Electrically Driven MHD Flow Between Two Parallel Slipping and Partly Conducting Infinite Plates

Abstract

The magnetohydrodynamic (MHD) flow between two parallel slipping and conducting infinite plates containing symmetrically placed electrodes is solved by using the dual reciprocity boundary element method (DRBEM). The flow is driven by the current traveling between the plates and the external magnetic field applied perpendicular to the plates. The coupled MHD equations are solved for the velocity of the fluid and the induced magnetic field as a whole without introducing an iteration. The effects of both the slip ratio and the length of the electrodes are discussed on the flow and magnetic field behavior for increasing values of Hartmann number (Ha). It is found that, an increase in the Hartmann number produces Hartmann layers of thickness 1∕Ha near the conducting parts and shear layers of order of thickness \(1/\sqrt {Ha}\) in front of the end points of electrodes. When the slip ratio increases Hartmann layers are weakened and the increase in the length of the electrodes retards this weakening effect of the slip on the Hartmann layers. The DRBEM discretizes only a finite portion of the plates and provides the solution inside the infinite region which is mostly concentrated in front of the electrodes. The aim of the study is to numerically simulate the MHD flow under the influence of the slipping velocity on the partly conducting plates which can not be treated theoretically.