The aim of the present paper is to study the effects of Hall current on steady hydro magnetic Couette flow within a parallel plate channel in a rotating system in the presence of a uniform magnetic field which is applied perpendicular to the plane of the plate. Exact solutions of the governing equations are obtained in closed form. Solutions in dimensionless form contains three parameters viz. M2 (the square of Hartmann number known as magnetic interaction parameter), K2 (the rotation parameter which is reciprocal of Ekman number) and m (the Hall current parameter). Asymptotic behavior of the solution is analyzed for small and large values of K2, M2 to gain some physical insight in the flow pattern. The expressions for the shear stress at the plates and mass flow rates are also derived. The numerical solution of the velocity and induced magnetic field is computed and depicted graphically in figures for various values of m, M2, K2. The numerical results of components of shear stress at both the plates and mass flow rates in the primary and secondary flow directions are presented in tables for various values of m, M2, K2.
It is observed that in a slowly rotating system when the conductivity of the fluid is low and or the applied magnetic field is weak, the primary and secondary velocities u and v respectively and induced magnetic field bx and by have considerable effects of rotation, Hall current and magnetic field. This is due to the fact that the hall current and rotation induces secondary flow. When K2 is large and M2 is of small order of magnitude, the fluid flow becomes boundary layer type.
When M2 is large and K2 is of small order of magnitude there arises a thin boundary layer. This boundary layer may be identified as modified hydromagnetic Hartmann, the thickness of this layer decreases with the increase in M2
