flow region. The validity of the solutions was checked by comparison
with the solutions obtained by direct numerical simulations. The
main effects of the magnetic field are first to decrease the strength of
the convective flow and then to cause a progressive modification of the
flow structure
followed by the appearance of Hartmann layers in the vicinity of the
rigid walls. When the Hartmann number is large enough,
Ha > 10, the decrease in the velocity
asymptotically approaches a power-law dependence on Hartmann number. All
these features are dependent on the dynamic boundary conditions, e.g.
confined cavity or cavity with a free upper surface, and on the type
of driving force, e.g. buoyancy and/or thermocapillary forces.
From this study we generate scaling laws that govern
the influence of applied magnetic fields on convection. Thus, the
influence of various flow parameters are isolated, and succinct
relationships for the influence of magnetic
field on convection are obtained. A linear stability analysis was
carried out in the case
of an infinite horizontal layer with upper free surface. The results
show essentially that
the vertical magnetic field stabilizes the flow by increasing the
values of the critical
Grashof number at which the system becomes unstable and modifies
the nature of the instability. In fact, the range of Prandtl number
over which transverse oscillatory
modes prevail shrinks progressively as the Hartmann number is
increased from zero to 5. Therefore, longitudinal oscillatory modes
become the preferred modes over a large range of Prandtl
number.
The convective instability problem of a horizontal layer of an electrically conducting fluid under a vertical magnetic field.