Meccanica

, 44:741 | Cite as

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

Article

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 M2 (Hartmann number squared) and K2 (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 K2, i.e. strong rotation of the channel. For slowly rotating systems (small K2), Hall current parameter (m) reduces primary mass flow rate (Qx/Rρv). Heat transfer rate at the upper plate (dθ/dη)η=1 decreases, while at the lower plate (dθ/dη)η=−1 increases, with increase in either K2 or m. For constant values of the rotation parameter, K2, 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 flow Hall effects Viscous effects Asymptotic behavior Heat transfer MHD energy systems Hartmann-Ekman boundary layers Backflow Secondary flow Astrophysical plasma flows Magneto-materials processing Propulsion 

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

μe

magnetic permeability

ν

kinematic coefficient of viscosity

Ω

angular velocity

ωe

cyclotron frequency

τe

electron collision time

M

Hartmann number

Pm

magnetic Prandtl number

R

dimensionless pressure gradient

K2

rotation parameter which is the reciprocal of Ekman number

m

Hall current parameter

cp

specific heat at constant pressure

K1

thermal conductivity

Pr

Prandtl number

Er

Eckert number

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Magnetohydrodynamics Research Program, Applied Mathematics Section, Department of MathematicsNarajole Raj CollegeMidnapore (West)India
  2. 2.Magneto-Fluid Dynamics, Biomechanics and Energy Systems Research, Mechanical Engineering Department, Sheaf BuildingSheffield Hallam UniversitySheffieldUK
  3. 3.Heat Transfer Research, Department of Electrical and Electronics EngineeringUnivertsiti Teknologi PetronasTronohMalaysia

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