Advertisement

Biophysical Reviews

, Volume 11, Issue 2, pp 139–147 | Cite as

Numerical study of hydromagnetic axisymmetric peristaltic flow at high Reynolds number and wave number

  • A. H. HamidEmail author
  • Tariq Javed
  • N. Ali
Commentary
  • 26 Downloads

Abstract

The computational study of MHD peristaltic motion is investigated for axisymmetric flow problem. The developed model is present in the form of partial differential equations. Then obtained partial differential equations are transferred into stream-vorticity (ψ − ω) form. Then Galerkin Finite element method is used to find the computational results of governing problem. The current study is compared with the existing well-known results at low Reynolds number and wave number. It is revealed that the present results are in well agreement with existing results in the literature. So, it is effective for higher values of Reynolds number and wave number. The variations of streamline are present graphically against high Reynolds number. It concludes that high Reynolds number and Hartmann number increase pressure rise per unit wavelength in positive pumping region sharply.

Keywords

Peristaltic motion High Reynolds numbers MHD Finite element method 

Notes

Compliance with ethical standards

Conflict of interest

A. H. Hamid declares that he has no conflict of interest. Tariq Javed declares that he has no conflict of interest. N. Ali declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Ali N, Hussain Q, Hayat T, Asghar S (2008) Slip effects on the peristaltic transport of MHD fluid with variable viscosity. Phys Lett A 372(9):1477–1489Google Scholar
  2. Brown TD, Hung TK (1977) Computational and experimental investigations of two-dimensional nonlinear peristaltic flows. J Fluid Mech 83(2):249–272Google Scholar
  3. Dennis SCR, Chang GZ (1969) Numerical Integration of the Navier‐Stokes Equations for Steady Two‐Dimensional Flow. Phys Fluids 12(12):II–88.Google Scholar
  4. Ebaid A (2008) A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method. Phys Lett A 372(32):5321–5328Google Scholar
  5. El Naby AEHA, El Misiery AEM, El Shamy I (2006) Hydromagnetic flow of generalized Newtonian fluid through a uniform tube with peristalsis. Appl Math Comput 173(2):856–871Google Scholar
  6. Fung YC, Yih CS (1968) Peristaltic transport. J Appl Mech 35(4):669–675Google Scholar
  7. Hayat T, Ali N (2006) Peristaltically induced motion of a MHD third grade fluid in a deformable tube. Physica A: Statistical Mechanics and its Applications 370(2):225–239Google Scholar
  8. Hayat T, Ali N (2007) A mathematical description of peristaltic hydromagnetic flow in a tube. Appl Math Comput 188(2):1491–1502Google Scholar
  9. Jaffrin MY (1973) Inertia and streamline curvature effects on peristaltic pumping. Int J Eng Sci 11(6):681–699Google Scholar
  10. Jaffrin MY, Shapiro AH (1971) Peristaltic pumping. Annu Rev Fluid Mech 3(1):13–37Google Scholar
  11. Kumar BR, Naidu KB (1995) A numerical study of peristaltic flows. Comput. Fluids 24(2):161–176Google Scholar
  12. Latham TW (1966) Fluid motions in a peristaltic pump (Doctoral dissertation, Massachusetts Institute of Technology)Google Scholar
  13. Lew HS, Fung YC, Lowenstein CB (1971) Peristaltic carrying and mixing of chyme in the small intestine (an analysis of a mathematical model of peristalsis of the small intestine). J Biomech 4(4):297–315Google Scholar
  14. Mekheimer KS (2004) Peristaltic flow of blood under effect of a magnetic field in a non-uniform channels. Appl Math Comput 153(3):763–777Google Scholar
  15. Mekheimer KS, Al-Arabi TH (2003) Nonlinear peristaltic transport of MHD flow through a porous medium. Int J Math Math Sci 2003(26):1663–1682Google Scholar
  16. Shapiro AH, Jaffrin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37(4):799–825Google Scholar
  17. Srinivas S, Pushparaj V (2008) Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 13(9):1782–1795Google Scholar
  18. Takabatake S (1990) Finite element analysis of two-dimensional peristaltic flow (2nd report, pressure-flow characteristics). Japan Society of Mechanical Engineering 56:3633–3637Google Scholar
  19. Takabatake S, Ayukawa K (1982) Numerical study of two-dimensional peristaltic flows. J Fluid Mech 122:439–465Google Scholar
  20. Takabatake S, Ayukawa K, Sawa M (1987) Finite-element analysis of two-dimensional peristaltic flows: 1st report, finite-element solutions. JSME Int J 30(270):2048–2049Google Scholar
  21. Takabatake S, Ayukawa K, Mori A (1988) Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J Fluid Mech 193:267–283Google Scholar
  22. Weinberg SL, Eckstein EC, Shapiro AH (1971) An experimental study of peristaltic pumping. J Fluid Mech 49(3):461–479Google Scholar
  23. Xiao Q, Damodaran M (2002) A numerical investigation of peristaltic waves in circular tubes. Int J Comp Fluid Dyn 16:201–216Google Scholar
  24. Yildirim A, Sezer SA (2010) Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. Math Comput Model 52(3–4):618–625Google Scholar
  25. Yin FCP, Fung YC (1971) Comparison of theory and experiment in peristaltic transport. J Fluid Mech 47(1):93–112Google Scholar
  26. Zien TF, Ostrach S (1970) A long wave approximation to peristaltic motion. J Biomech 3(1):63–75Google Scholar

Copyright information

© International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsInternational Islamic University IslamabadIslamabadPakistan

Personalised recommendations