Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 195360, 10 pages
http://dx.doi.org/10.1155/2013/195360
Research Article

Mixed Convection Boundary Layers with Prescribed Temperature in the Unsteady Stagnation Point Flow toward a Stretching Vertical Sheet

1Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Basic Science and Engineering, Faculty of Agriculture and Food Sciences, Universiti Putra Malaysia, Sarawak Campus, 97008 Bintulu, Sarawak, Malaysia

Received 26 February 2013; Accepted 26 April 2013

Academic Editor: Mohamed Abd El Aziz

Copyright © 2013 Nik Mohd Asri Nik Long 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. M. A. Elbashbeshy, “Heat transfer over a stretching surface with variable surface heat flux,” Journal of Physics D, vol. 31, no. 16, pp. 1951–1954, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. T. Fang, C. F. F. Lee, and J. Zhang, “The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer,” International Journal of Non-Linear Mechanics, vol. 46, no. 7, pp. 942–948, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. 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
  4. A. Ishak, R. Nazar, and I. Pop, “Steady and unsteady boundary layers due to a stretching vertical sheet in a porous medium using darcy-brinkman equation model,” International Journal of Applied Mechanics and Engineering, vol. 11, no. 3, pp. 623–637, 2006. View at Google Scholar
  5. A. Ishak, R. Nazar, and L. Pop, “Heat transfer over an unsteady stretching surface with prescribed heat flux,” Canadian Journal of Physics, vol. 86, no. 6, pp. 853–855, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Y. Lok, A. Ishak, and I. Pop, “MHD stagnation-point flow towards a shrinking sheet,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 21, no. 1, pp. 61–72, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. B. C. Sakiadis, “Boundary layer behavior on continuous solid surfaces,” The American Institute of Chemical Engineers Jounal, vol. 7, pp. 221–225, 1961. View at Google Scholar
  8. 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
  9. L. J. Grubka and K. M. Bobba, “Heat transfer characteristics of a continuous, stretching surface with variable temperature,” Journal of Heat Transfer, vol. 107, no. 1, pp. 248–250, 1985. View at Google Scholar · View at Scopus
  10. M. E. Ali, “Heat transfer characteristics of a continuous stretching surface,” Warme-Und Stoffubertragung, vol. 29, no. 4, pp. 227–234, 1994. View at Publisher · View at Google Scholar · View at Scopus
  11. M. E. Ali, “On thermal boundary layer on a power-law stretched surface with suction or injection,” International Journal of Heat and Fluid Flow, vol. 16, no. 4, pp. 280–290, 1995. View at Google Scholar · View at Scopus
  12. D. B. Ingham, “Singular and non-unique solutions of the boundary-layer equations for the flow due to free convection near a continuously moving vertical plate,” ZAMP Zeitschrift für Angewandte Mathematik und Physik ZAMP, vol. 37, no. 4, pp. 559–572, 1986. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Wang, “Liquid film on an unsteady stretching sheet,” Quarterly of Applied Mathematics, vol. 48, pp. 601–610, 1990. View at Google Scholar
  14. C. Wang, “Analytic solutions for a liquid film on an unsteady stretching surface,” Heat and Mass Transfer, vol. 42, no. 8, pp. 759–766, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. J. E. Daskalakis, “Free convection effects in the boundary layer along a vertically stretching at surface,” Canadian Journal of Physics, vol. 70, no. 12, pp. 1587–1597, 1993. View at Google Scholar
  16. 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 Google Scholar · View at Scopus
  17. 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 Google Scholar · View at Scopus
  18. A. J. Chamkha, “Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption,” International Journal of Heat and Fluid Flow, vol. 20, no. 1, pp. 84–92, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Ishak, R. Nazar, and I. Pop, “Mixed convection on the stagnation point flow toward a vertical, continously stretching sheet,” Journal of Heat Transfer, vol. 129, no. 8, pp. 1087–1090, 2007. View at Publisher · View at Google Scholar
  20. K. Vajravelu, “Viscous flow over a nonlinearly stretching sheet,” Applied Mathematics and Computation, vol. 124, no. 3, pp. 281–288, 2001. View at Publisher · View at Google Scholar · View at Scopus
  21. E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat transfer over an unsteady stretching surface with internal heat generation,” Applied Mathematics and Computation, vol. 138, no. 2-3, pp. 239–245, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat transfer over an unsteady stretching surface,” Heat and Mass Transfer, vol. 41, no. 1, pp. 1–4, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. R. Tsai, K. H. Huang, and J. S. Huang, “Flow and heat transfer over an unsteady stretching surface with non-uniform heat source,” International Communications in Heat and Mass Transfer, vol. 35, no. 10, pp. 1340–1343, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. A. Ishak and R. Nazar, “Laminar boundary layer flow along a stretching cylinder,” European Journal of Scientific Research, vol. 36, no. 1, pp. 22–29, 2009. View at Google Scholar · View at Scopus
  25. P. M. Patil, S. Roy, and A. J. Chamkha, “Mixed convection flow over a vertical power-law stretching sheet,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 20, no. 4, pp. 445–458, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. N. Bachok, A. Ishak, R. Nazar, and I. Pop, “Ingham problem for free convection near a continuously moving vertical permeable plate,” IMA Journal of Applied Mathematics, vol. 77, no. 4, pp. 578–589, 2011. View at Google Scholar
  27. N. Bachok and A. Ishak, “Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking sheet,” Sains Malaysiana, vol. 40, no. 11, pp. 1297–1300, 2011. View at Google Scholar · View at Scopus
  28. R. C. Aziz and I. Hashim, “Liquid film on unsteady stretching sheet with general surface temperature and viscous dissipation,” Chinese Physics Letters, vol. 27, no. 11, Article ID 110202, 4 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. A. J. Chamkha and S. E. Ahmed, “Similarity solution for unsteady MHD flow near a stagnation point of a three-dimensional porous body with heat and mass transfer, heat generation/absorption and chemical reaction,” Journal of Applied Fluid Mechanics, vol. 4, no. 2, pp. 87–94, 2011. View at Google Scholar · View at Scopus
  30. M. Suali, N. M. A. Nik Long, and N. M. Ariffin, “Unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction or injection,” Journal of Applied Mathematics, vol. 2012, Article ID 781845, 12 pages, 2012. View at Publisher · View at Google Scholar
  31. I. C. Liu and A. M. Megahed, “Homotopy perturbation method for thin film flow and heat transfer over an unsteady stretching sheet with internal heating and variable heat flux,” Journal of Applied Mathematics, vol. 2012, Article ID 418527, 12 pages, 2012. View at Publisher · View at Google Scholar
  32. N. M. A. Nik Long, M. Suali, A. Ishak, N. Bachok, and N. M. Arifin, “Unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet,” Journal of Applied Sciences, vol. 11, no. 20, pp. 3520–3524, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. A. Ishak, R. Nazar, and I. Pop, “Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet,” Mechanica, vol. 41, no. 5, pp. 509–518, 2006. View at Publisher · View at Google Scholar