Frontiers of Chemical Science and Engineering

, Volume 5, Issue 3, pp 376–384 | Cite as

Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection

Research Article

Abstract

In this paper, an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layer flow and heat transfer past a shrinking sheet with suction/injection. The flow is permeated by an externally applied magnetic field normal to the plane of flow. The self-similar equations corresponding to the velocity and temperature fields are obtained, and then solved numerically by finite difference method using quasilinearization technique. The study reveals that the momentum boundary layer thickness increases with increasing unsteadiness and decreases with magnetic field. The thermal boundary layer thickness decreases with Prandtl number, radiation parameter and heat sink parameter, but it increases with heat source parameter. Moreover, increasing unsteadiness, magnetic field strength, radiation and heat sink strength boost the heat transfer.

Keywords

MHD boundary layer unsteady flow heat transfer thermal radiation heat source/sink shrinking sheet suction/injection 

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References

  1. 1.
    Crane L J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 1970, 21(4): 645–647CrossRefGoogle Scholar
  2. 2.
    Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction and blowing. Canadian Journal of Chemical Engineering, 1977, 55(6): 744–746CrossRefGoogle Scholar
  3. 3.
    Wang C Y. The three dimensional flow due to a stretching flat surface. Physics of Fluids, 1984, 27(8): 1915–1917CrossRefGoogle Scholar
  4. 4.
    McLeod J B, Rajagopal K R. On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary. Archive for Rational Mechanics and Analysis, 1987, 98(4): 385–393CrossRefGoogle Scholar
  5. 5.
    Rajagopal K R, Na T Y, Gupta A S. Flow of a viscoclastic fluid over a stretching sheet. Rheologica Acta, 1984, 23(2): 213–215CrossRefGoogle Scholar
  6. 6.
    Andersson H I, Bech K H, Dandapat B S. Flow of a power-law fluid over a stretching sheet. International Journal of Non-Linear Mechanics, 1992, 27(6): 929–936CrossRefGoogle Scholar
  7. 7.
    Pavlov K B. Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a surface. Magnetohydrodynamics, 1974, 10(4): 146–148Google Scholar
  8. 8.
    Chakrabarti A, Gupta A S. Hydromagnetic flow and heat transfer over a stretching sheet. Quarterly of Applied Mathematics, 1979, 37: 73–78Google Scholar
  9. 9.
    Andersson H I. MHD flow of a viscoelastic fluid past a stretching surface. Acta Mechanica, 1992, 95(1–4): 227–230CrossRefGoogle Scholar
  10. 10.
    Pop I, Na T Y. A note on MHD flow over a stretching permeable surface. Mechanics Research Communications, 1998, 25(3): 263–269CrossRefGoogle Scholar
  11. 11.
    Hayat T, Javed T. On analytic solution for generalized threedimensional MHD flow over a porous stretching sheet. Physics Letters A, 2007, 370(3–4): 243–250CrossRefGoogle Scholar
  12. 12.
    Wang C Y. Liquid film on an unsteady stretching sheet. Quarterly of Applied Mathematics, 1990, 48: 601–610Google Scholar
  13. 13.
    Miklavčič M, Wang C Y. Viscous flow due a shrinking sheet. Quarterly of Applied Mathematics, 2006, 64: 283–290Google Scholar
  14. 14.
    Hayat T, Abbas Z, Sajid M. On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet. Journal of Applied Mechanics, 2007, 74(6): 1165–1171CrossRefGoogle Scholar
  15. 15.
    Hayat T, Javed T, Sajid M. Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface. Physics Letters A, 2008, 372(18): 3264–3273CrossRefGoogle Scholar
  16. 16.
    Muhaimin R K, Khamis A B. Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction. Applied Mathematics and Mechanics, 2008, 29(10): 1309–1317CrossRefGoogle Scholar
  17. 17.
    Fang T, Zhang J. Closed-form exact solution of MHD viscous flow over a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(7): 2853–2857CrossRefGoogle Scholar
  18. 18.
    Sajid M, Hayat T. The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos, Solitons and Fractals, 2009, 39(3): 1317–1323CrossRefGoogle Scholar
  19. 19.
    Hayat T, Abbas Z, Javed T, Sajid M. Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos, Solitons and Fractals, 2009, 39(4): 1615–1626CrossRefGoogle Scholar
  20. 20.
    Hayat T, Abbas Z, Ali N. MHD flow and mass transfer of a upperconvected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Physics Letters A, 2008, 372(26): 4698–4704CrossRefGoogle Scholar
  21. 21.
    Noor N F M, Kechil S A, Hashim I. Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(2): 144–148CrossRefGoogle Scholar
  22. 22.
    Hayat T, Iram S, Javed T, Asghar S. Shrinking flow of second grade fluid in a rotating frame: an analytic solution. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(10): 2932–2941CrossRefGoogle Scholar
  23. 23.
    Fang T, Zhang J. Thermal boundary layers over a shrinking sheet: an analytic solution. Acta Mechanica, 2010, 209(3–4): 325–343CrossRefGoogle Scholar
  24. 24.
    Devi C D S, Takhar H S, Nath G. Unsteady three-dimensional boundary layer flow due to a stretching surface. International Journal of Heat and Mass Transfer, 1986, 29(12): 1996–1999CrossRefGoogle Scholar
  25. 25.
    Smith S H. An exact solution of the unsteady Navier-Stokes equations resulting from a stretching surface. Journal of Applied Mechanics, 1994, 61(3): 629–633CrossRefGoogle Scholar
  26. 26.
    Pop I, Na T Y. Unsteady flow past a stretching sheet. Mechanics Research Communications, 1996, 23(4): 413–422CrossRefGoogle Scholar
  27. 27.
    Elbashbeshy E M A, Bazid M A A. Heat transfer over an unsteady stretching surface. Heat and Mass Transfer, 2004, 41(1): 1–4CrossRefGoogle Scholar
  28. 28.
    Tsai R, Huang K H, Huang J S. Flow and heat transfer over an unsteady stretching surface with a non-uniform heat source. International Communications in Heat and Mass Transfer, 2008, 35(10): 1340–1343CrossRefGoogle Scholar
  29. 29.
    Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. International Journal of Engineering Science, 2004, 42(11–12): 1241–1253CrossRefGoogle Scholar
  30. 30.
    Mukhopadhyay S, Andersson H I. Effects of slip and heat transfer analysis of flow over an unsteady stretching surface. Heat and Mass Transfer, 2009, 45(11): 1447–1452CrossRefGoogle Scholar
  31. 31.
    Hayat T, Mustafa M, Asghar S. Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction. Nonlinear Analysis: Real World Applications, 2010, 11(4): 3186–3197CrossRefGoogle Scholar
  32. 32.
    Hayat T, Qasim M, Abbas Z. Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9): 2375–2387CrossRefGoogle Scholar
  33. 33.
    Fang T G, Zhang J, Yao S S. Viscous flow over an unsteady shrinking sheet with mass transfer. Chinese Physics Letters, 2009, 26(1): 014703CrossRefGoogle Scholar
  34. 34.
    Merkin J H, Kumaran V. The unsteady MHD boundary-layer flow on a shrinking sheet. European Journal of Mechanics - B/Fluids, 2010, 29(5): 357–363CrossRefGoogle Scholar
  35. 35.
    Viskanta R, Grosh R J. Boundary layer in thermal radiation absorbing and emitting media. International Journal of Heat and Mass Transfer, 1962, 5(9): 795–806CrossRefGoogle Scholar
  36. 36.
    Chen T S, Ali M M, Armaly B F. Natural convection-radiation interaction in boundary layer flow over horizontal surfaces. AIAA Journal, 1984, 22(12): 1797–1803CrossRefGoogle Scholar
  37. 37.
    Elbashbeshy E M A. Radiation effect on heat transfer over a stretching surface. Canadian Journal of Physics, 2000, 78(12): 1107–1112CrossRefGoogle Scholar
  38. 38.
    Ouaf ME M. Exact solution of thermal radiation on MHD flow over a stretching porous sheet. Applied Mathematics and Computation, 2005, 170(2): 1117–1125CrossRefGoogle Scholar
  39. 39.
    Hayat T, Abbas Z, Sajid M, Asghar S. The influence of thermal radiation on MHD flow of a second grade fluid. International Journal of Heat and Mass Transfer, 2007, 50(5–6): 931–941CrossRefGoogle Scholar
  40. 40.
    Hayat T, Nawaz M, Sajid M, Asghar S. The effect of thermal radiation on the flow of a second grade fluid. Computers & Mathematics with Applications (Oxford, England), 2009, 58(2): 369–379CrossRefGoogle Scholar
  41. 41.
    Abd El-Aziz M. Radiation effect on the flow and heat transfer over an unsteady stretching sheet. International Communications in Heat and Mass Transfer, 2009, 36(5): 521–524CrossRefGoogle Scholar
  42. 42.
    Mukhopadhyay S. Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium. International Journal of Heat and Mass Transfer, 2009, 52(13–14): 3261–3265CrossRefGoogle Scholar
  43. 43.
    Hayat T, Qasim M, Abbas Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet. Zeitschrift fur Naturforschung. Section A. Physical Science, 2010, 65a: 231–239Google Scholar
  44. 44.
    Hayat T, Qasim M. Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet. International Journal for Numerical Methods in Fluids, 2010, 66(7), 820–832CrossRefGoogle Scholar
  45. 45.
    Brewster M Q. Thermal Radiative Transfer Properties. New York: John Wiley and Sons, 1972Google Scholar
  46. 46.
    Andersson H I, Aarseth J B, Dandapat B S. Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer, 2000, 43(1): 69–74CrossRefGoogle Scholar
  47. 47.
    Bellman R E, Kalaba R E. Quasilinearization and nonlinear boundary value problem. New York: American Elsevier Publishing Co Inc, 1965Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe University of BurdwanBurdwanIndia

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