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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 485418, 15 pages
http://dx.doi.org/10.1155/2012/485418
Research Article

Mixed Convection Flow over an Unsteady Stretching Surface in a Porous Medium with Heat Source

1Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, Pakistan
2Department of Mathematics, King Abdulaziz University, Jeddah 80200, Saudi Arabia

Received 27 March 2012; Revised 22 September 2012; Accepted 26 September 2012

Academic Editor: Trung Nguyen Thoi

Copyright © 2012 Syed Muhammad Imran 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. T. Altan, S. Oh, and H. Gegel, Metal Forming Fundamentals and Applications, American Society of Metal, Metals Park, Ohio, USA, 1979.
  2. E. G. Fisher, Extrusion of Plastics, John Wiley & Sons, New York, NY, USA, 1976.
  3. B. C. Sakiadis, “Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE Journal, vol. 7, pp. 26–28, 1961. View at Publisher · View at Google Scholar
  4. L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar · View at Scopus
  5. L. E. Erickson, L. T. Fan, and V. G. Fox, “Heat and mass transfer on a moving continuous flat plate with suction or injection,” Industrial and Engineering Chemistry Fundamentals, vol. 5, no. 1, pp. 19–25, 1966. 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. View at Publisher · View at Google Scholar
  7. 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 Scopus
  8. C. K. Chen and M. I. Char, “Heat transfer of a continuous, stretching surface with suction or blowing,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 568–580, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. E. Ali, “Heat transfer characteristics of a continuous stretching surface,” Heat Mass Transfer, vol. 29, no. 4, pp. 227–234, 1994. View at Publisher · View at Google Scholar · View at Scopus
  10. 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
  11. 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
  12. A. Ishak, R. Nazar, and I. Pop, “MHD boundary-layer flow due to a moving extensible surface,” Journal of Engineering Mathematics, vol. 62, no. 1, pp. 23–33, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. C. Y. Wang, “Analysis of viscous flow due to a stretching sheet with surface slip and suction,” Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 375–380, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. T. Hayat, Z. Abbas, and T. Javed, “Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet,” Physics Letters, Section A, vol. 372, no. 5, pp. 637–647, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Hayat, M. Sajid, and I. Pop, “Three-dimensional flow over a stretching surface in a viscoelastic fluid,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1811–1822, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. Awang Kechil and I. Hashim, “Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field,” Physics Letters, Section A, vol. 372, no. 13, pp. 2258–2263, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Y. Wang, “Liquid film on an unsteady stretching surface,” Quarterly of Applied Mathematics, vol. 48, no. 4, pp. 601–610, 1990. View at Zentralblatt MATH
  18. H. I. Andersson, J. B. Aarseth, N. Braud, and B. S. Dandapat, “Flow of a power-law fluid film on an unsteady stretching surface,” Journal of Non-Newtonian Fluid Mechanics, vol. 62, no. 1, pp. 1–8, 1996. View at Publisher · View at Google Scholar · View at Scopus
  19. I. Pop and T. Y. Na, “Unsteady flow past a stretching sheet,” Mechanics Research Communications, vol. 23, no. 4, pp. 413–422, 1996. View at Publisher · View at Google Scholar · View at Scopus
  20. J. B. Aarseth and J. B. Aarseth, “Heat transfer in a liquid film on an unsteady stretching surface,” International Journal of Heat and Mass Transfer, vol. 43, no. 1, pp. 69–74, 1999. 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,” Heat and Mass Transfer, vol. 41, no. 1, pp. 1–4, 2004. 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 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 Zentralblatt MATH
  23. 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.
  24. A. Ishak, R. Nazar, and I. Pop, “Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2909–2913, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. T. Hayat, M. Qasim, and Z. Abbas, “Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2375–2387, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. T. Fang, J. Zhang, and S. Yao, “A new family of unsteady boundary layers over a stretching surface,” Applied Mathematics and Computation, vol. 217, no. 8, pp. 3747–3755, 2010. View at Publisher · View at Google Scholar
  27. S. Nadeem, A. Hussain, and M. Khan, “HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 475–481, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. D. A. Nield and A. Bejan, Convection in Porous Media, Springer, New York, NY, USA, 3rd edition, 2006.
  29. I. Pop and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford, UK, 2001.
  30. D. B. Ingham and I. Pop, Eds., Transport Phenomena in Porous Media, vol. 2, Elsevier Science, 2002.
  31. A. Bejan, I. Dincer, S. Lorente, A. F. Miguel, and A. H. Reis, Porous and Complex Flow Structures in Modern Technologies, Springer, New York, NY, USA, 2004.
  32. D. B. Ingham and I. Pop, Eds., Transport Phenomena in Porous Media, vol. 3, Elsevier, Oxford, UK, 2005.
  33. D. B. Ingham, A. Bejan, E. Mamut, and I. Pop, Eds., Emerging Technologies and Techniques in Porous Media, Kluwer, Dordrecht, The Netherlands, 2004.
  34. K. Vafai, Ed., Handbook of Porous Media, Marcel Dekker, New York, NY, USA, 2000.
  35. K. Vafai, Handbook of Porous Media, Taylor and Francis, New York, NY, USA, 2nd edition, 2005.
  36. T. S. Chen and F. A. Strobel, “Buoyancy effects on heat and mass transfer in boundary layer on a continuous moving horizontal plate,” Numerical Heat Transfer, vol. 3, no. 1, pp. 115–130, 1980. View at Scopus
  37. F. A. Strobel and T. S. Chen, “Buoyancy effects on heat and mass transfer in boundary layers adjacent to inclined continuous moving sheets,” Numerical Heat Transfer, vol. 3, no. 4, pp. 461–481, 1980. View at Scopus
  38. A. Moutsoglou and T. S. Chen, “Buoyancy effects in boundary layers on inclined, continuous, moving sheets,” Journal of Heat Transfer, vol. 102, no. 2, pp. 371–373, 1980. View at Scopus
  39. J. R. Fan, J. M. Shi, and X. Z. Xu, “Similarity solution of mixed convection over a horizontal moving plate,” Heat and Mass Transfer, vol. 32, no. 3, pp. 199–206, 1997. View at Scopus
  40. 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
  41. 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
  42. C. H. Chen, “Mixed convection cooling of a heated, continuously stretching surface,” Heat Mass Transfer, vol. 36, no. 1, pp. 79–86, 2000. View at Scopus
  43. 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
  44. K. Vajravelu and A. Hadjinicolaou, “Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation,” International Communications in Heat and Mass Transfer, vol. 20, no. 3, pp. 417–430, 1993. View at Scopus