Magnetohydrodynamic flow in a rectangular duct in a cusped magnetic field

Liquid metal flow in a rectangular duct in a plane cusped magnetic field is considered with the main objective being to investigate the effect of the sidewalls on the flow. At high values of the Hartmann number Ha the velocity profile is characterized by the presence of three jets. One jet is at the symmetry plane, where the transverse component of the magnetic field changes sign, and the magnetic field is parallel to the flow. The other two are at the sidewalls parallel to the field. The overall flow balance is determined by the wall conductance ratios of the sidewalls and the Hartmann walls (these are the walls with a nonzero normal component of the field). If the sidewalls are conducting, the jet at the symmetry plane dominates. If the sidewalls are electrically insulating, the sidewall jets dominate. In the latter case the flow pattern exhibits only a small resemblance to the analogous flow between two parallel plates (no sidewalls), which was investigated before. The pressure drop is O(Ha(1/2)) higher than in the corresponding flow in a uniform, transverse magnetic field. This means that braking the flow by a cusped field is more effective, and this feature can be used in some applications of magnetohydrodynamics, such as electromagnetic brakes and semiconductor crystal growth from melts. (C) 1999 American Institute of Physics. [S1070-6631(99)00304-9].