Effects of the direction of a transverse magnetic field on unsteady MHD Couette flow with suction and injection

Abstract

In this paper, the problem of an unsteady magnetohydrodynamic viscous incompressible electrically conducting fluid flow subjected to a constant pressure gradient in the presence of a uniform transverse magnetic field applied parallel to one axis with the plates moving with a time dependent velocity is analyzed. Two cases where the plates are moving (i) in the same direction, (ii) in the opposite direction with different directions of the transverse magnetic field while fluid suction /injection takes place through the walls of the channels with a constant velocity for suction and injection has been investigated. The nonlinear partial differential equation governing the flow are solved numerically using the finite difference method. The results obtained are presented in graphs. The velocity profiles, the effect of the magnetic field direction, time and suction /injection on the flow are discussed. A change on the parameters is observed to either increase, decrease or to have no effect on the velocity profile. The MHD flow between porous plates studied in this work has many important applications in areas such as in controlling boundary layer flow over aircraft wings by injection or suction of fluid out of or into the wing, designing of cooling systems with liquid metals, in petroleum and mineral industries, in underground energy transport, accelerators, MHD generators, pumps, flow meters, purification of crude oil, geothermal reservoirs, and polymer technology.