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Journal of Applied Mathematics
Volume 2013, Article ID 634746, 8 pages
http://dx.doi.org/10.1155/2013/634746
Research Article

Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid

1Institute for Mathematical Research and Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
3Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Received 21 June 2013; Accepted 10 December 2013

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2013 Norihan Md. Arifin 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. Godson, B. Raja, D. M. Lal, and S. Wongwises, “Enhancement of heat transfer using nanofluids—an overview,” Renewable and Sustainable Energy Reviews, vol. 14, no. 2, pp. 629–641, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology, Wiley, Hoboken, NJ, USA, 2007.
  3. J. Buongiorno, “Convective transport in nanofluids,” Journal of Heat Transfer, vol. 128, no. 3, pp. 240–250, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. W. Daungthongsuk and S. Wongwises, “A critical review of convective heat transfer of nanofluids,” Renewable and Sustainable Energy Reviews, vol. 11, no. 5, pp. 797–817, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. V. Trisaksri and S. Wongwises, “Critical review of heat transfer characteristics of nanofluids,” Renewable and Sustainable Energy Reviews, vol. 11, no. 3, pp. 512–523, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. X.-Q. Wang and A. S. Mujumdar, “Heat transfer characteristics of nanofluids: a review,” International Journal of Thermal Sciences, vol. 46, no. 1, pp. 1–19, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. X.-Q. Wang and A. S. Mujumdar, “A review on nanofluids—part I: theoretical and numerical investigations,” Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp. 613–630, 2008. View at Google Scholar · View at Scopus
  8. S. Kakaç and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” International Journal of Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3187–3196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. N. Putra, W. Roetzel, and S. K. Das, “Natural convection of nano-fluids,” Heat and Mass Transfer, vol. 39, no. 8-9, pp. 775–784, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Wen and Y. Ding, “Formulation of nanofluids for natural convective heat transfer applications,” International Journal of Heat and Fluid Flow, vol. 26, no. 6, pp. 855–864, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. K. S. Hwang, J.-H. Lee, and S. P. Jang, “Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity,” International Journal of Heat and Mass Transfer, vol. 50, no. 19-20, pp. 4003–4010, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. X.-Q. Wang and A. S. Mujumdar, “A review on nanofluids—part II: experiments and applications,” Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp. 631–648, 2008. View at Google Scholar · View at Scopus
  13. D. M. Christopher and B. Wang, “Prandtl number effects for Marangoni convection over a flat surface,” International Journal of Thermal Sciences, vol. 40, no. 6, pp. 564–570, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. R. Tadmor, “Marangoni flow revisited,” Journal of Colloid and Interface Science, vol. 332, no. 2, pp. 451–454, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Golia and A. Viviani, “Non isobaric boundary layers related to Marangoni flows,” Meccanica, vol. 21, no. 4, pp. 200–204, 1986. View at Publisher · View at Google Scholar · View at Scopus
  16. I. Pop, A. Postelnicu, and T. Grosan, “Thermosolutal Marangoni forced convection boundary layers,” Meccanica, vol. 36, no. 5, pp. 555–571, 2001. View at Publisher · View at Google Scholar · View at Scopus
  17. A. J. Chamkha, I. Pop, and H. S. Takhar, “Marangoni mixed convection boundary layer flow,” Meccanica, vol. 41, no. 2, pp. 219–232, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. R. A. Hamid, N. M. Arifin, R. Nazar, F. M. Ali, and I. Pop, “Dual Solutions on thermosolutal Marangoni forced convection boundary layer with suction and injection,” Mathematical Problems in Engineering, vol. 2011, Article ID 875754, 19 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. N. Mat, N. M. Arifin, R. Nazar, F. Ismail, and I. Pop, “Radiation effects on Marangoni convection boundary layer over a permeable surface,” Meccanica, vol. 48, pp. 83–89, 2013. View at Publisher · View at Google Scholar
  20. R. K. Tiwari and M. K. Das, “Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids,” International Journal of Heat and Mass Transfer, vol. 50, no. 9-10, pp. 2002–2018, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. N. M. Arifin, R. Nazar, and I. Pop, “Non-Isobaric Marangoni boundary layer flow for Cu, Al2O3 and TiO2 nanoparticles in a water based fluid,” Meccanica, vol. 46, no. 4, pp. 833–843, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Remeli, N. M. Arifin, R. Nazar, F. Ismail, and I. Pop, “Marangoni-driven boundary layer flow in a nanofluid with suction and injection,” World Applied Sciences Journal, vol. 17, pp. 21–26, 2012. View at Google Scholar
  23. N. A. A. Mat, N. M. Arifin, R. Nazar, and F. Ismail, “Radiation effect on Marangoni convection boundary layer flow of a nanofluid,” Mathematical Sciences, vol. 6, article 21, 2012. View at Publisher · View at Google Scholar
  24. A. Al-Mudhaf and A. J. Chamkha, “Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects,” Heat and Mass Transfer, vol. 42, no. 2, pp. 112–121, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. E. Magyari and A. J. Chamkha, “Exact analytical results for the thermosolutal MHD Marangoni boundary layers,” International Journal of Thermal Sciences, vol. 47, no. 7, pp. 848–857, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. R. A. Hamid, N. M. Arifin, R. Nazar, and F. M. Ali, “Radiation effects on Marangoni convection over a flat surface with suction and injection,” Malaysian Journal of Mathematical Sciences, vol. 5, no. 1, pp. 13–25, 2011. View at Google Scholar · View at Scopus
  27. R. A. Hamid, W. M. K. A. W. Zaimi, N. M. Arifin, N. A. A. Bakar, and B. Bidin, “Thermal-diffusion and diffusion-thermo effects on MHD thermosolutal Marangoni convection boundary layer flow over a permeable surface,” Journal of Applied Mathematics, vol. 2012, Article ID 750939, 14 pages, 2012. View at Publisher · View at Google Scholar
  28. E. Abu-Nada, “Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step,” International Journal of Heat and Fluid Flow, vol. 29, no. 1, pp. 242–249, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” International Journal of Heat and Fluid Flow, vol. 29, no. 5, pp. 1326–1336, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. E. Abu-Nada and H. F. Oztop, “Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid,” International Journal of Heat and Fluid Flow, vol. 30, no. 4, pp. 669–678, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. M. Muthtamilselvan, P. Kandaswamy, and J. Lee, “Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1501–1510, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. N. Bachok, A. Ishak, R. Nazar, and N. Senu, “Stagnation-point flow over a permeable stretching/shrinking sheet in a copper-water nanofluid,” Boundary Value Problems, vol. 2013, article 39, 2013. View at Publisher · View at Google Scholar
  33. C. Golia and A. Viviani, “Marangoni buoyant boundary layers,” Aerotecnica Missili e Spazio, vol. 64, pp. 29–35, 1985. View at Google Scholar
  34. B. S. Dandapat, B. Santra, and H. I. Andersson, “Thermocapillarity in a liquid film on an unsteady stretching surface,” International Journal of Heat and Mass Transfer, vol. 46, no. 16, pp. 3009–3015, 2003. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1064–1068, 2009. View at Publisher · View at Google Scholar · View at Scopus