LIQUID-METAL FLOW IN AN INSULATED RECTANGULAR EXPANSION WITH A STRONGTRANSVERSE MAGNETIC-FIELD

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 fiel d, and the other pair diverges or converges symmetrically about a plan e which is perpendicular to the field. The magnetic field is assumed t o be sufficiently strong that inertial effects can be neglected and th at the well-known Hartmann-layer solution is valid for the boundary la yers on the walls which are not parallel to the magnetic field. A gene ral treatment of three-dimensional flows in constant-area ducts is pre sented. An error in the solution of Walker et al. (1972) is corrected. A smooth expansion between two different constant-area ducts is treat ed. In the expansion the flow is concentrated inside the boundary laye rs on the sides which are parallel to the magnetic field, while the fl ow at the centre of the duct is very small and may be negative for a l arge expansion slope. In each constant-area duct, the flow evolves fro m a concentration near the sides at the junction with the expansion to the appropriate fully developed flow far upstream or downstream of th e expansion. The pressure drop associated with the three-dimensional f low increases as the slope Increases.