Table of Contents
Physics Research International
Volume 2014 (2014), Article ID 592536, 12 pages
http://dx.doi.org/10.1155/2014/592536
Research Article

Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

Department of Mathematics, The University of Burdwan, Burdwan, West Bengal 713104, India

Received 19 October 2013; Accepted 7 December 2013; Published 8 January 2014

Academic Editor: Ali Hussain Reshak

Copyright © 2014 Krishnendu Bhattacharyya and G. C. Layek. 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. S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, vol. 66, pp. 99–105, San Francisco, Calif, USA, November 1995.
  2. H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles,” Netsu Bussei, vol. 7, pp. 227–233, 1993. View at Google Scholar
  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. D. A. Nield and A. V. Kuznetsov, “The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid,” International Journal of Heat and Mass Transfer, vol. 52, no. 25-26, pp. 5792–5795, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. 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
  6. L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar · View at Scopus
  7. P. S. Gupta and A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction and blowing,” The Canadian Journal of Chemical Engineering, vol. 55, no. 6, pp. 744–746, 1977. View at Publisher · View at Google Scholar
  8. B. K. Dutta, P. Roy, and A. S. Gupta, “Temperature field in flow over a stretching sheet with uniform heat flux,” International Communications in Heat and Mass Transfer, vol. 12, no. 1, pp. 89–94, 1985. View at Google Scholar · View at Scopus
  9. H. I. Andersson and B. S. Dandapat, “Flow of a power-law fluid over a stretching sheet,” Stability and Applied Analysis of Continuous Media, vol. 1, pp. 339–347, 1991. View at Google Scholar
  10. 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 Scopus
  11. K. Bhattacharyya and G. C. Layek, “Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing,” Chemical Engineering Communications, vol. 197, no. 12, pp. 1527–1540, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip effects on an unsteady boundary layer stagnation-point flow and heat transfer towards a stretching sheet,” Chinese Physics Letters, vol. 28, no. 9, Article ID 094702, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Bhattacharyya and G. C. Layek, “Slip effect on diffusion of chemically reactive species in boundary layer flow over a vertical stretching sheet with suction or blowing,” Chemical Engineering Communications, vol. 198, no. 11, pp. 1354–1365, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. K. Bhattacharyya, “Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection,” Frontiers of Chemical Science and Engineering, vol. 5, no. 3, pp. 376–384, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Bhattacharyya, M. G. Arif, and W. Ali Pramanik, “MHD boundary layer stagnation-point flow and mass transfer over a permeable shrinking sheet with suction/blowing and chemical reaction,” Acta Technica, vol. 57, pp. 1–15, 2012. View at Google Scholar
  16. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Unsteady MHD boundary layer flow with diffusion and first order chemical reaction over a permeable stretching sheet with suction or blowing,” Chemical Engineering Communications, vol. 200, no. 3, pp. 379–397, 2013. View at Publisher · View at Google Scholar
  17. K. Bhattacharyya, “Heat transfer in unsteady boundary layer stagnation-point flow towards a shrinking sheet,” Ain Shams Engineering Journal, vol. 4, no. 2, pp. 259–264, 2013. View at Publisher · View at Google Scholar
  18. E. Magyari and B. Keller, “Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” Journal of Physics D, vol. 32, no. 5, pp. 577–585, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. E. M. A. Elbashbeshy, “Heat transfer over an exponentially stretching continuous surface with suction,” Archives of Mechanics, vol. 53, no. 6, pp. 643–651, 2001. View at Google Scholar · View at Scopus
  20. S. K. Khan and E. Sanjayanand, “Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet,” International Journal of Heat and Mass Transfer, vol. 48, no. 8, pp. 1534–1542, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. M. K. Partha, P. V. S. N. Murthy, and G. P. Rajasekhar, “Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface,” Heat and Mass Transfer, vol. 41, no. 4, pp. 360–366, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. A. Ishak, “MHD boundary layer flow due to an exponentially stretching sheet with radiation effect,” Sains Malaysiana, vol. 40, no. 4, pp. 391–395, 2011. View at Google Scholar · View at Scopus
  23. K. Bhattacharyya, “Boundary layer flow and heat transfer over an exponentially shrinking sheet,” Chinese Physics Letters, vol. 28, no. 7, Article ID 074701, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. K. Bhattacharyya and I. Pop, “MHD boundary layer flow due to an exponentially shrinking sheet,” Magnetohydrodynamics, vol. 47, pp. 337–344, 2011. View at Google Scholar
  25. 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
  26. N. Bachok, A. Ishak, and I. Pop, “Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid,” International Journal of Heat and Mass Transfer, vol. 55, no. 25-26, pp. 8122–8128, 2012. View at Publisher · View at Google Scholar
  27. 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
  28. O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition,” The International Journal of Thermal Sciences, vol. 50, no. 7, pp. 1326–1332, 2011. View at Publisher · View at Google Scholar · View at Scopus
  29. R. Kandasamy, P. Loganathan, and P. Puvi Arasu, “Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection,” Nuclear Engineering and Design, vol. 241, no. 6, pp. 2053–2059, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Mustafa, T. Hayat, I. Pop, S. Asghar, and S. Obaidat, “Stagnation-point flow of a nanofluid towards a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 54, no. 25-26, pp. 5588–5594, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. 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
  32. F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, and M. R. Eid, “Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet,” Nanoscale Research Letters, vol. 7, article 229, 2012. View at Publisher · View at Google Scholar
  33. O. D. Makinde, W. A. Khan, and Z. H. Khan, “Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet,” International Journal of Heat and Mass Transfer, vol. 62, pp. 526–533, 2013. View at Publisher · View at Google Scholar
  34. N. Bachok, A. Ishak, and I. Pop, “Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet,” International Journal of Heat and Mass Transfer, vol. 55, no. 7-8, pp. 2102–2109, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. 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
  36. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “MHD boundary layer slip flow and heat transfer over a flat plate,” Chinese Physics Letters, vol. 28, no. 2, Article ID 024701, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. K. Bhattacharyya, “Dual solutions in unsteady stagnation-point flow over a shrinking sheet,” Chinese Physics Letters, vol. 28, no. 8, Article ID 084702, 2011. View at Publisher · View at Google Scholar · View at Scopus
  38. S. Mukhopadhyay, K. Bhattacharyya, and G. C. Layek, “Steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation,” International Journal of Heat and Mass Transfer, vol. 54, no. 13-14, pp. 2751–2757, 2011. View at Publisher · View at Google Scholar · View at Scopus
  39. K. Bhattacharyya, “Boundary layer flow with diffusion and first-order chemical reaction over a porous flat plate subject to suction/injection and with variable wall concentration,” Chemical Engineering Research Bulletin, vol. 15, no. 1, pp. 6–11, 2011. View at Publisher · View at Google Scholar · View at Scopus
  40. K. Bhattacharyya, “Effects of heat source/sink on MHD flow and heat transfer over a shrinking sheet with mass suction,” Chemical Engineering Research Bulletin, vol. 15, no. 1, pp. 12–17, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. K. Bhattacharyya, S. Mukhopadhyay, G. C. Layek, and I. Pop, “Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet,” International Journal of Heat and Mass Transfer, vol. 55, no. 11-12, pp. 2945–2952, 2012. View at Publisher · View at Google Scholar · View at Scopus