Table of Contents Author Guidelines Submit a Manuscript
Applied Bionics and Biomechanics
Volume 2015, Article ID 406195, 12 pages
http://dx.doi.org/10.1155/2015/406195
Research Article

Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamilnadu 620015, India

Received 19 September 2014; Accepted 18 February 2015

Academic Editor: Cecilia Laschi

Copyright © 2015 S. Priyadharshini and R. Ponalagusamy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. F. Young, “Effect of a time dependent stenosis of flow through a tube,” Journal of Engineering for Industry, vol. 90, pp. 248–254, 1968. View at Google Scholar
  2. D. F. Young and F. Y. Tsai, “Flow characteristics in models of arterial stenoses: I. Steady flow,” Journal of Biomechanics, vol. 6, no. 4, pp. 395–410, 1973. View at Publisher · View at Google Scholar · View at Scopus
  3. D. F. Young, “Fluid mechanics of arterial stenoses,” Journal of Biomechanical Engineering, vol. 101, no. 3, pp. 157–175, 1979. View at Publisher · View at Google Scholar
  4. R. Ponalagusamy, Blood flow through stenosed tube [Ph.D. thesis], IIT, Bombay, India, 1986.
  5. D. B. Clegg and G. Power, “Flow of a Bingham fluid in a slightly curved tube,” Applied Scientific Research: Section A, vol. 12, no. 2, pp. 199–212, 1963. View at Google Scholar · View at Scopus
  6. J. A. Greenwood and J. J. Kauzlarich, “EHD lubrication with Herschel-Bulkley model greases,” ASLE Transactions, vol. 4, pp. 269–278, 1972. View at Google Scholar
  7. P. Chaturani and R. Ponnalagarsamy, “Analysis of pulsatile blood flow through stenosed arteries and its applications to cardiovascular diseases,” in Proceedings of the 3rd National Conference on Fluid Mechanics and Fluid Power, pp. 463–468, 1984.
  8. R. Ponalagusamy, R. T. Selvi, and A. K. Banerjee, “Mathematical model of pulsatile flow of non-Newtonian fluid in tubes of varying cross-sections and its implications to blood flow,” Journal of the Franklin Institute, vol. 349, no. 5, pp. 1681–1698, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. C. Misra, M. K. Patra, and S. C. Misra, “A non-Newtonian fluid model for blood flow through arteries under stenotic conditions,” Journal of Biomechanics, vol. 26, no. 9, pp. 1129–1141, 1993. View at Publisher · View at Google Scholar · View at Scopus
  10. V. P. Srivastava, “Arterial blood flow through a non symmetric stenosis with applications,” Japanese Journal of Applied Physics, vol. 34, pp. 6539–6545, 1995. View at Google Scholar
  11. M. El-Shahed, “Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration,” Applied Mathematics and Computation, vol. 138, no. 2-3, pp. 479–488, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. E. F. Elshehawey, E. M. Elbarbary, N. A. S. Afifi, and M. El-Shahed, “Pulsatile flow of blood through a porous medium under periodic body acceleration,” International Journal of Theoretical Physics, vol. 39, no. 1, pp. 183–188, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. K. Sharma, K. Bansal, and S. Bansal, “Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field,” Korea Australia Rheology Journal, vol. 24, no. 3, pp. 181–189, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. P. K. Mandal, “An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis,” International Journal of Non-Linear Mechanics, vol. 40, no. 1, pp. 151–164, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. P. K. Mandal, S. Chakravarty, A. Mandal, and N. Amin, “Effect of body acceleration on unsteady pulsatile flow of non-Newtonian fluid through a stenosed artery,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 766–779, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. R. Ponalagusamy, “Mathematical analysis on effect of non-Newtonian behavior of blood on optimal geometry of microvascular bifurcation system,” Journal of the Franklin Institute, vol. 349, no. 9, pp. 2861–2874, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. Ponalagusamy, “Pulsatile flow of Herschel-Bulkley fluid in tapered blood vessels,” in Proceedings of the International Conference on Scientific Computing (CSC '13), and World Congress in Computer Science, Computer Engineering, and Applied Computing (WORLDCOMP '13), pp. 67–73, Las Vegas, Nev, USA, July 2013.
  18. P. Chaturani and R. Ponalagusamy, “Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow,” Biorheology, vol. 23, no. 5, pp. 499–511, 1986. View at Google Scholar · View at Scopus
  19. P. Chaturani and R. Ponalagarsamy, “Dilatency effects of blood on flow through arterial stenosis,” in Proceedings of the 28th Congress of the Indian Society of Theoretical and Applied Mechanics, pp. 87–96, 1983.
  20. S. Nadeem, N. S. Akbar, A. A. Hendi, and T. Hayat, “Power law fluid model for blood flow through a tapered artery with a stenosis,” Applied Mathematics and Computation, vol. 217, no. 17, pp. 7108–7116, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Z. Ismail, I. Abdullah, N. Mustapha, and N. Amin, “A power-law model of blood flow through a tapered overlapping stenosed artery,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 669–680, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. B. Pincombe, J. Mazumdar, and I. Hamilton-Craig, “Effects of multiple stenoses and post-stenotic dilatation on non-Newtonian blood flow in small arteries,” Medical and Biological Engineering and Computing, vol. 37, no. 5, pp. 595–599, 1999. View at Publisher · View at Google Scholar · View at Scopus
  23. G. W. Scott Blair and D. C. Spanner, An Introduction to Biorheology, Elsevier Scientific Publishing, Amsterdam, The Netherlands, 1974.
  24. A. H. Sacks, K. R. Raman, J. A. Burnell, and E. G. Tickner, “Auscultatory versus direct pressure measurements for newtonian fluids and for blood in simulated arteries,” VIDYA Report 119, 1963. View at Google Scholar
  25. P. Chaturani and R. Ponnalagarsamy, “A study of non Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases,” Biorheology, vol. 22, no. 6, pp. 521–531, 1985. View at Google Scholar
  26. D. Biswas and R. B. Laskar, “Steady flow of blood through a stenosed artery—a non-Newtonian fluid model,” Assam University Journal of Science and Technology, vol. 7, pp. 144–153, 2011. View at Google Scholar