Magnetohydrodynamic duct flow in a uniform transverse magnetic field of arbitrary orientation

Abstract

The paper presents an approximate analysis for high Hartmann number of the flow of an electrically conducting, incompressible fluid in a duct of square crosssection, having one pair of opposite walls insulating, and the other pair perfectly conducting and inclined at arbitrary orientation to a uniform transverse magnetic field. The flow is considered to be either pressure-driven with the two perfectly conducting electrodes short-circuited together or electrically driven by a potential difference applied between these electrodes in the absence of axial pressure gradient. The paper describes experiments on the pressure-driven, short circuited case using mercury in copper ducts to investigate the variation of the streamwise pressure gradient and of the potential distribution along one insulating wall with orientation, magnetic field and flow rate.At general orientations the analysis suggests and the experiments confirm the existence of regions of stationary fluid in the corners of the duct, together with viscous shear layers parallel to the magnetic field. For the case in which the electrodes are parallel to the magnetic field the experimental results for the pressure gradient, but not those for the potential distribution, agree reasonably well with Hunt & Stewartson's (1965) asymptotic solution. Both pressure gradient and potential results agree closely with the analysis by Hunt (1965) of the case in which the electrodes are perpendicular to the magnetic field.