Analysis and control of shear flow over a rotating plate in the presence of magnetic field

Abstract

AbstractShear flow of an incompressible viscous electrically conducting fluid past a uniformly rotating infinite impermeable flat plate in the presence of transverse magnetic field is investigated. The flow is assumed to be governed by Navier‐Stokes equations augmented with an applied magnetic field. Solutions of the corresponding equations are analyzed. It is noted that due to shear flow over a rotating plate, the problem has no axisymmetric solutions. But it is interesting to note that this problem has no unique solution for the secondary velocity components. It is remarkable to note that Navier‐Stokes equations for this problem admit a one parameter family of solutions. Inside the boundary layer, the momentum transfer of the outer shear flow is dominated by the pressure gradient. The secondary velocity component along x‐axis is a linear combination of velocity due to shear and translation. However, it is noted that the contribution from the shear dominates. It is observed that the primary and secondary velocity components can be controlled by the applied magnetic field. It is also found that the torque exerted by the fluid on the plate is influenced by the applied magnetic field but independent of the shear in the external flow.