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Three dimensional magnetohydrodynamic flow between two porous disks

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Abstract

This is a study of conducting flow in the gap between two parallel co-axial nonconducting disks of which one is rotating and the other stationary in the presence of a uniform axial magnetic field. The effect of uniform suction or injection on the velocity distribution is investigated and asymptotic solutions are obtained for R≪M 2. Expressions for the average normal force and the torque on the disks are obtained. We find that all components of velocity are affected by uniform suction or injection and in particular we note that the effect of suction or injection on the radial component of velocity predominates over the effect of rotation for a given Hartmann number.

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Abbreviations

B 0 :

impressed uniform magnetic field

C p :

pressure coefficient

E r :

radial component of electric field

E z :

axial component of electric field

E θ :

azimuthal component of electric field

f(ξ):

function defined in (21)

g(ξ):

function defined in (21)

2h :

channel width

J r :

radial component of current density

J z :

axial component of current density

J θ :

azimuthal component of current density

K :

constant defined in (45)

M :

Hartmann number, B 0 h(σ/ρν)1/2

N :

perturbation parameter, M 2/R

P :

pressure

q :

velocity vector

R :

suction Reynolds number, Uh/ν

R 1 :

rotation Reynolds number, ωh 2/ν

U :

suction or injection velocity

U r :

radial component of velocity

U z :

axial component of velocity

V θ :

azimuthal component of velocity

X :

constant defined in (45)

z, r :

axial and radial coordinates

α :

radius of the disk

λ :

ratio of Reynolds numbers, 2R 21 /R 2

μ :

absolute viscosity of the fluid

μ m :

magnetic permeability

ν :

kinematic viscosity of the fluid

ξ :

dimensionless axial co-ordinate

ρ :

density of the fluid

σ :

electrical conductivity of the fluid

τ :

torque on the disk

τ 0r :

torque on the rotating disk

Φ :

average normal torce defined in (51)

χ :

dimensionless quantity, ω av/Ω

ω av :

average velocity of the fluid

μm:

magnetic permeability

Ω :

angular velocity of the rotating disk

References

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Authors and Affiliations

  1. Department of Mathematics (Post-graduate Studies) Visvesvaraya College of Engineering, Bangalore University, Bangalore, India

    B. C. Chandrasekhara & N. Rudraiah

Authors
  1. B. C. Chandrasekhara
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  2. N. Rudraiah
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Chandrasekhara, B.C., Rudraiah, N. Three dimensional magnetohydrodynamic flow between two porous disks. Appl. Sci. Res. 25, 179–192 (1972). https://doi.org/10.1007/BF00382294

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  • DOI: https://doi.org/10.1007/BF00382294

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