Abstract
In the present analysis, we have modeled the governing equations of two dimensional hyperbolic tangent fluid model under the assumptions of long wavelength and low Reynolds number. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The governing equations of hyperbolic tangent fluid have been solved using regular perturbation method. The expression for pressure rise has been calculated using numerical integrations. The behavior of different physical parameters have been discussed graphically.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. D. Brown and T. K. Hung, “Computational and experimental investigations of two dimensional non linear peristaltic flows,” J. Fluid Mech. 83, 249–272 (1977).
S. Nadeem and Safia Akram, “Peristaltic flow of a Williamson fluid in an asymmetric channel,” Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2009.07.026.
Safia Akram and S. Nadeem, “Influence of induced magnetic field and heat transfer on the peristaltic motion of a Jeffrey fluid in an asymmetric channel: Closed form solutions,” J. Magn. Magn. Mater. 328, 11–20 (2013).
Safia Akram, S. Nadeem, and M. Hanif, “Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field,” J. Magn. Magn. Mater. 346, 142–151 (2013).
Kh. S. Mekheimer and Y. Abd elmaboud, “The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: Application of an endoscope,” Phys. Lett. A 372, 1657–1665 (2008).
T. Hayat and N. Ali, “Peristaltically induced motion of a MHD third grade fluid in a deformable tube”, Physica A 370, 225–239 (2006).
S. Nadeem, Safia Akram, and Noreen Sher Akbar, “Simulation of heat and chemical reactions on peristaltic flow of a Williamson fluid in an inclined asymmetric channel,” Iran. J. Chem. Chem. Eng. 32, 93–107 (2013).
Kh. S. Mekheimer, “Effect of the induced magnetic field on peristaltic flow of a couple stress fluid,” Phys. Lett. A 372, 4271–4278 (2008).
A. H. Shapiro, M. Y. Jaffrin, and S. L. Weinberg, “Peristaltic pumping with long wave length at low Reynolds number,” J. Fluid Mech. 37, 799–825 (1969).
T. W. Latham, M. Sci. Thesis (Massachusetts Institute of Technology, Cambridge, 1966).
Safia Akram and S. Nadeem, “Significance of nanofluid and partial slip on the peristaltic transport of a Jeffrey fluid model in an asymmetric channel with different wave forms,” IEEE Trans. Nanotech. 13, 375–385 (2014).
M. Mishra and A. R. Rao, “Peristaltic transport of a Newtonian fluid in an asymmetric channel,” Z. Angew. Math. Phys. 54, 532–550 (2004).
Safia Akram, Kh. S. Mekheimer, and S. Nadeem, “Influence of lateral walls on peristaltic flow of a couple stress fluid in a non-uniform rectangular due,” Appl. Math. Inf. Sci 3, 1127–1133 (2014).
M. H. Haroun, “Effect of Deborah number and phase difference on peristaltic transport in an asymmetric channel,” Commun. Nonlinear Sci. Numer. Simul. 12, 1464–1480 (2007).
Safia Akram and S. Nadeem, “Consequence of nanofluid on Peristaltic transport of a hyperbolic Tangent fluid model in the occurrence of apt (tending) magnetic field,” J. Magn. Magn. Mater. 358–359, 183–191 (2014).
G. Radhakrishnamacharya and Ch. Srinivasulu, “Influence of wall properties on peristaltic transport with heat transfer” C. R. Mecanique 335, 369–373 (2007).
T. Hayat, Q. Hussain, and N. Ali, “Influence of partial slip on the peristaltic flow in a porous medium,” Physica A 387, 3399–3409 (2008).
A. Ebaid, “Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel,” Phys. Lett. A 372, 4493–4489 (2008).
T. Hayat, M. Umar Qureshi, and N. Ali, “The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel,” Phys. Lett. A 372, 2653–2664 (2008).
S. Nadeem and Safia Akram, “Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field,” Int. J. Numer. Methods Fluids doi: 10.1002/fld.2081.
L. Ai and K. Vafai, “An investigation of Stokes second problem for non-Newtonian fluids,” Numer. Heat Transfer, Part A 47, 955–980 (2005).
S. Nadeem and Safia Akram, “Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel,” Z. Naturforschung A 64, 559–567 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Akram, S., Nadeem, S. Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. Comput. Math. and Math. Phys. 55, 1899–1912 (2015). https://doi.org/10.1134/S0965542515110147
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542515110147