Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham\r\nfluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to\r\nthe walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A\r\ndetailed analysis is conducted to determine the plug regions in relation to the values of the Bingham\r\nnumber, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases\r\nas the Bingham number increases. Detailed considerations are drawn for the occurrence of the\r\nreverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various\r\nparameters involved in the problem is presented and discussed.