Table of Contents
Journal of Thermodynamics
Volume 2013 (2013), Article ID 169674, 9 pages
http://dx.doi.org/10.1155/2013/169674
Research Article

MHD Stagnation-Point Flow of Casson Fluid and Heat Transfer over a Stretching Sheet with Thermal Radiation

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

Received 28 May 2013; Accepted 3 September 2013

Academic Editor: Felix Sharipov

Copyright © 2013 Krishnendu Bhattacharyya. 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. K. B. Pavlov, “Magnetohydrodynamic flow of an incompressible viscous fluid caused by the deformation of a plane surface,” Magnetohydrodynamics, vol. 10, pp. 146–148, 1974. View at Google Scholar
  3. H. I. Andersson, “MHD flow of a viscoelastic fluid past a stretching surface,” Acta Mechanica, vol. 95, no. 1–4, pp. 227–230, 1992. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Mukhopadhyay, G. C. Layek, and S. A. Samad, “Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity,” International Journal of Heat and Mass Transfer, vol. 48, no. 21-22, pp. 4460–4466, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. 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
  6. 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
  7. 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 Engineering in China, vol. 5, no. 3, pp. 376–384, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. 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
  9. 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
  10. H. Tabaei, M. A. Moghimi, A. Kimiaeifar, and M. A. Moghimi, “Homotopy analysis and differential quadrature solution of the problem of free-convective magnetohydrodynamic flow over a stretching sheet with the Hall effect and mass transfer taken into account,” Journal of Applied Mechanics and Technical Physics, vol. 52, no. 4, pp. 624–636, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Kandasamy, I. Muhaimin, and G. Kamachi, “Scaling group transformation for the effect of temperature-dependent nanofluid viscosity on an mhd boundary layer past a porous stretching surface,” Journal of Applied Mechanics and Technical Physics, vol. 52, no. 6, pp. 931–940, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. A. M. Salem and R. Fathy, “Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation,” Chinese Physics B, vol. 21, Article ID 054701, 2012. View at Google Scholar
  13. S. Mukhopadhyay and R. S. R. Gorla, “Effects of partial slip on boundary layer flow past a permeable exponential stretching sheet in presence of thermal radiation,” Heat and Mass Transfer, vol. 48, pp. 1773–1781, 2012. View at Google Scholar
  14. 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
  15. 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
  16. I. C. Mandal and S. Mukhopadhyay, “Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium,” Ain Shams Engineering Journal, vol. 4, pp. 103–110, 2013. View at Google Scholar
  17. T. C. Chiam, “Stagnation-point flow towards a stretching plate,” Journal of the Physical Society of Japan, vol. 63, no. 6, pp. 2443–2444, 1994. View at Google Scholar · View at Scopus
  18. T. R. Mahapatra and A. S. Gupta, “Magnetohydrodynamic stagnation-point flow towards a stretching sheet,” Acta Mechanica, vol. 152, no. 1-4, pp. 191–196, 2001. View at Publisher · View at Google Scholar · View at Scopus
  19. T. R. Mahapatra and A. S. Gupta, “Heat transfer in stagnation-point flow towards a stretching sheet,” Heat and Mass Transfer, vol. 38, no. 6, pp. 517–521, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Nazar, N. Amin, D. Filip, and I. Pop, “Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet,” International Journal of Engineering Science, vol. 42, no. 11-12, pp. 1241–1253, 2004. View at Publisher · View at Google Scholar · View at Scopus
  21. G. C. Layek, S. Mukhopadhyay, and S. A. Samad, “Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing,” International Communications in Heat and Mass Transfer, vol. 34, no. 3, pp. 347–356, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. 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
  23. K. Bhattacharyya, “Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet,” International Communications in Heat and Mass Transfer, vol. 38, no. 7, pp. 917–922, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. 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
  25. K. Bhattacharyya, “Heat transfer in unsteady boundary layer stagnation-point flow towards a shrinking sheet,” Ain Shams Engineering Journal, vol. 4, pp. 259–264, 2013. View at Google Scholar
  26. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Reactive solute transfer in magnetohydrodynamic boundary layer stagnation-point flow over a stretching sheet with suction/blowing,” Chemical Engineering Communications, vol. 199, no. 3, pp. 368–383, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. K. Bhattacharyya, M. G. Arif, and W. A. 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
  28. 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
  29. 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
  30. R. A. Van Gorder, K. Vajravelu, and I. Pop, “Hydromagnetic stagnation point flow of a viscous fluid over a stretching or shrinking sheet,” Meccanica, vol. 47, no. 1, pp. 31–50, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. W. L. Wilkinson, “The drainage of a maxwell liquid down a vertical plate,” The Chemical Engineering Journal, vol. 1, no. 3, pp. 255–257, 1970. View at Google Scholar · View at Scopus
  32. K. R. Rajagopal, “Viscometric flows of third grade fluids,” Mechanics Research Communications, vol. 7, no. 1, pp. 21–25, 1980. View at Google Scholar · View at Scopus
  33. 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
  34. C. Dorier and J. Tichy, “Behavior of a bingham-like viscous fluid in lubrication flows,” Journal of Non-Newtonian Fluid Mechanics, vol. 45, no. 3, pp. 291–310, 1992. View at Google Scholar · View at Scopus
  35. A. G. Fredrickson, Principles and Applications of Rheology, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
  36. M. Mustafa, T. Hayat, I. Pop, and A. Aziz, “Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate,” Heat Transfer, vol. 40, no. 6, pp. 563–576, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. K. Bhattacharyya, T. Hayat, and A. Alsaedi, “Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet,” Zeitschrift für Angewandte Mathematik und Mechanik, 2013. View at Publisher · View at Google Scholar
  38. K. Bhattacharyya, T. Hayat, and A. Alsaedi, “Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer,” Chinese Physics B, vol. 22, Article ID 024702, 2013. View at Google Scholar
  39. 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
  40. T. Hayat, S. Iram, T. Javed, and S. Asghar, “Shrinking flow of second grade fluid in a rotating frame: an analytic solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 2932–2941, 2010. View at Publisher · View at Google Scholar · View at Scopus
  41. K.-L. Hsiao, “Viscoelastic fluid over a stretching sheet with electromagnetic effects and nonuniform heat source/sink,” Mathematical Problems in Engineering, vol. 2010, Article ID 740943, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. B. Sahoo and S. Poncet, “Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition,” International Journal of Heat and Mass Transfer, vol. 54, no. 23-24, pp. 5010–5019, 2011. View at Publisher · View at Google Scholar · View at Scopus
  43. 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
  44. S. Mukhopadhyay, “Casson fluid flow and heat transfer over a nonlinearly stretching,” Chinese Physics B, vol. 22, Article ID 074701, 2013. View at Google Scholar
  45. S. Mukhopadhyay, P. R. De, and G. C. Layek, “Heat transfer characteristics for the Maxwell fluid flow past an unsteady stretching permeable surface embedded in a porous medium with thermal radiation,” Journal of Applied Mechanics and Technical Physics, vol. 54, pp. 385–396, 2013. View at Google Scholar
  46. T. Javed, N. Ali, Z. Abbas, and M. Sajid, “Flow of an Eyring-Powell non-Newtonian fluid over a stretching sheet,” Chemical Engineering Communications, vol. 200, pp. 327–336, 2013. View at Google Scholar
  47. M. Nakamura and T. Sawada, “Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis,” Journal of Biomechanical Engineering, vol. 110, no. 2, pp. 137–143, 1988. View at Google Scholar · View at Scopus
  48. M. Q. Brewster, Thermal Radiative Transfer Properties, John Wiley and Sons, 1972.
  49. 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
  50. 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
  51. K. Bhattacharyya, “Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet,” International Communications in Heat and Mass Transfer, vol. 38, no. 7, pp. 917–922, 2011. View at Publisher · View at Google Scholar · View at Scopus