This paper concerns a steady liquid-metal flow through an expansion or contraction with electrically insulated walls, with rectangular cross-sections and with a uniform, transverse, externally applied magnetic field. One pair of duct walls is parallel to the applied magnetic field, and the other pair diverges or converges symmetrically about a plane which is perpendicular to the field. The magnetic field is assumed to be sufficiently strong that inertial effects can be neglected and that the well-known Hartmann-layer solution is valid for the boundary layers on the walls which are not parallel to the magnetic field. A general treatment of three-dimensional flows in constant-area ducts is presented. An error in the solution of Walker et al. (1972) is corrected. A smooth expansion between two different constant-area ducts is treated. In the expansion the flow is concentrated inside the boundary layers on the sides which are parallel to the magnetic field, while the flow at the centre of the duct is very small and may be negative for a large expansion slope. In each constant-area duct, the flow evolves from a concentration near the sides at the junction with the expansion to the appropriate fully developed flow far upstream or downstream of the expansion. The pressure drop associated with the three-dimensional flow increases as the slope. increases.
Phase boundary dynamics of bubble flow in a thick liquid metal layer under an applied magnetic field
