Skip to main content
SpringerLink
Log in

Accelerated slip flow past a cylinder

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

This study deals with boundary layer flow along the entire length of a stationary semi-infinite cylinder under a steady, accelerated free-stream. Considering flow at reduced dimensions, the no-slip boundary condition is replaced with a Navier boundary condition. Asymptotic series solutions are obtained for the shear stress coefficient in terms of the Bingham number that corresponds to prescribed values of both the slip coefficient and the index of acceleration. By investigating motion at small and large axial distances, the series solutions are presented. For flow in the intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the shear stress along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.

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. Navier C.L.M.H.: Mémoire sur les lois du mouvement des fluides. Mém. Acad. Roy. Sci. Inst. France 6, 389–440 (1823)

    Google Scholar 

  2. Maxwell J.C.: On stresses in rarefied gases arising from inequalities of temperature. Philos. Trans. R. Soc. Lond. 170, 231–256 (1879)

    Article  Google Scholar 

  3. Goldstein S.: Modern Developments in Fluid Dynamics vol II, pp. 676–680. Dover Publications, NY (1965)

    Google Scholar 

  4. Matthews M.T., Hill J.M.: Nanofluidics and the Navier boundary condition. Int. J. Nanotechnol. 5(2/3), 218–242 (2008)

    Article  Google Scholar 

  5. Tabelling P.: Introduction to Microfluidics. Oxford University Press, Oxford (2005)

    Google Scholar 

  6. Gad-el-Hak M.: The fluid mechanics of microdevices—The freeman scholar lecture. J. Fluids Eng. 121(3), 5–53 (1999)

    Article  Google Scholar 

  7. DuPont Donaldson, C.: An approximate method for estimating the incompressible laminar boundary layer characteristics on a flat plate in slipping flow. NACA RM No L9C02 (1949)

  8. Fang T., Lee C.F.: A moving wall boundary layer flow on a slightly rarefied gas stream over a moving plate. Appl. Math. Lett. 18(5), 487–495 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Laurmann J.A.: Linearised slip flow past a semi infinite plate. J. Fluid Mech. 11, 82–96 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  10. Martin, M.J., Boyd, I.D.: Blasius boundary layer solution with slip flow conditions. In: Rarefied Gas Dynamics: 22nd International Symposium AIP Conference Proceeding, vol. 585–1, pp. 518–523. (2001)

  11. Murray J.D.: Incompressible viscous flow past a semi-infinite flat plate. J. Fluid Mech. 21, 337–344 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang C.Y.: Stagnation flows with slip: exact solutions of the Navier-Stokes equations. Z. Angew. Math. Phys. 54(1), 184–189 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Matthews M.T., Hill J.M.: Flow around nanospheres and nanocylinders. Q. Jl Mech. Appl. Math. 59(2), 191–210 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Spurk J.H.: Fluid Dynamics. Springer-Verlag, Berlin (1997)

    MATH  Google Scholar 

  15. Crane L.J.: Boundary layer flow on a circular cylinder moving in a fluid at rest. Z. Angew. Math. Phys. 23, 201–212 (1972)

    Article  MATH  Google Scholar 

  16. Glauert M.B., Lighthill M.J.: The axisymmetric boundary layer on a long thin cylinder. Proc. R. Soc. 230A, 188–203 (1955)

    MathSciNet  Google Scholar 

  17. Stewartson K.: The asymptotic boundary layer on a circular cylinder in axial incompressible flow. Q. J. Appl. Math. 13, 113–122 (1955)

    MATH  MathSciNet  Google Scholar 

  18. Crane, L.J., McVeigh, A.G.: Slip flow on a microcylinder. Z. Angew. Math. Phys. (2009). doi:10.1007/s00033-009-0019-x

Download references

Author information

Authors and Affiliations

  1. Institute for Numerical Computation and Analysis, 7-9 Dame Court, Dublin 2, Ireland

    L. J. Crane & A. G. McVeigh

Authors
  1. L. J. Crane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. G. McVeigh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. G. McVeigh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crane, L.J., McVeigh, A.G. Accelerated slip flow past a cylinder. Z. Angew. Math. Phys. 62, 365–376 (2011). https://doi.org/10.1007/s00033-010-0094-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00033-010-0094-z

Mathematics Subject Classification (2000)

Keywords

Search

Navigation