LIE GROUP METHOD FOR SOLVING THE MHD FLOW AROUND A CYLINDER IN CROSSED ELECTRIC AND STRONG MAGNETIC FIELDS

This paper is devoted to an analytical study of the laminar longitudinal MHD-flow which arises when a cylinder of infinite length and arbitrary electrical conductivity is placed into a conducting fluid which is subjected to crossed electric and strong magnetic fields that are homogeneous at infinity and perpendicular to the axis of the cylinder. We establish the complete Lie group of infinitesimal symmetries. The Lie group method, which is applied here, reduces the number of independent variables. Finally, the obtained system of ordinary differential equations with the appropriate corresponding conditions is solved analytically. The flow field, the induced magnetic field and the resulting forces on the cylinder are calculated.