Volume 3, Issue 1, January 2017, Page: 7-13
A Complex Variable Circle Theorem for Plane Stokes Flows
N. Akhtar, Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
G. A. H. Chowdhury, Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
Received: Sep. 14, 2016;       Accepted: Nov. 7, 2016;       Published: Dec. 12, 2016
DOI: 10.11648/j.ijamtp.20170301.12      View  2547      Downloads  119
Abstract
Two dimensional steady Stokes flow around a circular cylinder is examined in the light of complex variable theory and a circle theorem for the flow, are established. The theorem gives a complex variable expression of the velocity for a Stokes flow external to a circular cylinder, in terms of the same variable expression of the velocity for a slow and steady irrotational flow in unbounded incompressible viscous fluid, and also gives a formula for the steam function for the flow. A few illustrative solutions of Stokes flow around a circular cylinder are presented.
Keywords
Two Dimensional Stokes Flow, Complex Variable Theory, Circle Theorem
To cite this article
N. Akhtar, G. A. H. Chowdhury, A Complex Variable Circle Theorem for Plane Stokes Flows, International Journal of Applied Mathematics and Theoretical Physics. Vol. 3, No. 1, 2017, pp. 7-13. doi: 10.11648/j.ijamtp.20170301.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
G. G STOKES, Trans.Camb.Phil.SOC. 8 (1845), 287-319.
[2]
J. HAPPEL and H. BRENNER, Low Reynolds Number Hydrodynamics (4th print, Martinus, Nijhoff Publishers 1986).
[3]
A. AVUDAINAYAGAM, B. JOTHIRAM and J. Ramakrishna, Q. JI Mech appl. Math.39 (1986), 425-434.
[4]
S. K. SEN, Z. angew, Math. Phys (ZAMP), 40, (1989) 139-146.
[5]
R. USHA and K. Hemalatha, Z. angew, Math. Phys (ZAMP) 44, (1993), 73-84.
[6]
L. M. MILNE-THOMSON, Theoretical Hydrodynamics, 5th Edition, 1968.
[7]
E. W. Langlois, Slow Viaocus Flow, The Macmillan Company, New York, 1964, 159.
[8]
A. E. Green and W. Zerba, Theoretical elasticity 2nd edition, Oxford University pass, 1968, 286-287.
[9]
A. T CHWANG and T. Y. WU, J. PLUID. Mech.67 (1975).787-815.
[10]
A. T CHWANG and T. Y. WU. proc. ROY. Soc. B 178 (1971) 327-346.
[11]
G. K. BATCHELOR, J.Fluid.Mech.41 (1970a) 545-570.
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