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The effect of Hall currents on MHD flow and heat transfer between two parallel porous plates

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Abstract

The effect of Hall currents on magneto hydrodynamic (MHD) flow of an incompressible viscous electrically conducting fluid between two non-conducting porous plates in the presence of a strong uniform magnetic field is studied. The flow is generated by a small uniform suction at the plates. Solutions are obtained for suction Reynolds number R≪1, considering two cases for the imposed magnetic field, viz. (i) when the magnetic field is perpendicular to the plates (parallel to y-axis), and (ii) when the magnetic field is parallel to the plates and perpendicular to the primary flow direction (parallel to z-axis). The effect of the Hall currents on the flow as well as on the heat transfer is studied. It is observed that in the absence of Hall currents, the change of the direction of the applied magnetic field does not affect the primary flow.

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Abbreviations

B :

total magnetic induction vector

V :

velocity vector

E :

electric field vector

J :

current density vector

U 0 :

suction velocity

T :

temperature of the fluid at any point

B 0 :

imposed magnetic field

u :

x-component of fluid velocity

v :

y-component of fluid velocity

w :

z-component of fluid velocity

ρ :

density of the fluid

ν :

kinematic viscosity of the fluid

c p :

specific heat at constant pressure

p :

fluid pressure

σ :

electrical conductivity of the fluid

K :

coefficient of thermal conductivity

μ e :

magnetic permeability

n e :

number density of electrons

e :

electric charge

η :

dimensionless distance (=y/h)

f(η), g(η), Q(η), ψ(η):

dimensionless functions defined in (14)

R:

suction Reynolds number (=U 0 h/ν)

M:

Hartmann number (=B 0 h(σ/ρν)1/2)

m :

Hall parameter (=σB 0/en e)

Pr:

Prandtl number of the fluid (=ρνc p/K)

s :

dimensionless quantity defined as s=(T 1−T 0)/[vU 0/(hc p)]

References

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Authors and Affiliations

  1. Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India

    A. Bharali & A. K. Borkakati

Authors
  1. A. Bharali
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  2. A. K. Borkakati
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Bharali, A., Borkakati, A.K. The effect of Hall currents on MHD flow and heat transfer between two parallel porous plates. Appl. Sci. Res. 39, 155–165 (1982). https://doi.org/10.1007/BF00457017

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