Magnetohydrodynamic flow in rectangular ducts. II

Abstract

This paper is an extension of an earlier paper by Hunt (1965) on laminar motion of a conducting liquid in a rectangular duct under a uniform transverse magnetic field. The effect of the duct having conducting walls are further explored; in this case the duct considered has perfectly conducting walls parallel to the field and non-conducting walls perpendicular to the field. A solution is obtained for high Hartmann numbers by analysing the boundary layers on the walls. This solution involves an integral equation of a standard form. It is found that in this case, unlike the cases studied in the earlier paper, the velocity profiles in the boundary layers are monotonically decreasing. The effect of an external electrical circuit is examined, although it is found that it does not influence the form of the velocity profiles.