Skip to main content
SpringerLink
Log in

Exact solutions of thin film flows

  • Original Article
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This article studies the analytical solutions for two thin film flow problems on a moving belt. The reduction of the equations follows from their Lie point symmetry generators and conservation laws which are valid for the considered boundary conditions also. The solutions for the two problems are developed using the correct and nonlinear boundary condition for the free surface. Mathematica is adopted for some of the analysis.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rajagopal, K.R., Kaloni, P.K.: Continuum Mechanics and its Applications. Hemisphere Press, Washington, DC (1989)

    Google Scholar 

  2. Fetecau, C., Fetecau, C.: Starting solutions for some unsteady unidirectional flows of a second grade fluid. Int. J. Eng. Sci. 43, 781–789 (2005)

    Article  Google Scholar 

  3. Fetecau, C., Fetecau, C.: Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section. Int. J. Non-Linear Mech. 40, 1214–1219 (2005)

    Article  MATH  Google Scholar 

  4. Fetecau, C., Fetecau, C.: Decay of potential vortex in an Oldroyd-B fluid. Int. J. Eng. Sci. 43, 340–351 (2005)

    Article  Google Scholar 

  5. Tau, W.C., Matsuoka, T.: Stokes’ first problem for a second grade fluid in a porous half space with heated boudary. Int. J. Non-Linear Mech. 40, 515–522 (2005)

    Article  Google Scholar 

  6. Tau, W.C., Matsuoka, T.: Stokes’ first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluids 17, 0231011–0231017 (2005)

    Google Scholar 

  7. Wang, Y., Hayat, T., Hutter, K.: On nonlinear magnetohydrodynamic of an Oldroyd 6-constant fluid. Int. J. Non-Linear Mech. 40, 40–58 (2005).

    Google Scholar 

  8. Hayat, T., Hutter, K.: Rotating flow of a second order fluid on aporous plate. Int. J. Non-Linear Mech. 39, 767–777 (2004)

    Article  MATH  Google Scholar 

  9. Hayat, T., Asghar, S., Siddiqui, A.M.: Periodic flows of a non-Newtonian fluid. Acta Mech. 131, 169–175 (1998)

    Article  MATH  Google Scholar 

  10. Hayat, T., Kara, A.H., Momoniat, E.: Exact flow of a third grade fluid on a porous wall. Int. J. Non-Linear Mech. 38, 1533–1537 (2003)

    Article  MATH  Google Scholar 

  11. Hayat, T., Kara, A.H.: Couette flow of a third grade fluid with variable magnetic field. Math. Comput. Model. 43, 132–137 (2006)

    Article  MATH  Google Scholar 

  12. Pakdemirli, M.: The boundary layer equations of third grade fluids. Int. J. Non-Linear Mech. 27, 785–793 (1992)

    Article  MATH  Google Scholar 

  13. Pakdemirli, M.: Boundary layer flow of power law fluids past arbitrary profiles. IMA J. Appl. Math. 50, 133–148 (1993)

    Article  MATH  Google Scholar 

  14. Yürüsoy, M.: Unsteady boundary layer flow of power law fluid on stretching sheet surface. Int. J. Eng. Sc. 44, 325–332 (2006)

    Article  Google Scholar 

  15. Siddiqui, A.M., Ahmed, M., Ghori, Q.K.: Thin film flow of non-Newtonian fluids on a moving belt. Chaos, Solitons Fractals (in press)

  16. Siddiqui, A.M., Mahmood, R., Ghori, Q.K.: Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder. Phys. Lett. A 352, 404–410 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Technology, Islamabad, H-8, Pakistan

    S. Asghar

  2. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    T. Hayat

  3. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

    A. H. Kara

Authors
  1. S. Asghar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. H. Kara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. H. Kara.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Asghar, S., Hayat, T. & Kara, A.H. Exact solutions of thin film flows. Nonlinear Dyn 50, 229–233 (2007). https://doi.org/10.1007/s11071-006-9153-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-006-9153-6

Keywords

Search

Navigation