Skip to main content
Log in

Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionaless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bhattacharyya S N, Gupta A S. On the stability of viscous flow over a stretching sheet[J]. Quart Appl Math, 1985, 43(3):359–367. MR 0814233 (87a:76056)

    MATH  MathSciNet  Google Scholar 

  2. Brady J F, Acrivos A. Steady flow in a channel or tube with accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow[J]. J Fluid Mech, 1981, 112:127–150. MR 0639234 (82m:76017)

    Article  MATH  MathSciNet  Google Scholar 

  3. Crane L J. Flow past a stretching plate[J]. ZAMP, 1970, 21(4):645–647.

    Article  Google Scholar 

  4. Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction and blowing[J]. Can J Chem Eng, 1977, 55(1):744–746.

    Google Scholar 

  5. Jensen K F, Einset E O, Fotiadis D I. Flow phenomena in chemical vapor deposition of thin films[J]. Ann Rev Fluid Mech, 1991, 23(1):197–232.

    Article  Google Scholar 

  6. McLeod J B, Rajagopal K R. On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary[J]. Arch Rat Mech Anal, 1987, 98(4):385–393. MR 0872753 (88c:35131)

    Article  MATH  MathSciNet  Google Scholar 

  7. Troy W, Overman II E A, Ermentrout G B, Keener J P. Uniqueness of flow of a second-order fluid past a stretching sheet[J]. Quart Appl Math, 1987, 44(4):753–755. MR 0872826 (87m:76009)

    MATH  MathSciNet  Google Scholar 

  8. Usha R, Sridharan R. The axisymmetrical motion of a liquid film on an unsteady stretching surface[J]. J Fluids Eng, 1995, 117(1):81–85.

    Article  Google Scholar 

  9. Wang C Y. The three-dimensional flow due to a stretching flat surface[J]. Phys Fluids, 1984, 27(8):1915–1917. MR 0758728 (85g:76014)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang C Y. Fluid flow due to a stretching cylinder[J]. Phys Fluids, 1988, 31(3):466–468.

    Article  Google Scholar 

  11. Wang C Y. Liquid film on an unsteady stretching sheet[J]. Quart Appl Math, 1990, 48(4):601–610. MR 1079908 (91h:76025).

    MATH  MathSciNet  Google Scholar 

  12. EL-Hakiem M A, Mohammadein A A, EL-Kabeir S M M, Gorla R S R. Joule heating effects on MHD free convection flow of a micro polar fluid[J]. International Communications in Heat and Mass Transfer, 1999, 26(2):219–227.

    Article  Google Scholar 

  13. Kuo Bor-Lih. Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method[J]. Int J Heat Mass Transfer, 2005, 48(23/24):5036–5046.

    Article  Google Scholar 

  14. Cheng W T, Lin H T. Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge[J]. Int J Engg Sci, 2002, 40(5):531–548.

    Article  Google Scholar 

  15. Apelblat A. Mass transfer with a chemical reaction of the first order: effects of axial diffusion[J]. The Chemical Engineering Journal, 1982, 23(2):193–203.

    Article  Google Scholar 

  16. Cebeci T, Bradshaw P. Physical and computational aspects of convective heat transfer[M]. New York: Springer-Verlag, 1984, 79–80.

    Google Scholar 

  17. Schlichting H. Boundary layer theory[M]. New York: McGraw Hill Inc, 1979, 164.

    Google Scholar 

  18. Yih K A. Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux[J]. Acta Mech, 1998, 128(3/4):173–181.

    Article  MATH  Google Scholar 

  19. Watanabe T. Thermal boundary layers over a wedge with uniform suction or injection in forced flow[J]. Acta Mech, 1990, 83(3/4):119–126.

    Article  Google Scholar 

  20. Kafoussias N G, Nanousis N D. Magnetohydrodynamic laminar boundary-layer flow over a wedge with suction or injection[J]. Can J Phys, 1997, 75(10):733–745.

    Article  Google Scholar 

  21. Sajid M, Javed T, Hayat T. MHD rotating flow of a viscous fluid over a shrinking surface[J]. Nonlinear Dynamics, 2008, 51(1/2):259–265.

    MATH  Google Scholar 

  22. Hayat T, Abbas Z, Sajid, M. On the analytic solution of Magnetohydrodynamic flow of a second grade fluid over a shrinking sheet[J]. Journal of Applied Mechanics, 2007, 74(6):1165–1170.

    Article  Google Scholar 

  23. Sajid M, Hayat T. The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet[J]. Chaos, Solutions and Fractals, 2007 (in press).

  24. Miklavcic M, Wang C Y. Viscous flow due to a shrinking sheet[J]. Quart Appl Math, 2006, 64(2):283–290.

    MATH  MathSciNet  Google Scholar 

  25. Gill S. A process for the step-by-step integration of differential equations in an automatic digital computing machine[J]. Proceedings of the Cambridge Philosophical Society, 1951, 47(1):96–108.

    Article  MATH  MathSciNet  Google Scholar 

  26. Minkowycz W J, Sparrow E M, Schneider G E, Pletcher R H. Handbook of numerical heat transfer[M]. New York: John Wiley and Sons, 1988, 192–195.

    Google Scholar 

  27. Kafoussias N G, Karabis A G. Magnetohydrodynamic laminar boundary layer flow over a wedge[C]. In: Sotiropoulos D A and Beskos D E (eds). Proceedings of the 2nd National Congress on Computational Mechanics, Vol II, Chania, Greece, June 26–28, 1996, 801–809.

  28. Kafoussias N G, Williams E W. An improved approximation technique to obtain numerical solution of a class of two-point boundary value similarity problems in fluid mechanics[J]. Int J Num Methods Fluids, 1993, 17(2):145–162.

    Article  MATH  Google Scholar 

  29. Dirk Wilhelm, Carlos Hartel, Leonhard Kleiser. Computational analysis of the two-dimensional-three-dimensional transition in forward-facing step flow[J]. J Fluid Mech, 2003, 489:1–27.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Kandasamy.

Additional information

(Communicated by LIN Jian-zhong)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muhaimin, Kandasamy, R. & Khamis, A.B. Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction. Appl. Math. Mech.-Engl. Ed. 29, 1309–1317 (2008). https://doi.org/10.1007/s10483-008-1006-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-1006-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Navigation