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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 269420, 11 pages
http://dx.doi.org/10.1155/2013/269420
Research Article

Lie Group Analysis and Similarity Solutions for Mixed Convection Boundary Layers in the Stagnation-Point Flow toward a Stretching Vertical Sheet

Sarkhosh Seddighi Chaharborj,1,2,3,4 Fudziah Ismail,1 Yousof Gheisari,4 Reza Seddighi Chaharborj,5 Mohd Rizam Abu Bakar,1 and Zanariah Abdul Majid3

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia
2Nuclear Science Research School, Nuclear Science and Technology Research Institute (NSTRI), P.O. Box 14395-836, Tehran, Iran
3Institute of Mathematical Research, Universiti Putra Malaysia, 43400 Serdang Selangor, Darul Ehsan, Malaysia
4Department of Mathematics, Islamic Azad University, Bushehr Branch, 7514763448 Bushehr, Iran
5Department of Applied Mathematics and Computer Science, Eastern Mediterranean University, Famagusta, Northern Cyprus via Mersin 10, Turkey

Received 16 December 2012; Revised 18 January 2013; Accepted 18 January 2013

Academic Editor: Nail Migranov

Copyright © 2013 Sarkhosh Seddighi Chaharborj 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. M. V. Karwe and Y. Jaluria, “Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing,” Journal of Heat Transfer, vol. 113, no. 3, pp. 612–619, 1991. View at Scopus
  2. B. C. Sakiadis, “Boundary layer behaviour on continuous solid surfaces—ii. the boundary layer on a continuous flat surface,” AIChE Journal, vol. 7, pp. 221–225, 1961.
  3. L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar · View at Scopus
  4. P. Carragher and L. J. Crane, “Heat transfer on a continuous stretching sheet,” Journal of Applied Mathematics and Mechanics, vol. 62, pp. 564–565, 1982.
  5. E. M. A. Elbashbeshy and M. A. A. Bazid, “Effect of temperature-dependent viscosity on heat transfer over a continuous moving surface,” Journal of Physics D, vol. 33, no. 21, pp. 2716–2721, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. P. S. Gupta and A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing,” The Canadian Journal of Chemical Engineering, vol. 55, pp. 744–746, 1977.
  7. E. Magyari and B. Keller, “Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” Journal of Physics D, vol. 32, no. 5, pp. 577–585, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. E. Magyari and B. Keller, “Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls,” European Journal of Mechanics B, vol. 19, no. 1, pp. 109–122, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. E. Magyari, M. E. Ali, and B. Keller, “Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities,” Heat and Mass Transfer, vol. 38, no. 1, pp. 65–74, 2002. View at Scopus
  10. S. J. Liao and I. Pop, “On explicit analytic solutions of boundary-layer equations about flows in a porous medium or for a stretching wall,” International Journal of Heat and Mass Transfer, vol. 47, pp. 75–85, 2004.
  11. R. Nazar, N. Amin, D. Filip, and I. Pop, “Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet,” International Journal of Engineering Science, vol. 42, no. 11-12, pp. 1241–1253, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. I. Pop, “Mhd flow over asymmetric plane stagnation point,” Journal of Applied Mathematics and Mechanics, vol. 63, pp. 580–581, 1983.
  13. H. I. Andersson, “MHD flow of a viscoelastic fluid past a stretching surface,” Acta Mechanica, vol. 95, no. 1–4, pp. 227–230, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. S. Takhar and G. Nath, “Similarity solution of unsteady boundary layer equations with a magnetic fiield,” Meccanica, vol. 32, no. 2, pp. 157–163, 1997. View at MathSciNet · View at Scopus
  15. R. Nazar, N. Amin, and I. Pop, “Unsteady boundary layer flow due to a stretching surface in a rotating fluid,” Mechanics Research Communications, vol. 31, no. 1, pp. 121–128, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. C. H. Chen, “Laminar mixed convection adjacent to vertical, continuously stretching sheets,” Heat and Mass Transfer, vol. 33, no. 5-6, pp. 471–476, 1998. View at Scopus
  17. C. H. Chen, “Mixed convection cooling of a heated, continuously stretching surface,” Warme- und Stoffubertragung Zeitschrift, vol. 36, no. 1, pp. 79–86, 2000. View at Scopus
  18. C. R. Lin and C. K. Chen, “Exact solution of heat transfer from a stretching surface with variable heat flux,” Heat and Mass Transfer, vol. 33, no. 5-6, pp. 477–480, 1998. View at Scopus
  19. M. Ali and F. Al-Yousef, “Laminar mixed convection from a continuously moving vertical surface with suction or injection,” Heat and Mass Transfer, vol. 33, no. 4, pp. 301–306, 1998. View at Scopus
  20. M. Ali and F. Al-Yousef, “Laminar mixed convection boundary layers induced by a linearly stretching permeable surface,” International Journal of Heat and Mass Transfer, vol. 45, no. 21, pp. 4241–4250, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. M. E. Ali, “The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities,” Heat and Mass Transfer, vol. 40, no. 3-4, pp. 285–291, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. M. E. Ali, “The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface,” International Journal of Thermal Sciences, vol. 45, no. 1, pp. 60–69, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. E. M. Abo-Eldahab, “The effects of temperature-dependent fluid properties on free convective flow along a semi-infinite vertical plate by the presence of radiation,” Heat and Mass Transfer, vol. 41, no. 2, pp. 163–169, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Ishak, R. Nazar, and I. Pop, “Unsteady mixed convection boundary layer flow due to a stretching vertical surface,” Arabian Journal for Science and Engineering, vol. 31, no. 2 B, pp. 165–182, 2006. View at MathSciNet · View at Scopus
  25. T. R. Mahapatra and A. S. Gupta, “Unsteady mixed convection boundary layer flow due to a stretching vertical surface,” Arabian Journal for Science and Engineering, vol. 38, pp. 517–521, 2002.
  26. T. R. Mahapatra and A. S. Gupta, “Stagnation-point flow of a viscoelastic fluid towards a stretching surface,” International Journal of Non-Linear Mechanics, vol. 39, no. 5, pp. 811–820, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. F. Rabiei and F. Ismail, “Fifth-order improved runge-kutta method for solving ordinary differential equations,” Australian Journal of Basic and Applied Sciences, vol. 6, pp. 97–105, 2012.
  28. A. Ishak, R. Nazar, and I. Pop, “Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet,” Meccanica, vol. 41, no. 5, pp. 509–518, 2006. View at Publisher · View at Google Scholar · View at Scopus