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

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DOI: 10.1007/s11012-009-9210-6

- Cite this article as:
- Ghosh, S.K., Anwar Bég, O. & Narahari, M. Meccanica (2009) 44: 741. doi:10.1007/s11012-009-9210-6

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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.

### Keywords

MHD flowHall effectsViscous effectsAsymptotic behaviorHeat transferMHD energy systemsHartmann-Ekman boundary layersBackflowSecondary flowAstrophysical plasma flowsMagneto-materials processingPropulsion### List of symbols

**q**velocity vector

**H**magnetic filed vector

**E**electric field vector

**J**current density vector

*σ*electrical conductivity of Newtonian working fluid

*ρ*fluid density

*μ*_{e}magnetic permeability

*ν*kinematic coefficient of viscosity

*Ω*angular velocity

*ω*_{e}cyclotron frequency

*τ*_{e}electron collision time

*M*Hartmann number

*P*_{m}magnetic Prandtl number

*R*dimensionless pressure gradient

*K*^{2}rotation parameter which is the reciprocal of Ekman number

*m*Hall current parameter

*c*_{p}specific heat at constant pressure

*K*_{1}thermal conductivity

*P*_{r}Prandtl number

*E*_{r}Eckert number