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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
MISHRA M, RAO A R. Peristaltic transport of a Newtonian fluid in an asymmetric channel [J]. Z Angew Math Phys, 2003, 54: 532–550.
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.
NOREEN S, ALSAEDI A, HAYAT T. Peristaltic flow of pseudoplastic fluid in an asymmetric channel [J]. Journal of Applied Mechanics, 2012, 79: 1–6.
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.
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.
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.
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.
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.
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.
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.
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.
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.
SRINIVAS S, PUSHPARAJ V. Non-linear peristaltic transport in an inclined asymmetric channel [J]. Commun Nonlinear Sci Numer Simulat, 2008, 13: 1782–1795.
HAYAT T, MAHOMED F M, ASGHAR S. Peristaltic flow of a magnetohydrodynamic Johnson-Segalman fluid [J]. Nonlinear Dynamics, 2005, 40: 375–385.
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.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-015-2856-4