Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 257161, 5 pages
http://dx.doi.org/10.1155/2013/257161
Research Article

Micropolar Fluid Flow and Heat Transfer over a Nonlinearly Stretching Plate with Viscous Dissipation

1Department of Science in Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, Gombak, 50728 Kuala Lumpur, Malaysia
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 1 March 2013; Accepted 12 June 2013

Academic Editor: Xing-Gang Yan

Copyright © 2013 Kartini Ahmad 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. 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
  2. R. A. Van Gorder, K. Vajravelu, and F. T. Akyildiz, “Existence and uniqueness results for a nonlinear differential equation arising in viscous flow over a nonlinearly stretching sheet,” Applied Mathematics Letters, vol. 24, no. 2, pp. 238–242, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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 Zentralblatt MATH · View at MathSciNet
  4. R. Cortell, “Viscous flow and heat transfer over a nonlinearly stretching sheet,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 864–873, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Cortell, “Heat and fluid flow due to non-linearly stretching surfaces,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7564–7572, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. D. Ganji, H. Bararnia, S. Soleimani, and E. Ghasemi, “A nalytical solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet,” Modern Physics Letters B, vol. 23, no. 20-21, pp. 2541–2556, 2009. View at Google Scholar · View at Scopus
  7. A. Ishak, R. Nazar, and I. Pop, “Unsteady mixed convection boundary layer flow due to a stretching vertical surface,” The Arabian Journal for Science and Engineering B, vol. 31, no. 2, pp. 165–182, 2006. View at Google Scholar · View at MathSciNet
  8. K. V. Prasad, K. Vajravelu, and P. S. Datti, “Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties,” International Journal of Non-Linear Mechanics, vol. 45, no. 3, pp. 320–330, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Raftari, S. T. Mohyud-Din, and A. Yildirim, “Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method,” Science China, vol. 54, no. 2, pp. 342–345, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Abbas and T. Hayat, “Stagnation slip flow and heat transfer over a nonlinear stretching sheet,” Numerical Methods for Partial Differential Equations, vol. 27, no. 2, pp. 302–314, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. S. Abel, K. A. Kumar, and R. Ravikumar, “MHD flow and heat transfer with effects of buoyancy, viscous and Joules dissipation over a nonlinear vertical stretching porous sheet with partial slip,” Engineering, vol. 3, pp. 285–291, 2011. View at Google Scholar
  12. A. C. Eringen, “Theory of micropolar fluids,” vol. 16, pp. 1–18, 1966. View at Google Scholar · View at MathSciNet
  13. A. C. Eringen, “Theory of thermomicrofluids,” Journal of Mathematical Analysis and Applications, vol. 38, no. 2, pp. 480–496, 1972. View at Google Scholar · View at Scopus
  14. 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
  15. T. Hayat, T. Javed, and Z. Abbas, “MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface,” Nonlinear Analysis. Real World Applications, vol. 10, no. 3, pp. 1514–1526, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  16. M. M. Rahman, M. A. Rahman, M. A. Samad, and M. S. Alam, “Heat transfer in a micropolar fluid along a non-linear stretching sheet with a temperature-dependent viscosity and variable surface temperature,” International Journal of Thermophysics, vol. 30, no. 5, pp. 1649–1670, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. M. A. El-Aziz, “Viscous dissipation effect on mixed convection flow of a micropolar fluid over an exponentially stretching sheet,” Canadian Journal of Physics, vol. 87, no. 4, pp. 359–368, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. K. L. Hsiao, “Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet,” Heat and Mass Transfer, vol. 46, no. 4, pp. 413–419, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Iahak, R. Nazar, and I. Pop, “Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface,” Canadian Journal of Physics, vol. 84, no. 5, pp. 399–410, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Ishak, Y. Y. Lok, and I. Pop, “Stagnation-point flow over a shrinking sheet in a micropolar fluid,” Chemical Engineering Communications, vol. 197, no. 11, pp. 1417–1427, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. N. A. Yacob and A. Ishak, “Micropolar fluid flow over a shrinking sheet,” Meccanica, vol. 47, no. 2, pp. 293–299, 2012. View at Publisher · View at Google Scholar · View at Scopus
  22. N. A. Yacob and A. Ishak, “Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition,” Canadian Journal of Chemical Engineering, vol. 90, no. 3, pp. 621–626, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Rosali, A. Ishak, and I. Pop, “Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction,” International Communications in Heat and Mass Transfer, vol. 39, pp. 826–829, 2012. View at Google Scholar
  24. H. Hassan, N. Regnier, C. Pujos, and G. Defaye, “The effect of viscous dissipation on the polymer temperature during injection molding,” in Proceedings of the 5th European Thermal-Sciences Conference, Eindhoven, The Netherlands, 2008.
  25. A. Ishak, R. Nazar, and I. Pop, “Post-stagnation-point boundary layer flow and mixed convection heat transfer over a vertical, linearly stretching sheet,” Archives of Mechanics, vol. 60, no. 4, pp. 303–322, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Z. Ziabakhsh, G. Domairry, and H. Bararnia, “Analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation,” Journal of the Taiwan Institute of Chemical Engineers, vol. 40, no. 4, pp. 443–451, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. G. Ahmadi, “Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate,” International Journal of Engineering Science, vol. 14, no. 7, pp. 639–646, 1976. View at Google Scholar · View at Scopus
  28. A. Yücel, “Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer,” International Journal of Engineering Science, vol. 27, no. 12, pp. 1593–1602, 1989. View at Google Scholar · View at Scopus
  29. 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
  30. T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer Study Editions, Springer, New York, NY, USA, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  31. 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
  32. M. S. Alam, M. A. Sattar, M. M. Rahman, and A. Postelnicu, “Local similarity solution of unsteady hydromagnetic convection flow of a micropolar fluid along a continuously moving permeable plate,” International Journal of Heat and Technology, vol. 28, no. 2, pp. 95–105, 2010. View at Google Scholar · View at Scopus