Table of Contents
Journal of Thermodynamics
Volume 2013, Article ID 764827, 12 pages
http://dx.doi.org/10.1155/2013/764827
Research Article

Stagnation Point Flow of a Nanofluid toward an Exponentially Stretching Sheet with Nonuniform Heat Generation/Absorption

1Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, P.O. Box 15875-4413, Tehran, Iran
2Department of Mechanical Engineering, Islamic Azad University, Sari Branch, Sari, Iran
3Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol 47148-71167, Iran

Received 1 May 2013; Accepted 8 July 2013

Academic Editor: Mohammad Al-Nimr

Copyright © 2013 A. Malvandi 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. K. Hiemenz, “Die Grenzschicht an einem in den gleichformingen Flussigkeitsstrom eingetauchten graden Kreiszylinder,” Dingler's Polytechnic Journal, vol. 326, pp. 321–324, 1911. View at Google Scholar
  2. F. Homann, “Der Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die Kugel,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 16, no. 3, pp. 153–164, 1936. View at Publisher · View at Google Scholar
  3. H. A. Attia, “Homann magnetic flow and heat transfer with uniform suction or injection,” Canadian Journal of Physics, vol. 81, no. 10, pp. 1223–1230, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Bhattacharyya and K. Vajravelu, “Stagnation-point flow and heat transfer over an exponentially shrinking sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 7, pp. 2728–2734, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Malvandi, “The unsteady flow of a nanofluid in the stagnation point region of a time-dependent rotating sphere,” THERMAL SCIENCE, 2013. View at Publisher · View at Google Scholar
  6. V. Kumaran, R. Tamizharasi, and K. Vajravelu, “Approximate analytic solutions of stagnation point flow in a porous medium,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 6, pp. 2677–2688, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. M. A. A. Hamad and M. Ferdows, “Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: a Lie group analysis,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 132–140, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. 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
  9. Z. Ziabakhsh, G. Domairry, and H. R. Ghazizadeh, “Analytical solution of the stagnation-point flow in a porous medium by using the homotopy analysis method,” Journal of the Taiwan Institute of Chemical Engineers, vol. 40, no. 1, pp. 91–97, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. 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
  11. S. Yao, T. Fang, and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 752–760, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. K. R. Rajagopal, T. Y. Na, and A. S. Gupta, “Flow of a viscoelastic fluid over a stretching sheet,” Rheologica Acta, vol. 23, no. 2, pp. 213–215, 1984. View at Publisher · View at Google Scholar · View at Scopus
  13. R. Nazar, N. Amin, D. Filip, and I. Pop, “Stagnation point flow of a micropolar fluid towards a stretching sheet,” International Journal of Non-Linear Mechanics, vol. 39, no. 7, pp. 1227–1235, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. M. A. A. Hamad, “Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field,” International Communications in Heat and Mass Transfer, vol. 38, no. 4, pp. 487–492, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Ziabakhsh, G. Domairry, M. Mozaffari, and M. Mahbobifar, “Analytical solution of heat transfer over an unsteady stretching permeable surface with prescribed wall temperature,” Journal of the Taiwan Institute of Chemical Engineers, vol. 41, no. 2, pp. 169–177, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. 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 Scopus
  17. M. M. Nandeppanavar, K. Vajravelu, M. Subhas Abel, S. Ravi, and H. Jyoti, “Heat transfer in a liquid film over an unsteady stretching sheet,” International Journal of Heat and Mass Transfer, vol. 55, no. 4, pp. 1316–1324, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Malvandi, F. Hedayati, and D. D. Ganji, “Thermodynamic optimization of fluid flow over an isothermal moving plate,” Alexandria Engineering Journal, 2013. View at Publisher · View at Google Scholar
  19. A. K. Singh, “Heat source and radiation effects on magneto-convection flow of a viscoelastic fluid past a stretching sheet: analysis with Kummer's functions,” International Communications in Heat and Mass Transfer, vol. 35, no. 5, pp. 637–642, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Nadeem and C. Lee, “Boundary layer flow of nanofluid over an exponentially stretching surface,” Nanoscale Research Letters, vol. 7, article 94, pp. 1–15, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. M. R. H. Nobari and A. Malvandi, “Torsion and curvature effects on fluid flow in a helical annulus,” International Journal of Non-Linear Mechanics, vol. 57, pp. 90–101, 2013. View at Publisher · View at Google Scholar
  22. S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in Developments and Applications of Non-Newtonian Flows, D. A. Siginer and H. P. Wang, Eds., pp. 99–105, ASME, 1995. View at Google Scholar
  23. H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of thermalconductivity and viscosity of liquid by dispersing ultra-fine particles. Dispersion of Al2O3, SiO2 and TiO2 ultra-fine particles,” Netsu Bussei, vol. 7, no. 4, pp. 227–233, 1993. View at Google Scholar
  24. 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
  25. A. V. Kuznetsov and D. A. Nield, “Natural convective boundary-layer flow of a nanofluid past a vertical plate,” International Journal of Thermal Sciences, vol. 49, no. 2, pp. 243–247, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 53, no. 11-12, pp. 2477–2483, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. N. Bachok, A. Ishak, and I. Pop, “Boundary-layer flow of nanofluids over a moving surface in a flowing fluid,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1663–1668, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. A. Alsaedi, M. Awais, and T. Hayat, “Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4210–4223, 2012. View at Publisher · View at Google Scholar · View at Scopus
  29. P. Rana and R. Bhargava, “Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 212–226, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. 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
  31. 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
  32. 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
  33. S. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Scopus
  34. B. Wu and H. Zhong, “Summation of perturbation solutions to nonlinear oscillations,” Acta Mechanica, vol. 154, no. 1–4, pp. 121–127, 2002. View at Publisher · View at Google Scholar · View at Scopus
  35. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Google Scholar · View at Scopus
  36. J.-H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Google Scholar · View at Scopus
  37. F. Hedayati, D. Ganji, S. Hamidi, and A. Malvandi, “An analytical study on a model describing heat conduction in rectangular radial fin with temperature-dependent thermal conductivity,” International Journal of Thermophysics, vol. 33, no. 6, pp. 1042–1054, 2012. View at Google Scholar
  38. A. Malvandi, D. D. Ganji, F. Hedayati, M. H. Kaffash, and M. Jamshidi, “Series solution of entropy generation toward an isothermal flat plate,” Thermal Science, vol. 16, no. 5, pp. 1289–1295, 2012. View at Google Scholar
  39. S. Liao, “On the relationship between the homotopy analysis method and Euler transform,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1421–1431, 2010. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Liao, “Homotopy analysis method: a new analytical technique for nonlinear problems,” Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 2, pp. 95–100, 1997. View at Publisher · View at Google Scholar · View at Scopus
  41. S.-I. Liao, “A short review on the homotopy analysis method in fluid mechanics,” Journal of Hydrodynamics, vol. 22, no. 5, pp. 839–841, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. D. G. Domairry, A. Mohsenzadeh, and M. Famouri, “The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 1, pp. 85–95, 2009. View at Publisher · View at Google Scholar · View at Scopus
  43. G. Domairry and M. Fazeli, “Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 489–499, 2009. View at Publisher · View at Google Scholar · View at Scopus
  44. G. Domairry and N. Nadim, “Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation,” International Communications in Heat and Mass Transfer, vol. 35, no. 1, pp. 93–102, 2008. View at Publisher · View at Google Scholar · View at Scopus
  45. S.-J. Liao, “An explicit, totally analytic approximate solution for Blasius' viscous flow problems,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 759–778, 1999. View at Google Scholar · View at Scopus
  46. S. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2003–2016, 2010. View at Publisher · View at Google Scholar · View at Scopus
  47. M. Hassani, M. Mohammad Tabar, H. Nemati, G. Domairry, and F. Noori, “An analytical solution for boundary layer flow of a nanofluid past a stretching sheet,” International Journal of Thermal Sciences, vol. 50, no. 11, pp. 2256–2263, 2011. View at Publisher · View at Google Scholar · View at Scopus
  48. N. Bachok, A. Ishak, and I. Pop, “On the stagnation-point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4296–4302, 2011. View at Publisher · View at Google Scholar · View at Scopus
  49. G. Domairry and Z. Ziabakhsh, “Solution of boundary layer flow and heat transfer of an electrically conducting micropolar fluid in a non-Darcian porous medium,” Meccanica, vol. 47, no. 1, pp. 195–202, 2012. View at Publisher · View at Google Scholar · View at Scopus
  50. A. A. Joneidi, G. Domairry, and M. Babaelahi, “Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction,” Journal of the Taiwan Institute of Chemical Engineers, vol. 41, no. 1, pp. 35–43, 2010. View at Publisher · View at Google Scholar · View at Scopus
  51. Z. Ziabakhsh, G. Domairry, H. Bararnia, and H. Babazadeh, “Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium,” Journal of the Taiwan Institute of Chemical Engineers, vol. 41, no. 1, pp. 22–28, 2010. View at Publisher · View at Google Scholar · View at Scopus
  52. K. Yabushita, M. Yamashita, and K. Tsuboi, “An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method,” Journal of Physics A, vol. 40, no. 29, pp. 8403–8416, 2007. View at Publisher · View at Google Scholar · View at Scopus
  53. Z. Niu and C. Wang, “A one-step optimal homotopy analysis method for nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2026–2036, 2010. View at Publisher · View at Google Scholar · View at Scopus