, Volume 44, Issue 6, pp 741-765
Date: 01 Apr 2009

Hall effects on MHD flow in a rotating system with heat transfer characteristics

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Abstract

Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large M 2 (Hartmann number squared) and K 2 (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary layers arise close to the channel walls for large K 2, i.e. strong rotation of the channel. For slowly rotating systems (small K 2), Hall current parameter (m) reduces primary mass flow rate (Q x /R ρ v). Heat transfer rate at the upper plate (d θ/d η) η=1 decreases, while at the lower plate (d θ/d η) η=−1 increases, with increase in either K 2 or m. For constant values of the rotation parameter, K 2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc.

Dedicated to the late Dr. Hannes O. G. Alfvén (May 30, 1908–April 2, 1995), Nobel Prize Winner in Physics (1970), for his monumental contributions to plasma physics and magnetohydrodynamics.