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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 780415, 19 pages
http://dx.doi.org/10.1155/2012/780415
Research Article

Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

1Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran
2Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa

Received 3 August 2012; Accepted 15 September 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 M. M. Rashidi 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. S. Abel, K. V. Prasad, and A. Mahaboob, “Buoyancy force and thermal radiation effects in MHD boundary layer visco-elastic fluid flow over continuously moving stretching surface,” International Journal of Thermal Sciences, vol. 44, no. 5, pp. 465–476, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. R. Tamizharasi and V. Kumaran, “Pressure in MHD/Brinkman flow past a stretching sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 12, pp. 4671–4681, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. N. C. Ghosh, B. C. Ghosh, and L. Debnath, “The hydromagnetic flow of a dusty visco-elastic fluid between two infinite parallel plates,” Computers & Mathematics with Applications, vol. 39, no. 1-2, pp. 103–116, 2000. View at Publisher · View at Google Scholar
  4. P. S. Datti, K. V. Prasad, M. S. Abel, and A. Joshi, “MHD visco-elastic fluid flow over a non-isothermal stretching sheet,” International Journal of Engineering Science, vol. 42, no. 8-9, pp. 935–946, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. C. H. Chen, “Effects of magnetic field and suction/injection on convection heat transfer of non-Newtonian power-law fluids past a power-law stretched sheet with surface heat flux,” International Journal of Thermal Sciences, vol. 47, no. 7, pp. 954–961, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. O. A. Bég, V. R. Prasad, B. Vasu, N. B. Reddy, Q. Li, and R. Bhargava, “Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects,” International Journal of Heat and Mass Transfer, vol. 54, no. 1–3, pp. 9–18, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. M. H. Kamel, “Unsteady MHD convection through porous medium with combined heat and mass transfer with heat source/sink,” Energy Conversion and Management, vol. 42, no. 4, pp. 393–405, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, vol. 2, Chapman & Hall, New York, NY, USA, 2004.
  9. S. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. Khan and J. Farooq, “On heat transfer analysis of a magneto-hydrodynamic sisko fluid through a porous medium,” Journal of Porous Media, vol. 13, no. 3, pp. 287–294, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. M. M. Rashidi and S. A. M. Pour, “Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method,” Lithuanian Association of Nonlinear Analysts, vol. 15, no. 1, pp. 83–95, 2010. View at Google Scholar · View at Zentralblatt MATH
  12. T. Hayat, M. Mustafa, and I. Pop, “Heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 5, pp. 1183–1196, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Z. Abbas, Y. Wang, T. Hayat, and M. Oberlack, “Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3218–3228, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. M. Khan and A. Shahzad, “On axisymmetric flow of Sisko fluid over a radially stretching sheet,” International Journal of Non-Linear Mechanics, vol. 47, pp. 999–1007, 2012. View at Google Scholar
  15. M. Khan and A. Shahzad, “Falkner-skan boundary layer flow of a sisko fluid,” Zeitschrift für Naturforschung A, vol. 67a, pp. 469–478, 2012. View at Google Scholar
  16. M. Khan, S. Munawar, and S. Abbasbandy, “Steady flow and heat transfer of a Sisko fluid in annular pipe,” International Journal of Heat and Mass Transfer, vol. 53, no. 7-8, pp. 1290–1297, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. M. M. Rashidi, T. Hayat, E. Erfani, S. A. M. Pour, and A. A. Hendi, “Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4303–4317, 2011. View at Publisher · View at Google Scholar
  18. S. Abbasbandy, E. Magyari, and E. Shivanian, “The homotopy analysis method for multiple solutions of nonlinear boundary value problems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 9-10, pp. 3530–3536, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. T. Hayat and M. Sajid, “Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid,” International Journal of Engineering Science, vol. 45, no. 2–8, pp. 393–401, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. M. Khan, Qurrat-ul-Ain, and M. Sajid, “Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, pp. 1347–1355, 2011. View at Google Scholar
  21. M. M. Rashidi, G. Domairry, and S. Dinarvand, “Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 708–717, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. M. M. Rashidi, S. A. M. Pour, and S. Abbasbandy, “Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1874–1889, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Sajid, M. Awais, S. Nadeem, and T. Hayat, “The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method,” Computers & Mathematics with Applications, vol. 56, no. 8, pp. 2019–2026, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. Z. Ziabakhsh and G. Domairry, “Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 1868–1880, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. V. Aliakbar, A. Alizadeh-Pahlavan, and K. Sadeghy, “The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 779–794, 2009. View at Google Scholar