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On the effects of uniform high suction on the rotationally symmetric flow of a conducting liquid near a stationary disc in the presence of a transverse magnetic field

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Abstract

In the present paper an attempt has been made to find out effects of uniform high suction in the presence of a transverse magnetic field, on the motion near a stationary plate when the fluid at a large distance above it rotates with a constant angular velocity. Series solutions for velocity components, displacement thickness and momentum thickness are obtained in the descending powers of the suction parameter a. The solutions obtained are valid for small values of the non-dimensional magnetic parameter m (= 4πσμ 2e H 20 /ρω) and large values of a (a≥2).

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Abbreviations

a :

suction parameter

E :

electric field

E r , E θ , E z :

radial, azimuthal and axial components of electric field

F, G, H :

reduced radial, azimuthal and axial velocity components

H :

magnetic field

H r , H θ , H z :

radial, azimuthal and axial components of magnetic field

H 0 :

uniform magnetic field

H*:

displacement thickness and momentum thickness ratio, δ*/θ

h :

induced magnetic field

h r , h θ , h z :

radial, azimuthal and axial components of induced magnetic field

J :

current density

m :

nondimensional magnetic parameter

p :

pressure

P :

reduced pressure

R :

Reynolds number

U 0 :

representative velocity

V :

velocity

V r , V θ , V z :

radial, azimuthal and axial velocity components

w 0 :

uniform suction through the disc.

ρ :

density

σ :

electrical conductivity

ν :

kinematic viscosity

μ e :

magnetic permeability

ξ :

a parameter, (ω/ν)1/2 z

η :

a parameter, ξa

δ*:

displacement thickness

ϑ :

momentum thickness

ω :

angular velocity

References

  1. Bödewadt, U. T., Z. angew. Math. Mech. 20 (1940) 241.

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  2. Stuart, J. T., Quart. J. Mech. App. Math. 7 (1954) 446.

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Authors and Affiliations

  1. M.N.R. Engineering College, Allahabad, India

    V. Kumar

Authors
  1. V. Kumar
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Kumar, V. On the effects of uniform high suction on the rotationally symmetric flow of a conducting liquid near a stationary disc in the presence of a transverse magnetic field. Appl. Sci. Res. 27, 463–477 (1973). https://doi.org/10.1007/BF00382508

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  • DOI: https://doi.org/10.1007/BF00382508

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