Unsteady Hartmann flow in a rotating channel with arbitrary conducting walls

Unsteady hydromagnetic flow of a viscous incompressible electrically conducting fluid in a rotating channel with finitely conducting walls, induced due to an oscillating pressure gradient, in the presence of a uniform transverse magnetic field is studied. An exact solution of the governing equations is obtained in closed form. The expression for the shear stress at the walls due to primary and secondary flows is also derived. The solutions valid for small and vanishing magnetic Prandtl number PmPm are derived from the general solution and the asymptotic solutions valid for a large value of frequency parameter ωω are also obtained in both the cases to study the nature of boundary layer type flow arising due to the large frequency of oscillations.