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Magnetohydrodynamic flow between rotating coaxial disks

Published online by Cambridge University Press:  29 March 2006

C. J. Stephenson
C. J. Stephenson
Affiliation:
University Engineering Department, Cambridge Present address: IBM Research Center, Yorktown Heights, N.Y.
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Abstract

This is a study of the magnetohydrodynamic flow of an incompressible viscous fluid between coaxial disks, with a uniform axial magnetic field B. The fluid has density ρ, viseosity η and electrical conductivity σ. The flow is assumed to be steady, and to be similar in the sense that the radial and tangential components of velocity increase linearly with radial distance from the axis of rotation. Most of the work is concerned with disks which are electrical insulators, one of which rotates while the other remains stationary. The imposed conditions can then be represented by the Reynolds number R = ρΩad2/η and the Hartmann number M2 = σB2d2/η, where Ωa is the angular velocity of the rotating disk and d is the gap between the disks. Asymptotic solutions are given for R [Lt ] M2, and numerical solutions are obtained for values of R and M2 up to 512. Experimental measurements are presented which are in general agreement with the theoretical flows, and the results for small values of the Hartmann number provide the first known experimental support for the purely hydrodynamic solutions in the range 100 < R < 800.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 2 , 3 September 1969 , pp. 335 - 352
Copyright
© 1969 Cambridge University Press

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References

Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow Quart. J. Mech. Appl. Math. 4, 29.Google Scholar
Bödewadt, U. T. 1940 Die Drehströmung über festem Grunde Z. Ang. Math. Mech. 20, 241.Google Scholar
Kakutani, T. 1962 Hydromagnetic flow due to a rotating disk J. Phys. Soc. Japan, 17, 1496.Google Scholar
King, W. S. & Lewellen, W. S. 1964 Boundary layer similarity solutions for rotating flows with and without magnetic interaction Phys. Fluids, 7, 1674.Google Scholar
Lance, G. N. & Rogers, M. H. 1962 The axially asymmetric flow of a viscous fluid between two infinite rotating disks. Proc. Roy. Soc. A 266, 109.Google Scholar
Mellor, G. L., Chapple, P. J. & Stokes, V. K. 1968 On the flow between a rotating and a stationary disk J. Fluid Mech. 31, 95.Google Scholar
Pearson, C. E. 1965 Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks J. Fluid Mech. 21, 623.Google Scholar
Picha, K. G. & Eckert, E. R. G. 1958 Study of the air flow between coaxial disks rotating with arbitrary velocities in an open or enclosed space. Proc. 3rd U.S. Nat. Congr. Appl. Mech. p. 791.Google Scholar
Rizvi, S. A. T. 1962 On the steady rotation of a disk in magnetohydrodynamics. Appl. Sci. Res. B 10, 62.Google Scholar
Rogers, M. H. & Lance, G. N. 1964 The boundary layer on a disk of finite radius in a rotating fluid Quart. J. Mech. Appl. Math. 17, 319.Google Scholar
Rott, N. & Lewellen, W. S. 1966 Flow between a rotating and stationary disk Prog. Aeron. Sci. 7, 136.Google Scholar
Shercliff, J. A. 1965 A Textbook of Magnetohydrodynamics. Oxford: Pergamon.
Sparrow, E. M. & Cess, R. D. 1962 Magnetohydrodynamic flow and heat transfer about a rotating disk J. Appl. Mech. 29, 181.Google Scholar
Srivistava, A. C. & Sharma, S. K. 1961 The effect of a transverse magnetic field on the flow between two infinite disks—one rotating and the other at rest. Bull. Acad. Pol. Sci. (ser. Sci. Tech.) 9, 639.Google Scholar
Stephenson, C. J. 1967 Ph.D. thesis. University of Cambridge.
Stewartson, K. 1953 On the flow between two rotating coaxial disks Proc. Camb. Phil. Soc. 49, 533.Google Scholar
Von Kármán, Th. 1921 Über laminare und turbulente Reibung Z. Ang. Math. Mech. 1, 233. Translated: On laminar and turbulent friction. NACA Tech. Memo. no. 1092.Google Scholar