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Magnetohydrodynamic laminar source flow between two parallel disks

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Abstract

The steady axisymmetrical laminar source flow of an incompressible conducting fluid between two circular parallel disks in the presence of a transverse magnetic field is analytically investigated. A solution is obtained by expanding the velocity and the pressure distribution in terms of a power series of 1/r. Velocity, induced magnetic field, pressure and shear stress distributions are determined and compared with the case of the hydrodynamic solution. Pressure is found to be a function of both r and z in the general case and the flow is not parallel. At high magnetic fields, the velocity distribution degenerates to a uniform core surrounded by a boundary layer near the disks.

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Abbreviations

C f :

skin friction coefficient

H 0 :

impressed magnetic field

H r :

induced magnetic field in the radial direction, H r /H 0

M :

Hartmann number, μH 0 t(σ/ρν)1/2

P :

dimensionless static pressure, P*t 4/ρQ

P*:

static pressure

P 0 :

reference dimensionless pressure

Q :

source discharge

R :

outer radius of disks

Rm :

magnetic Reynolds number, σμQ/t

Re :

Reynolds number, Q/νt

2t :

channel width

u :

dimensionless radial component of the velocity, u*t 2/Q

u*:

radial component of the velocity

w :

dimensionless axial component of the velocity, w*t 2/Q

w*:

axial component of the velocity

z, r :

dimensionless axial and radial directions, z*/t and r*/t, respectively

z*, r*:

axial and radial direction, respectively

μ :

magnetic permeability

ν :

coefficient of kinematic viscosity

ρ :

density

σ :

electrical conductivity

▽2 :

LaPlacian operator in axisymmetrical cylindrical coordinates

References

  1. Hughes, W. F. and R. A. Elco, J. Fluid Mech. 13 (1962) 21.

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  3. Ramanaiah, G., Appl. Sci. Res. B17 (1967) 296.

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  4. Kreiger, R. J., H. J. Day and W. F. Hughes, J. Lub. Tech., ASME, 89 (1967) 307.

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, Auburn University, Auburn, Alabama, USA

    M. S. Khader & J. S. Goodling

Authors
  1. M. S. Khader
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  2. J. S. Goodling
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Khader, M.S., Goodling, J.S. Magnetohydrodynamic laminar source flow between two parallel disks. Appl. Sci. Res. 27, 93–102 (1973). https://doi.org/10.1007/BF00382479

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  • DOI: https://doi.org/10.1007/BF00382479

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