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A Complex Variable Circle Theorem for Plane Stokes Flows

Received: 14 September 2016     Accepted: 7 November 2016     Published: 12 December 2016
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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.

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 1)
DOI 10.11648/j.ijamtp.20170301.12
Page(s) 7-13
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Two Dimensional Stokes Flow, Complex Variable Theory, Circle Theorem

References
[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.
Cite This Article
  • APA Style

    N. Akhtar, G. A. H. Chowdhury. (2016). A Complex Variable Circle Theorem for Plane Stokes Flows. International Journal of Applied Mathematics and Theoretical Physics, 3(1), 7-13. https://doi.org/10.11648/j.ijamtp.20170301.12

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    ACS Style

    N. Akhtar; G. A. H. Chowdhury. A Complex Variable Circle Theorem for Plane Stokes Flows. Int. J. Appl. Math. Theor. Phys. 2016, 3(1), 7-13. doi: 10.11648/j.ijamtp.20170301.12

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    AMA Style

    N. Akhtar, G. A. H. Chowdhury. A Complex Variable Circle Theorem for Plane Stokes Flows. Int J Appl Math Theor Phys. 2016;3(1):7-13. doi: 10.11648/j.ijamtp.20170301.12

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  • @article{10.11648/j.ijamtp.20170301.12,
      author = {N. Akhtar and G. A. H. Chowdhury},
      title = {A Complex Variable Circle Theorem for Plane Stokes Flows},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {3},
      number = {1},
      pages = {7-13},
      doi = {10.11648/j.ijamtp.20170301.12},
      url = {https://doi.org/10.11648/j.ijamtp.20170301.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20170301.12},
      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.},
     year = {2016}
    }
    

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    T1  - A Complex Variable Circle Theorem for Plane Stokes Flows
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    AU  - G. A. H. Chowdhury
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    T2  - International Journal of Applied Mathematics and Theoretical Physics
    JF  - International Journal of Applied Mathematics and Theoretical Physics
    JO  - International Journal of Applied Mathematics and Theoretical Physics
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    UR  - https://doi.org/10.11648/j.ijamtp.20170301.12
    AB  - 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.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh

  • Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh

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