Electrically driven plane free shear flow in a duct under an oblique transverse uniform magnetic field

Yu. Kolesnikov¹ - H. Kalis²

¹ Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Ilmenau 98693, Germany
² Institute of Mathematics and Computer Science, University of Latvia, Riga LV-1586, Latvia

Abstract
A mathematical model of electrically driven laminar free shear flows in a straight duct under the action of an applied oblique transverse uniform magnetic field is considered. The mathematical approach is similar to that used in [1]. A system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field is solved. Three different cases of electric current supply to the liquid are considered. An electric current is introduced into the liquid first by one pair of linear electrodes, and in two other cases by two pairs of electrodes located on the upper and lower walls of the duct. The cases are analyzed when the angle of inclination of the magnetic field vector to these walls is ϕ₀ = π/4. Depending on the direction of the electric current supplied to the pairs of electrodes, two coinciding in direction or two opposite inclined flows are driven in the zone between these walls. Increasing the magnetic field only leads to an internal rearrangement of the flows. The Hartmann number Ha ranges from 1 to 10, at which MHD effects distinctly enough are already displayed. Figs 19, Refs 11.