Skip to main content
Log in

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

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

Abstract

This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method (HAM). Two-dimensional and axisymmetric shrinking flow cases are discussed.

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. Sajid, M., Ahmad, I., Hayat, T., and Ayub, M. Unsteady flow and heat transfer of a second grade fluid over a stretching sheet. Comm. Nonl. Sci. Num. Sim. 14(1), 96–108(2009)

    Article  MathSciNet  Google Scholar 

  2. Cortell, R. A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Int. J. Nonlin. Mech. 41(1), 78–85 (2006)

    Article  MATH  Google Scholar 

  3. Cortell, R. Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet. Phys. Lett. A 357(4–5), 298–305 (2006)

    Article  MATH  Google Scholar 

  4. Hayat, T. and Sajid, M. Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. Int. J. Heat Mass Tran. 50(1–2), 75–84 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hayat, T., Saif, S., and Abbas, Z. The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet. Phys. Lett. A 372(30), 5037–5045 (2008)

    Article  Google Scholar 

  6. Fetecau, C., Hayat, T., Fetecau, Corina, and Ali, N. Unsteady flow of a second grade fluid between two side walls perpendicular to a plate. Nonlinear Anal.: Real World Appl. 9(3), 1236–1252 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Vajravelu, K. and Rollins, D. Hydromagnetic flow of a second grade fluid over a stretching sheet. Appl. Math. Comput. 148(3), 783–791 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sakiadis, B. C. Boundary layer behaviour on continuous solid surfaces. AIChE J. 7(1), 26–28 (1961)

    Article  Google Scholar 

  9. Liao, S. J. An analytic solution of unsteady boundary layer flows caused by an impulsive stretching plate. Comm. Nonl. Sci. Num. Sim. 11(3), 326–339 (2006)

    Article  MATH  Google Scholar 

  10. Hayat, T. and Sajid, M. Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid. Int. J. Eng. Sci. 45(2–8), 93–401 (2007)

    MathSciNet  Google Scholar 

  11. Ishak, A., Nazar, R., and Pop, I. MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux. Comm. Nonl. Sci. Num. Sim. 14(1) 109–118 (2009)

    Article  MathSciNet  Google Scholar 

  12. Bose, S. and Chakraborty, S. A boundary layer analysis of electro-magneto-hydrodynamic forced convective transport over a melting slab. Int. J. Heat Mass Tran. 51(21–22), 5465–5474 (2008)

    Article  MATH  Google Scholar 

  13. Nadeem, S. and Awais, M. Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity. Phys. Lett. A 372(30), 4965–4972 (2008)

    Article  Google Scholar 

  14. Hayat, T., Javed, T., and Sajid, M. Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface. Phys. Lett. A 372(18), 3264–3273 (2008)

    Article  MathSciNet  Google Scholar 

  15. Wang, C. Y. Stagnation flow towards a shrinking sheet. Int. J. Nonl. Mech. 43(5), 377–382 (2008)

    Article  Google Scholar 

  16. Liao, S. J. Beyond Perturbation Introduction to Homotopy Analysis Method, Hall/CRC Press, Boca Raton Chapman (2003)

    Google Scholar 

  17. Abbasbandy, S. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem. Eng. J. 136(2–3), 144–150 (2008)

    Article  Google Scholar 

  18. Abbasbandy, S. Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method. Appl. Math. Model. 32(12), 2706–2714 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sajid, M., Awais, M., Nadeem, S., and Hayat, T. The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method. Comp. Math. Appl. 56(8), 2019–2026 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  20. Chowdhury, M. S. H., Hashim, I., and Abdulaziz, O. Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems. Comm. Nonl. Sci. Num. Sim. 14(2), 371–378 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Nadeem.

Additional information

Communicated by Zhe-wei ZHOU

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadeem, S., Hussain, A., Malik, M.Y. et al. Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet. Appl. Math. Mech.-Engl. Ed. 30, 1255–1262 (2009). https://doi.org/10.1007/s10483-009-1005-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-009-1005-6

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Navigation