Solution of the flow over the roughness elements of special shape in a strong magnetic field

M. Ya. Antimirov - I. A. Chaddad

Riga Technical University, Riga, Latvia

Abstract
An analytical solution of the MHD flow of a conducting fluid in half space [(z)\tilde] > 0 with roughness of special shape at the boundary [(z)\tilde] = 0 is obtained. An external magnetic field is perpendicular to the boundary [(z)\tilde] = 0. There is also an external current, which is parallel to the boundary [(z)\tilde] = 0, if the roughness is absent. The fluid flow appears only, if the roughness of the boundary [(z)\tilde] = 0 exists. The choice of the roughness shaped as an infinitely long prism with a constant rectangular cross-section allows to obtain an analytical solution of this problem at an assumption that the height of this cross-section is small. An asymptotic solution of the problem at large Hartmann numbers is obtained. In this case various boundary layers of the flow and the induced current are found. The results of numerical calculations of the x- and y-components and the streamlines of the induced current are presented. Figs 6, Refs 5.