A study of unsteady rotating hydromagnet

A theoretical analysis is presented for transient, fully-developed magnetohydrodynamic free and forced convection flow of a viscous, incompressible, Newtonian fluid in a rotating horizontal parallel-plate channel subjected to a uniform strength, static, oblique magnetic field acting at an angle θ to the positive direction of the axis of rotation. A constant pressure gradient is imposed along the longitudinal axis of the channel. Magnetic Reynolds number is sufficiently small to negate the effects of magnetic induction. The channel plates are electrically non-conducting. The conservation equations are formulated in an (x,y,z) coordinate system and normalized using appropriate transformations. The resulting non-dimensional coupled ordinary differential equations for primary and secondary velocity components and transformed boundary conditions are found to be reciprocal of the Ekman number (2K = 1/Ek), non-dimensional pressure gradient parameter (Px), Hartmann number (2M), Grashof number (Gr), magnetic field inclination (θ) and oscillation frequency (ω). Complex variables are employed to solve the two-point boundary value problem. A steady state resonance of the velocity field is identified and further solutions indicate conditions signifying an oscillatory turbulent dynamo mechanism. A critical Grashof number is evaluated for primary helicity conservation.