Singularity Induced Interior Stokes Flows

N. Akhtar; G. A. H. Chowdhury

doi:doi:10.11648/j.ijtam.20170301.11

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Singularity Induced Interior Stokes Flows

N. Akhtar, G. A. H. Chowdhury

Received: 18 September 2016 Accepted: 10 November 2016 Published: 9 December 2016

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Abstract

Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.

DOI	10.11648/j.ijtam.20170301.11
Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1, February 2017)
Page(s)	1-10
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

Complex Variable Theory, Rotlet, Stokeslet, Stresslet, Stokes Flows

References

[1]	Sen S K, A reflection theorem for plane Stokes flow, (under consideration for publication), presented in 15^th Mathematic conf. 29 to 31 December 2007, Dhaka, Bangladesh.
[2]	L. M. Milne- Thomson, Hydrodynamical images, Proc. Camb. Phil. Soc., 36, 1940, 246-247.
[3]	L. M. Milne-Thomson, Theoretical Hydrodynamics, 5^th Edition 1972, pp. 157-158., 181-190.
[4]	A. Avudainayagam and B. Jothiram, A circle theorem for plane Stokes flows, Q. J. Mech. A ppl. Math., 41, 1988, pt.3, 383-393.
[5]	S. K. Sen, Circle theorems for steady Stokes flows, Z. angew. Math. Phys. (ZAMP), 40, 1989, 139-146.
[6]	K. B. Ranger, Eddies in two-dimensional Stokes flow, Int. J. Eng. Sci., 18, 1980.
[7]	V. V. Meleshko and H. Arof, A blinking rotlet model for chaotic advection, Phys. Fluids A, 8, 1996, 3215.
[8]	Chowdhury G A H, Studies on flows in a viscous fluid, Ph. D Thesis, 2001, Research centre for Mathematical and Physical Sciences, (RCMPS), University of Chittagong, Bangladesh.
[9]	Chowdhury G A H and Sen S K, A note on Stokes flow within a circular cylinder, GANIT; J. Bangladesh Math. Soc, 26, 2006, 43-50.
[10]	Prabir Daripa and D. Palaniappan, Singularity induced exterior and interior Stokes flows, Phys. Fiuids 13 (11), 2001, 3134-3154.
[11]	Chowdhury G A H and Sen S K, Stokes flow before a plane boundary, Indian J. pure appl. Math., 34 (2), 2003, 353-361.
[12]	Sen S K, Studies on flows in viscous and non-viscous Fluids, Ph. D. Thesis, 1993, Research Centre for Mathematical and Physical Sciences, (RCMPS), University of Chittagong, Bangladesh.
[13]	F. Chorlton, Text Book of Fluid Dynamics,Van Nostrand Reinhold, London, 1967, PP187-188.
[14]	W. E. Langlois, Slow Viscous Flow, The Macmillan Company, New York, 1964, p. 159.

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APA Style

N. Akhtar, G. A. H. Chowdhury. (2016). Singularity Induced Interior Stokes Flows. International Journal of Theoretical and Applied Mathematics, 3(1), 1-10. https://doi.org/10.11648/j.ijtam.20170301.11

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ACS Style

N. Akhtar; G. A. H. Chowdhury. Singularity Induced Interior Stokes Flows. Int. J. Theor. Appl. Math. 2016, 3(1), 1-10. doi: 10.11648/j.ijtam.20170301.11

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AMA Style

N. Akhtar, G. A. H. Chowdhury. Singularity Induced Interior Stokes Flows. Int J Theor Appl Math. 2016;3(1):1-10. doi: 10.11648/j.ijtam.20170301.11

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@article{10.11648/j.ijtam.20170301.11,
  author = {N. Akhtar and G. A. H. Chowdhury},
  title = {Singularity Induced Interior Stokes Flows},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ijtam.20170301.11},
  url = {https://doi.org/10.11648/j.ijtam.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.11},
  abstract = {Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.},
 year = {2016}
}

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TY  - JOUR
T1  - Singularity Induced Interior Stokes Flows
AU  - N. Akhtar
AU  - G. A. H. Chowdhury
Y1  - 2016/12/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20170301.11
DO  - 10.11648/j.ijtam.20170301.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2575-5080
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AB  - Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.
VL  - 3
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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). Singularity Induced Interior Stokes Flows. International Journal of Theoretical and Applied Mathematics, 3(1), 1-10. https://doi.org/10.11648/j.ijtam.20170301.11

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ACS Style

N. Akhtar; G. A. H. Chowdhury. Singularity Induced Interior Stokes Flows. Int. J. Theor. Appl. Math. 2016, 3(1), 1-10. doi: 10.11648/j.ijtam.20170301.11

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AMA Style

N. Akhtar, G. A. H. Chowdhury. Singularity Induced Interior Stokes Flows. Int J Theor Appl Math. 2016;3(1):1-10. doi: 10.11648/j.ijtam.20170301.11

Copy | Download

@article{10.11648/j.ijtam.20170301.11,
  author = {N. Akhtar and G. A. H. Chowdhury},
  title = {Singularity Induced Interior Stokes Flows},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ijtam.20170301.11},
  url = {https://doi.org/10.11648/j.ijtam.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.11},
  abstract = {Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Singularity Induced Interior Stokes Flows
AU  - N. Akhtar
AU  - G. A. H. Chowdhury
Y1  - 2016/12/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20170301.11
DO  - 10.11648/j.ijtam.20170301.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170301.11
AB  - Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.
VL  - 3
IS  - 1
ER  -

Copy | Download