A Complex Variable Circle Theorem for Plane Stokes Flows

N. Akhtar; G. A. H. Chowdhury

doi:doi:10.11648/j.ijamtp.20170301.12

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A Complex Variable Circle Theorem for Plane Stokes Flows

N. Akhtar, G. A. H. Chowdhury

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 1)

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), 2024. 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.

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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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TY  - JOUR
T1  - A Complex Variable Circle Theorem for Plane Stokes Flows
AU  - N. Akhtar
AU  - G. A. H. Chowdhury
Y1  - 2016/12/12
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20170301.12
DO  - 10.11648/j.ijamtp.20170301.12
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
SP  - 7
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5927
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

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - A Complex Variable Circle Theorem for Plane Stokes Flows
AU  - N. Akhtar
AU  - G. A. H. Chowdhury
Y1  - 2016/12/12
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20170301.12
DO  - 10.11648/j.ijamtp.20170301.12
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
SP  - 7
EP  - 13
PB  - Science Publishing Group
SN  - 2575-5927
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  -

Copy | Download