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Effects of hall current on MHD Couette flow in a channel partially filled with a porous medium in a rotating system

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Abstract

MHD Couette flow in a channel with non-conducting walls, partially filled with a porous medium, is investigated in the presence of an inclined magnetic field in a rotating system. It is observed that the MHD flow behaviour in the channel has been influenced significantly by the Coriolis force, the hydromagnetic force with an inclusion of Hall current and the permeability of the porous medium. Effects of the parameters of these forces on the velocity distributions, induced magnetic field distributions and the skin friction have been depicted graphically and discussed.

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Abbreviations

c e :

Electron thermal velocity

E x :

Induced electric field in clear fluid in x-direction

\(\bar{E}_{x}\) :

Induced electric field in porous medium in x-direction

E y :

Induced electric field in clear fluid in y-direction

\(\bar{E}_{y}\) :

Induced electric field in porous medium in y-direction

E z :

Induced electric field in clear fluid in z-direction

\(\bar{E}_{z}\) :

Induced electric field in porous medium in z-direction

H 0 :

Applied magnetic field

H x :

Induced magnetic field in clear fluid in x-direction

\(\bar{H}_{x}\) :

Induced magnetic field in porous medium in x-direction

H z :

Induced magnetic field in clear fluid in z-direction

\(\bar{H}_{z}\) :

Induced magnetic field in porous medium in z-direction

J x :

Current density in clear fluid in x-direction

\(\bar{J}_{x}\) :

Current density in porous medium in x-direction

J z :

Current density in clear fluid in z-direction

\(\bar{J}_{z}\) :

Current density in porous medium in z-direction

k 0 :

permeability of porous layer

k :

Non-dimensional permeability of porous layer (=k 0/d 2)

m :

Hall Current parameter (=τ e ω e )

m e :

Electron mass

M :

Hartmann Number (=μ e H 0 d(σ/ρυ)1/2)

R :

Rotation parameter (=Ωd 2/υ)

u :

Velocity in clear fluid in x-direction

\(\bar{u}\) :

Velocity in porous medium in x-direction

w :

Velocity in clear fluid in z-direction

\(\bar{w}\) :

Velocity in porous medium in z-direction

ϵ :

porosity of the porous medium

φ :

Viscosity ratio \(( = \bar{\mu} / \mu)\)

μ :

Viscosity of the clear fluid

\(\bar{\mu}\) :

Effective viscosity of fluid in porous medium

μ e :

Magnetic permeability

λ :

Electron mean free path

θ :

Angle of inclination of magnetic field with axis of rotation

ρ :

Fluid density

σ :

Electrical conductivity

τ e :

Electron collision time

υ :

Kinematic coefficient of viscosity

ω e :

Cyclotron frequency

Ω:

Angular velocity

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Authors and Affiliations

  1. Department of Mathematics, University of Rajasthan, Jaipur, 302055, India

    Dileep Singh Chauhan & Rashmi Agrawal

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  1. Dileep Singh Chauhan
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  2. Rashmi Agrawal
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Correspondence to Dileep Singh Chauhan.

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Chauhan, D.S., Agrawal, R. Effects of hall current on MHD Couette flow in a channel partially filled with a porous medium in a rotating system. Meccanica 47, 405–421 (2012). https://doi.org/10.1007/s11012-011-9446-9

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  • DOI: https://doi.org/10.1007/s11012-011-9446-9

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