Abstract
The development of the velocity profile, from a uniform one at the entrance, for an electrically conducting fluid entering a semi-infinite flat duct with a transversely applied magnetic field is investigated. It is assumed that the fluid has constant physical properties, the duct walls are electrically nonconducting, a uniform magnetic field is imposed perpendicular to the duct walls, and there can be a net electrical current flow parallel to the walls and perpendicular to the flow direction with a variable external resistance connecting the two side plates, which are displaced at infinity. The basic governing continuity and momentum equations are expressed in finite difference form and solved numerically on a high-speed digital computer with a mesh network superimposed on the flow field. A practical mesh size ratio suitable for computation was determined. Results were obtained for the variations of velocity and pressure distribution between the inlet and the region for the fully developed velocity profile for Hartmann numbers of 0, 4, and 10.
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