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Mathematical Problems in Engineering
Volume 2012, Article ID 329639, 24 pages
http://dx.doi.org/10.1155/2012/329639
Research Article

Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium

1Department of Mathematics and Statistics, FBAS, IIU, Islamabad 44000, Pakistan
2Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
3Mechanical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Received 27 January 2012; Revised 21 March 2012; Accepted 21 March 2012

Academic Editor: Anuar Ishak

Copyright © 2012 R. Ellahi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. F. Elshehawey, N. T. Eldabe, E. M. Elghazy, and A. Ebaid, “Peristaltic transport in an asymmetric channel through a porous medium,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 140–150, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. S. Nadeem and N. S. Akbar, “Influence of heat transfer on peristaltic transport of a Johnson-Segalman fluid in an inclined asymmetric channel,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 2860–2877, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Nadeem and S. Akram, “Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 107–119, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Nadeem and S. Akram, “Heat transfer in a peristaltic flow of MHD fluid with partial slip,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 312–321, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. N. S. Akbar, T. Hayat, S. Nadeem, and A. A. Hendi, “Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel,” International Journal of Heat and Mass Transfer, vol. 54, no. 7-8, pp. 1654–1664, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Nadeem and S. Akram, “Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel,” Zeitschrift fur Naturforschung, vol. 64, no. 9-10, pp. 559–567, 2009. View at Google Scholar · View at Scopus
  7. S. Nadeem and S. Akram, “Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field,” International Journal for Numerical Methods in Fluids, vol. 63, no. 3, pp. 374–394, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Nadeem and S. Akram, “Peristaltic flow of a couple stress fluid under the effect of induced magnetic field in an asymmetric channel,” Archive of Applied Mechanics, vol. 81, no. 1, pp. 97–109, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Nadeem and N. S. Akbar, “Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of Adomian decomposition method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3844–3855, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Nadeem, T. Hayat, N. S. Akbar, and M. Y. Malik, “On the influence of heat transfer in peristalsis with variable viscosity,” International Journal of Heat and Mass Transfer, vol. 52, no. 21-22, pp. 4722–4730, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Nadeem and N. S. Akbar, “Influence of heat transfer on a peristaltic transport of Herschel-Bulkley fluid in a non-uniform inclined tube,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 12, pp. 4100–4113, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Nadeem and S. Akram, “Heat transfer in a peristaltic flow of MHD fluid with partial slip,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 312–321, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. S. K. Pandey and M. K. Chaube, “Peristaltic flow of a micropolar fluid through a porous medium in the presence of an external magnetic field,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3591–3601, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. N. A. S. Afifi and N. S. Gad, “Interaction of peristaltic flow with pulsatile fluid through a porous medium,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 167–176, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. A. R. Rao and M. Mishra, “Peristaltic transport of a power-law fluid in a porous tube,” Journal of Non-Newtonian Fluid Mechanics, vol. 121, no. 2-3, pp. 163–174, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Mishra and A. R. Rao, “Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract,” Journal of Biomechanics, vol. 38, no. 4, pp. 779–789, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. O. Eytan and D. Elad, “Analysis of intra-uterine fluid motion induced by uterine contractions,” Bulletin of Mathematical Biology, vol. 61, no. 2, pp. 221–238, 1999. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Nadeem and S. Akram, “Peristaltic flow of a Williamson fluid in an asymmetric channel,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1705–1716, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Srinivas and M. Kothandapani, “Peristaltic transport in an asymmetric channel with heat transfer—a note,” International Communications in Heat and Mass Transfer, vol. 35, no. 4, pp. 514–522, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Srinivas and R. Gayathri, “Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 185–196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. K. Vajravelu, S. Sreenadh, and V. R. Babu, “Peristaltic pumping of a Herschel-Bulkley fluid in a channel,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 726–735, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Nadeem and N. S. Akbar, “Effects of temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid in a non-uniform vertical tube,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3950–3964, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. D. Srinivasacharya, M. Mishra, and A. R. Rao, “Peristaltic pumping of a micropolar fluid in a tube,” Acta Mechanica, vol. 161, no. 3-4, pp. 165–178, 2003. View at Google Scholar · View at Scopus
  24. M. Elshahed and M. H. Haroun, “Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field,” Mathematical Problems in Engineering, vol. 2005, no. 6, pp. 663–677, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. M. H. Haroun, “Non-linear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel,” Computational Materials Science, vol. 39, no. 2, pp. 324–333, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. M. V. S. Reddy, M. Mishra, S. Sreenadh, and A. R. Rao, “Influence of lateral walls on peristaltic flow in a rectangular duct,” Journal of Fluids Engineering, vol. 127, no. 4, pp. 824–827, 2005. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Nadeem and S. Akram, “Peristaltic flow of a Jeffrey fluid in a rectangular duct,” Nonlinear Analysis, vol. 11, no. 5, pp. 4238–4247, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. J. H. He, “A note on the homotopy perturbation method,” Thermal Science, vol. 14, no. 2, pp. 565–568, 2010. View at Google Scholar · View at Scopus
  29. J. H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. J. H. He, “An elementary introduction to the homotopy perturbation method,” Computers and Mathematics with Applications, vol. 57, no. 3, pp. 410–412, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Yldrm, “Applying He's variational iteration method for solving differential-difference equation,” Mathematical Problems in Engineering, vol. 2008, Article ID 869614, 7 pages, 2008. View at Publisher · View at Google Scholar
  32. S. T. Mohyud-Din and A. Yildirim, “Solving nonlinear boundary value problems using He's polynomials and Padé approximants,” Mathematical Problems in Engineering, vol. 2009, Article ID 690547, 17 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  33. S. T. Mohyud-Din, A. Yildirim, S. A. Sezer, and M. Usman, “Modified variational iteration method for free-convective boundary-layer equation using padé approximation,” Mathematical Problems in Engineering, vol. 2010, Article ID 318298, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. G. Domairry, M. Ahangari, and M. Jamshidi, “Exact and analytical solution for nonlinear dispersive K (m, p) equations using homotopy perturbation method,” Physics Letters A, vol. 368, no. 3-4, pp. 266–270, 2007. View at Publisher · View at Google Scholar · View at Scopus
  35. S. S. Ganji, A. Barari, M. G. Sfahani, G. Domairry, and P. T. Baboli, “Consideration of transient stream/aquifer interaction with the nonlinear Boussinesq equation using HPM,” Journal of King Saud University, vol. 23, no. 2, pp. 211–219, 2011. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Jalaal, D. D. Ganji, and G. Ahmadi, “Analytical investigation on acceleration motion of a vertically falling spherical particle in incompressible Newtonian media,” Advanced Powder Technology, vol. 21, no. 3, pp. 298–304, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. M. Jalaal and D. D. Ganji, “On unsteady rolling motion of spheres in inclined tubes filled with incompressible Newtonian fluids,” Advanced Powder Technology, vol. 22, no. 1, pp. 58–67, 2011. View at Publisher · View at Google Scholar · View at Scopus
  38. M. Jalaal and D. D. Ganji, “An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid,” Powder Technology, vol. 198, no. 1, pp. 82–92, 2010. View at Publisher · View at Google Scholar · View at Scopus
  39. M. Jalaal, D. D. Ganji, and G. Ahmadi, “An analytical study on settling of non-spherical particles,” Asia-Pacific Journal of Chemical Engineering, vol. 7, pp. 63–72, 2012. View at Google Scholar
  40. D. D. Ganji and A. Sadighi, “Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 4, pp. 411–418, 2006. View at Google Scholar · View at Scopus
  41. H. Tari, D. D. Ganji, and H. Babazadeh, “The application of He's variational iteration method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 363, no. 3, pp. 213–217, 2007. View at Publisher · View at Google Scholar · View at Scopus
  42. D. D. Ganji and A. Rajabi, “Assessment of homotopy-perturbation and perturbation methods in heat radiation equations,” International Communications in Heat and Mass Transfer, vol. 33, no. 3, pp. 391–400, 2006. View at Publisher · View at Google Scholar · View at Scopus
  43. D. D. Ganji, M. Rafei, A. Sadighi, and Z. Z. Ganji, “A comparative comparison of He's method with perturbation and numerical methods for nonlinear vibrations equations,” International Journal of Nonlinear Dynamics in Engineering and Sciences, vol. 1, no. 1, pp. 1–20, 2009. View at Google Scholar
  44. Z. Z. Ganji, D. D. Ganji, and E. Esmaeilpour, “Study on nonlinear Jeffery-Hamel flow by He's semi-analytical methods and comparison with numerical results,” Computers and Mathematics with Applications, vol. 58, no. 11-12, pp. 2107–2116, 2009. View at Publisher · View at Google Scholar · View at Scopus