About this Journal Submit a Manuscript Table of Contents
ISRN Thermodynamics
Volume 2012 (2012), Article ID 214362, 9 pages
http://dx.doi.org/10.5402/2012/214362
Research Article

Radiative Boundary Layer Flow in Porous Medium due to Exponentially Shrinking Permeable Sheet

1Department of Mathematics, University of Rajasthan, Jaipur 302004, India
2Department of Mathematics, Poornima University, Jaipur 303905, India

Received 24 September 2012; Accepted 10 October 2012

Academic Editors: D. Bratko and Q. Zhang

Copyright © 2012 Paresh Vyas and Nupur Srivastava. 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 ZAMP, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar · View at Scopus
  2. S. J. Liao, “On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet,” Journal of Fluid Mechanics, no. 488, pp. 189–212, 2003. View at Publisher · View at Google Scholar · View at Scopus
  3. 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
  4. 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
  5. K. R. Rajgopal, T. Y. Na, and A. S. Gupta, “Flow of a visco-elastic fluid over a stretching sheet,” RheolActa, vol. 23, pp. 213–215, 1984.
  6. P. H. Veena, S. Abel, K. Rajagopal, and V. K. Pravin, “Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation,” Zeitschrift fur Angewandte Mathematik und Physik, vol. 57, no. 3, pp. 447–463, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Ahmad, R. Nazar, A. Ishak, and I. Pop, “Unsteady three-dimensional boundary layer flow due to a stretching surface in a micropolar fluid,” International Journal for Numerical Methods in Fluids, vol. 28, pp. 118–122, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. H. I. Andersson and O. A. Valnes, “Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole,” Acta Mechanica, vol. 128, no. 1-2, pp. 39–47, 1998. View at Scopus
  9. D. S. Chauhan and R. Agrawal, “MHD flow through a porous medium adjacent to a stretching sheet: numerical and an approximate solution,” European Physical Journal Plus, vol. 126, no. 5, pp. 1–14, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Liao, “A new branch of solutions of boundary-layer flows over an impermeable stretched plate,” International Journal of Heat and Mass Transfer, vol. 48, no. 12, pp. 2529–2539, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. S. J. Liao, “A new branch of solutions of boundary-layer flows over a permeable stretching plate,” International Journal of Non-Linear Mechanics, vol. 42, no. 6, pp. 819–830, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. 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
  13. 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 Scopus
  14. R. A. M. Q. Al-Odat, T. A. Damesh, and T. A. Al-Azab, “Thermal boundary layer on an exponentially stretching continuous surface in the presence of magnetic field effect,” International Journal of Applied Mechanics and Engineering, vol. 11, pp. 289–299, 2006.
  15. 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
  16. E. Sanjayanand and S. K. Khan, “On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet,” International Journal of Thermal Sciences, vol. 45, no. 8, pp. 819–828, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. 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
  18. M. Sajid and T. Hayat, “Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet,” International Communications in Heat and Mass Transfer, vol. 35, no. 3, pp. 347–356, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. C. Y. Wang, “Liquid film on an unsteady stretching sheet, Quart,” Applied Mathematics, vol. 48, pp. 601–610, 1990.
  20. M. Miklavčič and C. Y. Wang, “Viscous flow due to a shrinking sheet,” Quarterly of Applied Mathematics, vol. 64, no. 2, pp. 283–290, 2006. View at Scopus
  21. C. Y. Wang, “Stagnation flow towards a shrinking sheet,” International Journal of Non-Linear Mechanics, vol. 43, no. 5, pp. 377–382, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Hayat, Z. Abbas, and N. Ali, “MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species,” Physics Letters, Section A, vol. 372, no. 26, pp. 4698–4704, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. T. Fang, “Boundary layer flow over a shrinking sheet with power-law velocity,” International Journal of Heat and Mass Transfer, vol. 51, no. 25-26, pp. 5838–5843, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. T. Fang and J. Zhang, “Closed-form exact solutions of MHD viscous flow over a shrinking sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 2853–2857, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. T. G. Fang, J. Zhang, and S. S. Yao, “Viscous flow over an unsteady shrinking sheet with mass transfer,” Chinese Physics Letters, vol. 26, no. 1, Article ID 014703, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. N. F. M. Noor, S. Awang Kechil, and I. Hashim, “Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 144–148, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Hayat, Z. Abbas, and M. Sajid, “On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet,” Journal of Applied Mechanics, Transactions ASME, vol. 74, no. 6, pp. 1165–1171, 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. T. Fang, W. Liang, and C. F. F. Lee, “A new solution branch for the Blasius equation-A shrinking sheet problem,” Computers and Mathematics with Applications, vol. 56, no. 12, pp. 3088–3095, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. N. F. Mohd and I. Hashim, “MHD flow and heat transfer adjacent to a permeable shrinking sheet embedded in a porous medium,” Sains Malaysiana, vol. 38, no. 4, pp. 559–565, 2009. View at Scopus
  30. D. S. Chauhan and R. Agrawal, “MHD flow and heat transfer in a channel bounded by a shrinking sheet and a plate with a porous substrate,” Journal of Engineering Physics and Thermophysics, vol. 84, no. 5, pp. 1034–1046, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. 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
  32. B. S. Dandapat, B. Santra, and K. Vajravelu, “The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet,” International Journal of Heat and Mass Transfer, vol. 50, no. 5-6, pp. 991–996, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. P. Vyas and A. Rai, “Radiative flow with variable thermal conductivity over a noniIsothermal Stretching sheet in a porous medium, Int,” Journal of Contemporary Mathematical Sciences, vol. 5, pp. 2685–2698, 2010.
  34. U. Sarma and G. C. Hazarika, “Effects of variable viscosity and thermal conductivity on heat and mass transfer flow along a vertical plate in the presence of a magnetic field,” Latin-American Journal of Physics Education, vol. 5, pp. 100–106, 2011.
  35. Y. Khan, Q. Wu, N. Faraz, and A. Yildirim, “The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet,” Computers and Mathematics with Applications, vol. 61, no. 11, pp. 3391–3399, 2011. View at Publisher · View at Google Scholar · View at Scopus
  36. P. Vyas and N. Srivastava, “Radiative MHD flow over a non-isothermal stretching sheet in a porous medium,” Applied Mathematical Sciences, vol. 4, no. 49–52, pp. 2475–2484, 2010. View at Scopus
  37. P. Vyas and A. Ranjan, “Dissipative MHD boundary-layer flow in a porous medium over a sheet stretching nonlinearly in the presence of radiation,” Applied Mathematical Sciences, vol. 4, no. 61–64, pp. 3133–3142, 2010. View at Scopus
  38. D. S. Chauhan and V. Kumar, “Radiation effects on unsteady flow through a porous medium channel with velocity and temperature slip boundary conditions,” Applied Mathematical Sciences, vol. 6, no. 33–36, pp. 1759–1769, 2012.
  39. D. S. Chauhan and R. Agarwal, “MHD coupled flow and heat transfer across a porous layer due to an oscillating plate with radiation,” Afrika Mathematica. In press. View at Publisher · View at Google Scholar
  40. T. Hayat, S. A. Shehzad, M. Qasim, and A. Alsaedi, “Radiative flow with variable thermal conductivity in porous medium,” Zeitschrift für Naturforschung, vol. 67, no. 3-4, pp. 153–159, 2012. View at Publisher · View at Google Scholar · View at Scopus
  41. E. M. A. Elbashbeshy and T. G. Emam, “Effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink,” Thermal Science, vol. 15, no. 2, pp. 477–485, 2011. View at Publisher · View at Google Scholar · View at Scopus
  42. T. C. Chiam, “Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet,” Acta Mechanica, vol. 129, no. 1-2, pp. 63–72, 1998. View at Scopus