Unsteady MHD Hartmann-Couette Flow Due to Time Dependent Movement of the Plate

What is it about?

Unsteady MHD Hartmann – Couette flow of a viscous, incompressible and electrically conducting fluid within parallel plate porous Darcian channel with Hall current and ion-slip effects is carried-out. Fluid flow within the channel is induced due to time dependent movement of the upper plate of the channel and by a constant pressure gradient applied along the axis of the plates of the Darcian channel. Fluid flow within the Darcian channel is permeated by a uniform transverse magnetic field, which is fixed relative to the stationary plate. Laplace transform technique is used to obtain an exact solution of the governing equations. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. To highlight the transient approach to the final steady state flow and the effects of Hall current, ion-slip, magnetic field, permeability and suction/injection, asymptotic behavior of the solution is analyzed for small and large values of time. It is noticed that, at the starting stage, secondary velocity is independent of permeability and there are no flows in the secondary flow direction in the absence of Hall current. At the final stage, fluid flow is in quasi-steady state. Steady state flow executes spatial oscillations in the flow-field whereas unsteady state flow exhibits spatial as well as inertial oscillation in the flow-field. Inertial oscillations in the flow-field are due to presence of Hall current. Numerical values of primary and secondary fluid velocities and that of shear stress at the moving plate of the Darcian channel due to primary and secondary flows are represented graphically for various values of pertinent flow parameters.

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