Analysis of unsteady hydromagnetic couette flow with magnetic field lines fixed relative to the moving upper plate

Abstract

In the present study, an unsteady magnetohydrodynamic viscous incompressible electrically conducting fluid flow between two parallel porous plates of infinite length in and directions subjected to a constant pressure gradient in the presence of a uniform transverse magnetic field applied parallel to the axis with the upper plate moving with a time dependent velocity in the direction. The lower plate is fixed while fluid suction/injection takes place through the walls of the channel 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 and implemented in MATLAB. The results obtained are presented in graphs. The velocity profiles, the effect of pressure gradient, magnetic field, time and suction /injection on the flow and the effects of varying the various parameters on the velocity profile 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 the designing of cooling systems with liquid metals, geothermal reservoirs, in petroleum and mineral industries, in underground energy transport, accelerators, MHD generators, pumps, flow meters, purification of crude oil, polymer technology and in controlling boundary layer flow over aircraft wings by injection or suction of fluid out of or into the wing among many other areas.