Magnetohydrodynamic Flow in Tubes of Arbitrary Contour

The effect of the cross-sectional shape on the steady flow of a Newtonian fluid in long tubes under an electromagnetic force is explored. A general method of analysis is presented, which draws on previous results of the authors in the study of flow in tubes of arbitrary contours. The velocity field is determined and analyzed for a variety of cross-sectional shapes that include the triangle, square and others. These results aim, in part, at providing a basis for the investigation of more complex flows, such as magnetorheological flows, in tubes of non-circular shapes. Such flows are important in many applications as related to damping devices and others where controlled modulation of resistance forces is desired.