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MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann number M and interaction parameter N have very large values and the magnetic Reynolds number is extremely small. The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.