Mathematical Modelling Electrically Driven Free Shear Flows in a Duct under Uniform Magnetic Field

We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22, 23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.