Time-dependent MHD Couette flow of rotating fluid with Hall and ion-slip currents

The unsteady magnehydrodynamics (MHD) Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions are obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction are discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip parameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.