Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 707286, 14 pages
http://dx.doi.org/10.1155/2013/707286
Research Article

MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions

1Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan
2Department of Mathematics, UET, Peshawar, Pakistan

Received 23 May 2013; Accepted 14 August 2013

Academic Editor: Oluwole Daniel Makinde

Copyright © 2013 Taza Gul 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. N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and P. G. Datskos, “Gold nano-structures for transduction of biomolecular interactions into micrometer scale movements,” Biomedical Microdevices, vol. 3, no. 1, pp. 35–44, 2001. View at Publisher · View at Google Scholar · View at Scopus
  2. A. R. A. Khaled and K. Vafai, “Hydromagnetic squeezed flow and heat transfer over a sensor surface,” International Journal of Engineering Science, vol. 42, pp. 509–519, 2004. View at Publisher · View at Google Scholar
  3. S. Nadeem and M. Awais, “Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity,” Physics Letters A, vol. 372, no. 30, pp. 4965–4972, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. B. R. Munson and D. F. Young, Fundamentals of Fluid Mechanics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1994.
  5. M. K. Alam, A. M. Siddiqui, M. T. Rahim, and S. Islam, “Thin-film flow of magnetohydrodynamic (MHD) Johnson-Segalman fluid on vertical surfaces using the Adomian decomposition method,” Applied Mathematics and Computation, vol. 219, pp. 3956–3974, 2012. View at Google Scholar
  6. M. Hameed and R. Ellahi, “Thin film flow of non-Newtonian MHD fluid on a vertically moving belt,” International Journal for Numerical Methods in Fluids, vol. 66, no. 11, pp. 1409–1419, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. M. Aiyesimi and G. T. Okedao, “MHD flow of a third grade fluid with heat transfer down an inclined plane,” Mathematical Theory and Modeling, vol. 2, no. 9, pp. 108–119, 2012. View at Google Scholar
  8. N. Khan and T. Mahmood, “The influence of slip condition on the thin film flow of a third order fluid,” International Journal of Nonlinear Science, vol. 13, no. 1, pp. 105–116, 2012. View at Google Scholar · View at MathSciNet
  9. A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York, NY, USA, 1973. View at MathSciNet
  10. N. Jamshidi and D. D. Ganji, “Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire,” Current Applied Physics, vol. 10, no. 2, pp. 484–486, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. D. D. Ganji, “A semi-analytical Technique for non-linear setting particle equation of motion original,” Journal of Hydro-Environment Research, vol. 6, no. 4, pp. 323–327, 2012. View at Google Scholar
  12. M. Jalaal, D. D. Ganji, and G. Ahmad, “An analytical study on settling of non-spherical particles,” Asia-Pacific Journal of Chemical Engineering, vol. 7, no. 1, pp. 63–72, 2012. View at Publisher · View at Google Scholar
  13. M. Rafei, H. Daniali, and D. D. Ganji, “Variational iteration method for solving the epidemic model and the prey and predator problem,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 1701–1709, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. 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
  15. M. Omidvar, A. Barari, M. Momeni, and D. Ganji, “New class of solutions for water infiltration problems in unsaturated soils,” Geomechanics and Geoengineering, vol. 5, no. 2, pp. 127–135, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane,” Chaos, Solitons and Fractals, vol. 35, no. 1, pp. 140–147, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. 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
  18. 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
  19. M. Esmaeilpour and D. D. Ganji, “Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate,” Physics Letters A, vol. 372, no. 1, pp. 33–38, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. D. G. Domairry, A. Mohsenzadeh, and M. Famouri, “The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 1, pp. 85–95, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. R. Ghotbi, H. Bararnia, G. Domairry, and A. Barari, “Investigation of a powerful analytical method into natural convection boundary layer flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2222–2228, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2003. View at MathSciNet
  23. V. Marinca, N. Herişanu, and I. Nemeş, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, no. 3, pp. 648–653, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. N. Herişanu and V. Marinca, “Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia,” Meccanica, vol. 45, no. 6, pp. 847–855, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. A. M. Siddiqui, M. Ahmed, and Q. K. Ghori, “Thin film flow of non-Newtonian fluids on a moving belt,” Chaos, Solitons and Fractals, vol. 33, no. 3, pp. 1006–1016, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder,” Physics Letters A, vol. 352, no. 4-5, pp. 404–410, 2006. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Chakraborty and S. K. Som, “Heat transfer in an evaporating thin liquid film moving slowly along the walls of an inclined microchannel,” International Journal of Heat and Mass Transfer, vol. 48, no. 13, pp. 2801–2805, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. G. Adomian, Solving Frontier Problems of Physics: the Decomposition Method, Kluwer Academic Publishers, 1994. View at MathSciNet
  29. G. Adomian, “A review of the decomposition method and some recent results for nonlinear equations,” Mathematical and Computer Modelling, vol. 13, no. 7, pp. 17–43, 1990. View at Google Scholar · View at MathSciNet · View at Scopus
  30. A.-M. Wazwaz, “Adomian decomposition method for a reliable treatment of the Bratu-type equations,” Applied Mathematics and Computation, vol. 166, no. 3, pp. 652–663, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. A.-M. Wazwaz, “Adomian decomposition method for a reliable treatment of the Emden-Fowler equation,” Applied Mathematics and Computation, vol. 161, no. 2, pp. 543–560, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus