Unsteady hydromagnetic flow in a rotating channel in the presence of inclined magnetic field

Abstract Unsteady hydromagnetic flow of a viscous incompressible electrically conducting fluid in a rotating channel under the influence of a periodic pressure gradient and of uniform magnetic field, which is inclined with the axis of rotation, is investigated. Exact solution of the governing equations for the fully developed flow is obtained in closed form. The solution in dimensionless form contains three flow parameters, viz., M (the Hartmann number), K 2 (the rotation parameter), ω (the frequency parameter) and one geometric parameter θ (angle of inclination of the magnetic field with the positive direction of the axis of rotation). Asymptotic behaviour of the solution is analysed for large as well as small values of M 2 , K 2 and ω. For large values of M 2 , K 2 and ω the flow is divided into two regions, viz., (i) boundary layer region and (ii) central core region. It is observed that there arise flow reversals in the direction of the pressure gradient for large values of K 2 and ω when ω ≷ 2K 2 and for small values of K 2 and ω when ω 2 .