Skip to main content
SpringerLink
Log in

Peristaltic transport of MHD Williamson fluid in an inclined asymmetric channel through porous medium with heat transfer

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model.

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. MISHRA M, RAO A R. Peristaltic transport of a Newtonian fluid in an asymmetric channel [J]. Z Angew Math Phys, 2003, 54: 532–550.

    Article  MathSciNet  MATH  Google Scholar 

  2. NASIR A L I, HAYAT T. Peristaltic flow of a micropolar fluid in an asymmetric channel [J]. Computers and Mathematics with Applications, 2008, 55: 589–608.

    Article  MathSciNet  MATH  Google Scholar 

  3. NOREEN S, ALSAEDI A, HAYAT T. Peristaltic flow of pseudoplastic fluid in an asymmetric channel [J]. Journal of Applied Mechanics, 2012, 79: 1–6.

    Article  Google Scholar 

  4. NAGA R P, SAROJAMMA G. Peristaltic transport of a Casson fluid in an asymmetric channel [J]. Australasian Physical and Engineering Sciences in Medicine, 2004, 27: 49–59.

    Article  Google Scholar 

  5. HAYAT T, AMBREEN A, KHAN M, ASGHAR S. Peristaltic transport of a third order fluid under the effect of a magnetic field [J]. Computers and Mathematics with Applications, 2007, 53: 1074–1087.

    Article  MathSciNet  MATH  Google Scholar 

  6. VAJRAVELU K, SREENADH S, RAJANIKANTH K, LEE C H. Peristaltic transport of a Williamson fluid in asymmetric channels with permeable walls [J]. Nonlinear Analysis: Real World Applications, 2012, 13: 2804–2822.

    Article  MathSciNet  MATH  Google Scholar 

  7. ELMABOUD A Y, MEKHEIMER K H S. Non-linear peristaltic transport of a second order fluid through a porous medium [J]. Applied Mathematical Modelling, 2011, 35: 2695–2710.

    Article  MathSciNet  MATH  Google Scholar 

  8. TRIPATHI D, ANWAR B O. A numerical study of oscillating peristaltic flow of generalized maxwell viscoelastic fluids through a porous medium [J]. Transp Porous Med, 2012, 95: 337–348.

    Article  Google Scholar 

  9. ELSHEHAWEY E F, HUSSENY S Z A. Effects of porous boundaries on peristaltic transport through a porous medium [J]. Acta Mechanica, 2000, 143: 165–177.

    Article  Google Scholar 

  10. NADEEM S, AKRAM S. Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel [J]. Mathematical and Computer Modelling, 2010, 52: 107–119.

    Article  MathSciNet  MATH  Google Scholar 

  11. NADEEM S, AKRAM S. Peristaltic flow of a couple stress fluid under the effect of induced magnetic field in an asymmetric channel [J]. Arch Appl Mech, 2011, 81: 97–109.

    Article  MATH  Google Scholar 

  12. WANG Yong-qi, ALI N, HAYAT T. Peristaltic motion of a magnetohydrodynamic generalized second-order fluid in an asymmetric channel [J]. Numerical Methods for Partial Differential Equations, 2009, 27: 415–435.

    Article  MathSciNet  Google Scholar 

  13. SRINIVAS S, PUSHPARAJ V. Non-linear peristaltic transport in an inclined asymmetric channel [J]. Commun Nonlinear Sci Numer Simulat, 2008, 13: 1782–1795.

    Article  Google Scholar 

  14. HAYAT T, MAHOMED F M, ASGHAR S. Peristaltic flow of a magnetohydrodynamic Johnson-Segalman fluid [J]. Nonlinear Dynamics, 2005, 40: 375–385.

    Article  MathSciNet  MATH  Google Scholar 

  15. HAYAT T, AFSAR A, KHAN M, ASGHAR S. Peristaltic transport of a third order fluid under the effect of a magnetic field [J]. Computers and Mathematics with Applications, 2007, 53: 1074–1087.

    Article  MathSciNet  MATH  Google Scholar 

  16. NADEEM S, AKBAR N S. Influence of heat transfer on peristaltic transport of a Johnson-Segalman fluid in an inclined asymmetric channel [J]. Commun Nonlinear Sci Numer Simulat, 2010, 15: 2860–2877.

    Article  MathSciNet  MATH  Google Scholar 

  17. NADEEM S, AKBAR N S. Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel [J]. Appl Math Mech Engl Ed, 2010, 31(8): 969–978.

    Article  MathSciNet  MATH  Google Scholar 

  18. NADEEM S, AKRAM S. Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer [J]. Acta Mech Sin, 2011, 27(2): 237–250.

    Article  MathSciNet  MATH  Google Scholar 

  19. MEHMOOD O U, MUSTAPHA N, SHAFIE S. Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip [J]. Appl Math Mech Engl Ed, 2012, 33(10): 1313–1328.

    Article  MathSciNet  Google Scholar 

  20. HAYAT T, SALEEM N, ASGHAR S, ALHOTHUALI M S, ALHOMAIDAN A. Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid [J]. Commun Nonlinear Sci Numer Simulat, 2011, 16: 3559–3577.

    Article  MATH  Google Scholar 

  21. SRINIVAS S, MUTHURAJ R. Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis [J]. Mathematical and Computer Modelling, 2011, 54: 1213–1227.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    K. Ramesh & M. Devakar

Authors
  1. K. Ramesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Devakar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Devakar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramesh, K., Devakar, M. Peristaltic transport of MHD Williamson fluid in an inclined asymmetric channel through porous medium with heat transfer. J. Cent. South Univ. 22, 3189–3201 (2015). https://doi.org/10.1007/s11771-015-2856-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2856-4

Keywords

Search

Navigation