Abstract and Applied Analysis

The Flow Separation of Peristaltic Transport for Maxwell Fluid between Two Coaxial Tubes

S. Z. A. Husseny, Y. Abd elmaboud, and Kh. S. Mekheimer

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We study the peristaltic mechanism of an incompressible non-Newtonian biofluid (namely, Maxwell model) in the annular region between two coaxial tubes. The inner tube represents the endoscope tube. The system of the governing nonlinear PDE is solved by using the perturbation method to the first order in dimensionless wavenumber. The modified Newton-Raphson method is used to predict the flow separation points along the peristaltic wall and the endoscope tube. The results show that the presence of the endoscope (catheter) tube in the artery increases the pressure gradient and shear stress. Such a result seems too reasonable from the physical and medical point of view.

Article information

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 269151, 17 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Husseny, S. Z. A.; Abd elmaboud, Y.; Mekheimer, Kh. S. The Flow Separation of Peristaltic Transport for Maxwell Fluid between Two Coaxial Tubes. Abstr. Appl. Anal. 2014 (2014), Article ID 269151, 17 pages. doi:10.1155/2014/269151. https://projecteuclid.org/euclid.aaa/1412277021

Export citation


  • T. W. Latham, Fluid motion in a peristaltic pump [M.Sc. thesis], Massachusetts Institute of Technology, Cambridge, Mass, USA, 1966.
  • A. H. Shapiro, M. Y. Jaffrin, and S. L. Weinberg, “Peristaltic pumping with long wavelength at low Reynolds number,” Journal of Fluid Mechanics, vol. 37, no. 4, pp. 799–825, 1969.
  • T. F. Zien and S. A. Ostrach, “A long wave approximation to peristaltic motion,” Journal of Biomechanics, vol. 3, no. 1, pp. 63–75, 1970.
  • R. A. Ramachandra and S. Usha, “Peristaltic transport of two immiscible viscous fluids in a circular tube,” Journal of Fluid Mechanics, vol. 298, pp. 271–285, 1995.
  • Kh. S. Mekheimer, E. F. El Shehawey, and A. M. Elaw, “Peristaltic motion of a particle-fluid suspension in a planar channel,” International Journal of Theoretical Physics, vol. 37, no. 11, pp. 2895–2920, 1998.
  • R. B. Bird, R. G. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Fluid Mechanics, vol. 1, John Wiley & Sons, New York, NY, USA, 1987.
  • J. G. Oldroyd, “On the formulation of rheological equations of state,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 200, pp. 523–541, 1950.
  • T. Hayat, A. Afsar, M. Khan, and S. Asghar, “Peristaltic transport of a third order fluid under the effect of a magnetic field,” Computers & Mathematics with Applications, vol. 53, no. 7, pp. 1074–1087, 2007.
  • Y. Abd elmaboud and Kh. S. Mekheimer, “Non-linear peristaltic transport of a second-order fluid through a porous medium,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 2695–2710, 2011.
  • A. E. H. Abd El Naby, A. E. M. El Misery, and M. F. Abd El Kareem, “Effects of a magnetic field on trapping through peristaltic motion for generalized Newtonian fluid in channel,” Physica A: Statistical Mechanics and Its Applications, vol. 367, pp. 79–92, 2006.
  • T. Hayat, M. Khan, A. M. Siddiqui, and S. Asghar, “Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 6, pp. 910–919, 2007.
  • D. Tsiklauri and I. Beresnev, “Non-Newtonian effects in the peristaltic flow of a Maxwell fluid,” Physical Review E, vol. 64, no. 2, part 2, Article ID 036303, 2001.
  • Kh. S. Mekheimer and A. N. Abdel-Wahab, “Net annulus flow of a compressible viscous liquid with peristalsis,” Journal of Aerospace Engineering, vol. 25, no. 4, pp. 660–669, 2012.
  • A. M. Siddiqui and W. H. Schwarz, “Peristaltic flow of a second-order fluid in tubes,” Journal of Non-Newtonian Fluid Mechanics, vol. 53, pp. 257–284, 1994.
  • Kh. S. Mekheimer and A. N. Abdel-Wahab, “Compressibility effects on peristaltic flow of a non-Newtonian Maxwell fluid through an annulus,” in Fluid Transport: Theory, Dynamics and Transport, pp. 219–235, Nova Science Publishers, 2011.
  • K. Vajravelu, S. Sreenadh, and V. R. Babu, “Peristaltic transport of a Herschel–-Bulkley fluid in an inclined tube,” International Journal of Non-Linear Mechanics, vol. 40, no. 1, pp. 83–90, 2005.
  • A. V. Mernone and J. N. Mazumdar, “A mathematical study of peristaltic transport of a casson fluid,” Mathematical and Computer Modelling, vol. 35, no. 7-8, pp. 895–912, 2002.
  • Kh. S. Mekheimer, “Peristaltic transport of a Newtonian fluid through a uniform and non-uniform annulus,” The Arabian Journal for Science and Engineering, vol. 30, no. 1A, p. 69, 2005.
  • A. E. H. Abd El Naby and A. E. M. El Misiery, “Effects of an endoscope and generalized Newtonian fluid on peristaltic motion,” Applied Mathematics and Computation, vol. 128, no. 1, pp. 19–35, 2002.
  • A. E. H. Abd El Naby, A. E. M. El Misery, and I. I. El Shamy, “Effects of an endoscope and fluid with variable viscosity on peristaltic motion,” Applied Mathematics and Computation, vol. 158, no. 2, pp. 497–511, 2004.
  • T. Hayat, N. Ali, S. Asghar, and A. M. Siddiqui, “Exact peristaltic flow in tubes with an endoscope,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 359–368, 2006.
  • Kh. S. Mekheimer and Y. Abd Elmaboud, “Peristaltic flow through a porous medium in an annulus: application of an endoscope,” Applied Mathematics & Information Sciences, vol. 2, no. 1, pp. 103–121, 2008.
  • A. Chorin and J. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer, New York, NY, USA, 1997.
  • R. L. Burden and J. D. Faires, Numerical Analysis, Brooks Cole, Florence, Ky, USA, 9th edition, 2010. \endinput