Transient hydromagnetic flow in a rotating channel permeated by an inclined magnetic field with magnetic induction and Maxwell displacement current effects
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- Ghosh, S.K., Bég, O.A., Zueco, J. et al. Z. Angew. Math. Phys. (2010) 61: 147. doi:10.1007/s00033-009-0006-2
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Closed-form solutions are presented for the transient hydromagnetic flow in a rotating channel with inclined applied magnetic field under the influence of a forced oscillation. Magnetic Reynolds number is large enough to permit the inclusion of magnetic induction effects. The Maxwell displacement current effect is also included and simulated via a dielectric strength parameter. The governing momentum and magnetic induction conservation equations are normalized with appropriate transformations and the resulting quartet of partial differential equations are solved exactly. A parametric study is performed of the influence of oscillation frequency parameter (ω), time (T), inverse Ekman number, i.e. rotation parameter (K2), square of the Hartmann magnetohydrodynamic (MHD) parameter (M2), and magnetic field inclination (θ) on the primary and secondary induced magnetic field components (bx, by) and velocity components (u, v) across the channel. Network solutions are also obtained to validate the exact solutions and shown to be in excellent agreement. Applications of the study arise in planetary plasma physics and rotating MHD induction power generators and also astronautical flows.