Skip to main content
SpringerLink
Log in

Peristaltic Flow of Viscous Fluid in a Rectangular Duct with Compliant Walls

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

In the present article, we have examined the peristaltic flow of a viscous fluid in a rectangular channel with compliant walls. The long wavelength and low Reynolds number approximations are employed to simplify the governing equations. The reduced linear nonhomogeneous partial differential equations are solved by using the eigenfunction expansion method. The physical features of pertinent parameters have been discussed by plotting graphs of velocity for both two-dimensional and three-dimensional cases. The trapping phenomenon is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. H. Shapiro, M. Y. Jaffrin, S. L. Weinberg, “Peristaltic pumping with long wavelengths at low Reynolds number,” J. Fluid Mech., 37, 799–825 (1969).

    Article  Google Scholar 

  2. T. K. Mitra and S. N. Prasad, “On the influence of wall properties and Poiseuille flow in peristalsis,” J. Biomech., 6, 681–693 (1973).

    Article  Google Scholar 

  3. S. Nadeem and S. Akram, “Peristaltic flow of a Williamson fluid in an asymmetric channel,” Commun. Nonlinear Sci. Numer. Simul., 15, 1705–1716 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Tsangaris and N. W. Vlachakis, “Exact solution of the Navier Stokes equations for the fully developed. Pulsating flow in a rectangular duct with constant cross-sectional velocity,” ASME J. Fluids Eng., 125, 382–385 (2003).

    Article  Google Scholar 

  5. S. Nadeem and N. S. Akbar, “Influence of heat transfer on a peristaltic transport of a Herschel Bulkley fluid in a non-uniform tube,” Commun. Nonlinear Sci. Numer. Simul., 14, 4100–4113 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Nadeem and Safia Akram, “Heat transfer in a peristaltic flow of MHD fluid with partial slip,” Commun. Nonlinear Sci. Numer. Simul., 15, 312–321 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  7. Kh.S. Mekheimer, “Effect of the induced magnetic field on peristaltic flow of a couple stress fluid,” Phys. Lett. A, 372, 4271–4278 (2008).

    Article  MATH  Google Scholar 

  8. Abd El Hakeem, Abd El Naby, A.E.M. El Misiery, and I. El Shamy, “Hydromagnetic flow of generalized Newtonian fluid through a uniform tube with peristalsis,” Appl. Math. Comput., 173, 856–871 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Hayat, M. Javed, and S. Asghar, Slip Effects in Peristalsis, Numer. Methods Partial Differ. Equ. (2011), doi:10.1002/num.20564.

  10. O. Eytan and D. Elad, “Analysis of intra-uterine fluid motion induced by uterine contractions,” Bull. Math. Biol., 61, 221–238 (1999).

    Article  Google Scholar 

  11. M. V. Subba Reddy, M. Mishra, S. Sreenadh, and A. R. Rao, “Influence of lateral walls on peristaltic flow in a rectangular duct,” J. Fluids Eng., 127, 824–827 (2005).

    Article  Google Scholar 

  12. S. Nadeem and Safia Akram, “Peristaltic flow of a Jeffrey fluid in a rectangular duct,” Nonlinear Anal.: Real World Appl., 11, 4238–4247 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  13. S. Srinivas and M. Kothandapani, “The influence of heat and mass transfer on MHD peristaltic flow through a porous space with complaints walls,” Appl. Math. Comput., 213, 197–208 (2009).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan

    S. Nadeem & Arshad Riaz

  2. Department of Mathematics and Statistics, FBAS, IIU, Islamabad, 44000, Pakistan

    R. Ellahi

Authors
  1. S. Nadeem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arshad Riaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Ellahi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Nadeem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nadeem, S., Riaz, A. & Ellahi, R. Peristaltic Flow of Viscous Fluid in a Rectangular Duct with Compliant Walls. Comput Math Model 25, 404–415 (2014). https://doi.org/10.1007/s10598-014-9235-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-014-9235-0

Keywords

Search

Navigation