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Singularity Induced Interior Stokes Flows

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.

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)
DOI 10.11648/j.ijtam.20170301.11
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), 2016. 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 15th 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, 5th 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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    JO  - International Journal of Theoretical and Applied Mathematics
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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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