About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 417643, 11 pages
http://dx.doi.org/10.1155/2014/417643
Research Article

Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method

1Department of Mechanics and Vibration, Politehnica University of Timişoara, 300222 Timişoara, Romania
2Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romania Academy, 300223 Timişoara, Romania
3Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania

Received 9 January 2014; Revised 10 February 2014; Accepted 17 February 2014; Published 25 March 2014

Academic Editor: Waqar Ahmed Khan

Copyright © 2014 Vasile Marinca and Remus-Daniel Ene. 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. Uchida and H. Aoki, “Unsteady flows in a semi-infinite contracting or expanding pipe,” Journal of Fluid Mechanics, vol. 82, no. 2, pp. 371–387, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. M. Skalak and C. Y. Wang, “On the unsteady squeezing of viscous fluid from a tube,” Journal of the Australian Mathematical Society B, vol. 21, pp. 65–74, 1979.
  3. M. Miklavčič and C. Y. Wang, “Viscous flow due to a shrinking sheet,” Quarterly of Applied Mathematics, vol. 64, no. 2, pp. 283–290, 2006. View at Zentralblatt MATH · View at MathSciNet
  4. A. Ishak, R. Nazar, and I. Pop, “Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder,” Applied Mathematical Modelling, vol. 32, no. 10, pp. 2059–2066, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. T. G. Fang, J. Zhang, and S. S. Yao, “Viscous flow over an unsteady shrinking sheet with mass transfer,” Chinese Physics Letters, vol. 26, no. 1, Article ID 014703, 4 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. T. G. Fang, S. S. Yao, J. Zhang, and A. Aziz, “Viscous flow over a shrinking sheet with a second order slip flow model,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1831–1842, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. M. K. A. W. Zaimi, A. Ishak, and I. Pop, “Unsteady viscous flow over a shrinking cylinder,” Journal of King Saud University—Science, vol. 25, no. 2, pp. 143–148, 2013. View at Publisher · View at Google Scholar
  8. K. Zaimi, A. Ishak, and I. Pop, “Unsteady flow due to a contracting cylinder in a nanofluid using Buongiorno's model,” International Journal of Heat and Mass Transfer, vol. 68, pp. 509–513, 2014. View at Publisher · View at Google Scholar
  9. A. Nayfeh, Problems in Perturbation, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1985. View at MathSciNet
  10. Z. H. Khan, R. Gul, and W. A. Khan, “Effect of variable thermal conductivity on heat transfer from a hollow sphere with heat generation using homotopy perturbation method,” in Proceedings of the ASME Heat Transfer Theory and Fundamental Research, vol. 1, pp. 301–309, Jacksonville, Fla, USA, August 2008. View at Scopus
  11. R. Gul, Z. H. Khan, and W. A. Khan, “Heat transfer from solids with variable thermal conductivity and uniform internal heat generation using homotopy perturbation method,” in Proceedings of the ASME Heat Transfer Theory and Fundamental Research, vol. 1, pp. 311–319, Jacksonville, Fla, USA, August 2008. View at Scopus
  12. Z. H. Khan, R. Gul, and W. A. Khan, “Application of adomian decomposition method for Sudumu transform,” NUST Journal of Engineering Sciences, vol. 12, no. 1, pp. 40–44, 2008.
  13. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. H. He, “Modified Lindstedt-Poincaré methods for some strongly non-linear oscillations. I. Expansion of a constant,” International Journal of Non-Linear Mechanics, vol. 37, no. 2, pp. 309–314, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. Belendez, C. Pascual, C. Neipp, T. Belendez, and A. Hernandez, “An equivalent linearization method for conservative nonlinear oscillations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, pp. 9–19, 2001.
  16. N. Herişanu and V. Marinca, “Optimal homotopy perturbation method for a non-conservative dynamical system of a rotating electrical machine,” Zeitschrift für Naturforschung A, vol. 67, pp. 509–516, 2012. View at Publisher · View at Google Scholar
  17. V. Marinca and N. Herişanu, “Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method,” Journal of Sound and Vibration, vol. 329, no. 9, pp. 1450–1459, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. V. Marinca, N. Herişanu, C. Bota, and B. Marinca, “An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate,” Applied Mathematics Letters, vol. 22, no. 2, pp. 245–251, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. V. Marinca and N. Herişanu, Nonlinear Dynamical Systems in Engineering—Some Approximate Approaches, Springer, Heidelberg, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. V. Marinca and N. Herişanu, “An optimal homotopy asymptotic approach applied to nonlinear MHD Jeffery-Hamel flow,” Mathematical Problems in Engineering, vol. 2011, Article ID 169056, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. V. Marinca and N. Herişanu, “Optimal homotopy asymptotic approach to nonlinear oscillators with discontinuities,” Scientific Research and Essays, vol. 8, no. 4, pp. 161–167, 2013.