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Mathematical Problems in Engineering
Volume 2010, Article ID 579162, 20 pages
http://dx.doi.org/10.1155/2010/579162
Research Article

Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

Department of Mathematics, Faculty of Science, Benha University, Qalyubia 13518, Egypt

Received 27 April 2010; Revised 20 June 2010; Accepted 21 July 2010

Academic Editor: Cristian Toma

Copyright © 2010 Mostafa Mahmoud and Shimaa Waheed. 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. A. C. Eringen, “Theory of micropolar fluids,” Journal of Mathematics and Mechanics, vol. 16, pp. 1–18, 1966. View at Google Scholar
  2. A. C. Eringen, “Theory of thermo micropolar fluids,” Journal of Applied Mathematics, vol. 38, pp. 480–495, 1972. View at Google Scholar · View at Scopus
  3. J. D. Lee and A. C. Eringen, “Wave propagation in nematic liquid crystals,” The Journal of Chemical Physics, vol. 54, no. 12, pp. 5027–5034, 1971. View at Google Scholar · View at Scopus
  4. J. D. Lee and A. C. Eringen, “Boundary effects of orientation of nematic liquid crystals,” The Journal of Chemical Physics, vol. 55, no. 9, pp. 4509–4512, 1971. View at Google Scholar · View at Scopus
  5. T. Ariman, M. A. Turk, and N. D. Sylvester, “Applications of microcontinuum fluid mechanics,” International Journal of Engineering Science, vol. 12, no. 4, pp. 273–293, 1974. View at Google Scholar · View at Scopus
  6. T. Ariman, M. A. Turk, and N. D. Sylvester, “Microcontinuum fluid mechanics-a review,” International Journal of Engineering Science, vol. 11, no. 8, pp. 905–915, 1973. View at Google Scholar · View at Scopus
  7. K. A. Kline and S. J. Allen, “Pulsatile blood flow investigation of particle concentration effects,” Biorheology, vol. 6, pp. 99–110, 1969. View at Google Scholar
  8. T. Ariman, “On the analysis of blood flow,” Journal of Biomechanics, vol. 4, no. 3, pp. 185–192, 1971. View at Google Scholar · View at Scopus
  9. T. Ariman, “Heat conduction in blood,” in Proceedings of the ASCE Engineering Mechanics Division Specialty Conference, January 1971.
  10. J. C. Misra and K. Roychoudhury, “Non linear stress field in blood vessels under the actionof connective tissues,” Blood Vessels, vol. 19, pp. 19–29, 1982. View at Google Scholar
  11. Y. Y. Lok, N. Amin, and I. Pop, “Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface,” International Journal of Thermal Sciences, vol. 45, no. 12, pp. 1149–1157, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Chandra, “Instability of fluids heated from below,” Proceedings of the Royal Society A, vol. 164, pp. 231–224, 1938. View at Google Scholar · View at Scopus
  13. S. Allen and K. Kline, “Lubrication theory for micropolar fluids,” Journal of Applied Mechanics, vol. 38, pp. 646–656, 1971. View at Google Scholar · View at Scopus
  14. M. M. Khonsari, “On the self-excited whirl orbits of a journal in a sleeve bearing lubricated with micropolar fluids,” Acta Mechanica, vol. 81, no. 3-4, pp. 235–244, 1990. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Prakash and P. Sinha, “Lubrication theory for micropolar fluids and its application to a journal bearing,” International Journal of Engineering Science, vol. 13, no. 3, pp. 217–232, 1975. View at Google Scholar · View at Scopus
  16. N. Tipei, “Lubrication with micropolar liquids and its application to short bearings,” Journal of Lubrication Technology, vol. 101, no. 3, pp. 356–363, 1979. View at Google Scholar · View at Scopus
  17. Y. J. Kim and A. G. Fedorov, “Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate,” International Journal of Heat and Mass Transfer, vol. 46, no. 10, pp. 1751–1758, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Bhargava, L. Kumar, and H. S. Takhar, “Mixed convection from a continuous surface in a parallel moving stream of a micropolar fluid,” Heat and Mass Transfer, vol. 39, no. 5-6, pp. 407–413, 2003. View at Google Scholar · View at Scopus
  19. M. M. Rahman and M. A. Sattar, “Transient convective flow of micropolar fluid past a continuouslymoving vertical porous plate in the presence of radiation,” International Journal of Applied Mechanics and Engineering, vol. 12, pp. 497–513, 2007. View at Google Scholar
  20. M. M. Rahman and M. A. Sattar, “Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption,” Journal of Heat Transfer, vol. 128, no. 2, pp. 142–152, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Ishak, R. Nazar, and I. Pop, “Heat transfer over a stretching surface with variable heat flux in micropolar fluids,” Physics Letters A, vol. 372, no. 5, pp. 559–561, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Ishak, R. Nazar, and I. Pop, “Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet,” Meccanica, vol. 43, no. 4, pp. 411–418, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Ishak, R. Nazar, and I. Pop, “Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface,” Computers and Mathematics with Applications, vol. 56, no. 12, pp. 3188–3194, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. A. Ishak, Y. Y. Lok, and I. Pop, “Stagnation-point flow over a shrinking sheet in a micropolarfluid,” Chemical Engineering Communications, vol. 197, pp. 1417–1427, 2010. View at Google Scholar
  25. T. Hayat, Z. Abbas, and T. Javed, “Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet,” Physics Letters A, vol. 372, no. 5, pp. 637–647, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. C. L. M. Navier, “Sur les lois du mouvement des fluides,” Memoires de l'Academie Royale des Sciences, vol. 6, pp. 389–440, 1827. View at Google Scholar · View at Scopus
  27. P. D. Ariel, T. Hayat, and S. Asghar, “The flow of an elastico-viscous fluid past a stretching sheet with partial slip,” Acta Mechanica, vol. 187, no. 1–4, pp. 29–35, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. T. Hayat, T. Javed, and Z. Abbas, “Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space,” International Journal of Heat and Mass Transfer, vol. 51, no. 17-18, pp. 4528–4534, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. T. Hayat, M. Khan, and M. Ayub, “The effect of the slip condition on flows of an Oldroyd 6-constant fluid,” Journal of Computational and Applied Mathematics, vol. 202, no. 2, pp. 402–413, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. R. I. Tanner, “Partial wall slip in polymer flow,” Industrial and Engineering Chemistry Research, vol. 33, no. 10, pp. 2434–2436, 1994. View at Google Scholar · View at Scopus
  31. C. Le Roux, “Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions,” Archive for Rational Mechanics and Analysis, vol. 148, no. 4, pp. 309–356, 1999. View at Google Scholar · View at MathSciNet · View at Scopus
  32. K. Vajravelu and A. Hadjinicolaou, “Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream,” International Journal of Engineering Science, vol. 35, no. 12-13, pp. 1237–1244, 1997. View at Google Scholar · View at Scopus
  33. M. A. Delichatsios, “Air entrainment into buoyant jet flames and pool fires,” Combustion and Flame, vol. 70, no. 1, pp. 33–46, 1987. View at Google Scholar · View at Scopus
  34. J. C. Crepeau and R. Clarksean, “Similarity solutions of natural convection with internal heat generation,” Journal of Heat Transfer, vol. 119, no. 1, pp. 183–185, 1997. View at Google Scholar · View at Scopus
  35. R. C. Bataller, “Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet,” Computers and Mathematics with Applications, vol. 53, no. 2, pp. 305–316, 2007. View at Publisher · View at Google Scholar · View at Scopus
  36. G. Ahmadi, “Self-similar solution of incompressible micropolar boundary layer flow over asemi-infinite plate,” International Journal of Engineering Science, vol. 14, pp. 639–646, 1976. View at Google Scholar
  37. K. A. Kline, “A spin-vorticity relation for unidirectional plane flows of micropolar fluids,” International Journal of Engineering Science, vol. 15, no. 2, pp. 131–134, 1977. View at Google Scholar · View at Scopus
  38. S. K. Jena and M. N. Mathur, “Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate,” International Journal of Engineering Science, vol. 19, no. 11, pp. 1431–1439, 1981. View at Google Scholar · View at Scopus
  39. J. Peddieson and R. P. Mcnitt, “Boundary layer theory for a micropolar fluid,” Recent Advances in Engineering Science, vol. 5, pp. 405–426, 1970. View at Google Scholar
  40. S. E. El-Gendi, “Chebyshev solution of differential, integral and integro-differential equations,” Computer Journal, vol. 12, pp. 282–287, 1969. View at Google Scholar
  41. Y. Morchoisn, “Pseudo-spectral space-time calculations of incompressible viscous flows,” AIAA Journal, vol. 19, pp. 81–82, 1981. View at Google Scholar · View at Scopus
  42. R. Nazar, A. Ishak, and I. Pop, “Unsteady boundary layer flow over a stretching sheet in a micropolar fluid,” International Journal of Mathematical, Physical and Engineering Sciences, vol. 2, pp. 161–168, 2008. View at Google Scholar
  43. A. Ishak, “Thermal boundary layer flow over a stretching sheet inamicropolar fluid with radiation effect,” Meccanica, vol. 45, pp. 367–373, 2010. View at Publisher · View at Google Scholar · View at Scopus
  44. 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
  45. 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
  46. 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 Google Scholar · View at Scopus