Summary
The unsteady flow of an incompressible and electrically conducting fluid between two infinite discs rotating in the presence of a uniform axial magnetic field is discussed. The solution for small values of the flowReynolds number and magneticPrandtl number is obtained in the form of series expansion about the quasi-steady state. The effect of magnetic field on the flow characteristics and the quasi-steady criteria is studied.
Zusammenfassung
Die instationäre Strömung einer inkompressiblen, elektrisch leitenden Flüssigkeit zwischen zwei unendlichen rotierenden Scheiben bei Einwirkung eines homogenen axialen Magnetfeldes wird untersucht. Für kleineReynolds-Zahlen und kleine magnetischePrandtl-Zahlen wird die Lösung in Form einer Reihenentwicklung in der Nähe des quasistationären Zustandes erhalten. Der Einfluß des Magnetfeldes auf die Strömungscharakteristiken und die quasistationären Kriterien wird studiert.
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References
Batchelor, G. K.: Note on a class of solutions of theNavier-Stokes equatiosn representing steady rotationally symmetric flow. Quart. J. Mech. Appl. Math.4, 29 (1951).
Stewartson, K.: On the flow between two rotating coaxial discs. Proc. Camb. Phil. Soc.49, 333 (1953).
Lance, G. N. andM. H. Rogers: The axially symmetric flow of a viscous fluid between two infinite rotating disks. Proc. Roy. Soc. London, A266, 109 (1962).
Balaram, M.: Doctoral Thesis. Indian Institute of Technology, Kharagpur, 1963.
Srivastava, A. C. andS. K. Sharma: The effect of a transverse magnetic field on the flow between two infinite discs — one rotating and the other at rest. Bull. Acad. Pol. Sci.9, 639 (1961).
Dutta, N.: Doctoral Thesis. Indian Institute of Technology. Kharagpur, 1966.
Grenespan, H. P. andL. N. Howard: On a time-dependent motion of a rotating fluid. J. Fluid Mech.17, 385 (1963).
Pearson, C. E.: Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks. J. Fluid Mech.21, 623 (1965).
Sparrow, E. M. andJ. L. Gregg: Flow about an unsteadily rotating disc. J. Aero-Space Sci.27, 252 (1960).
Subba Raju, P. V.: Flow between two unsteadily rotating disks. Appl. Sci. Res.16, 395 (1966).
Subba Raju, P. V.: Doctoral Thesis, Indian Institute of Technology, Kharagpur, 1967.
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Govindarajulu, T. Time dependent hydromagnetic flow between two slowly rotating discs. Acta Mechanica 8, 53–62 (1969). https://doi.org/10.1007/BF01178533
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DOI: https://doi.org/10.1007/BF01178533