Skip to main content
SpringerLink
Log in

Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall heat flux case

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A theoretical study of the heat transfer in the unsteady thermal boundary layer associated with the forced convection flow past a sharp, semi-infinite wedge that is started impulsively from rest and for which the constant heat flux at the walls is suddenly changed is presented in this paper. The velocity far from the wedge is given by u e (x) = x m, where x is the coordinate measured along the wedge and m is a constant. Using appropriate non-dimensional transformations, the number of independent variables in the governing boundary-layer equations is reduced from three to two. These equations are then solved numerically for both small (initial) and large (steady-state) times. It is found that for the steady-state flow the Blasius-like solutions exist for each value of m in the range m* ≤ m < ∞, where m* is the value of the power law exponent m that corresponds to a self-similar solution profile with vanishing skin friction.

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. Goldstein S., Rosenhead L.: Boundary-layer growth. Proc. Camb. Phil. Soc. 32, 392–401 (1936)

    Article  MATH  Google Scholar 

  2. Square L.C.: Boundary-layer growth in three dimensions. Phil. Mag. 45, 1272–83 (1954)

    MathSciNet  Google Scholar 

  3. Riley N.: Unsteady laminar boundary layers. SIAM Rev. 17, 274–97 (1975)

    Article  MATH  Google Scholar 

  4. Riley N.: Unsteady viscous flows. Sci. Progress Oxford 74, 361–77 (1990)

    Google Scholar 

  5. Telionis D.R.: Review—Unsteady boundary layers, separated and attached. J. Fluids Eng. 101, 29–43 (1979)

    Google Scholar 

  6. Telionis D.R.: Unsteady Viscous Flows. Springer, New York (1981)

    MATH  Google Scholar 

  7. Ludlow D.K., Clarkson P.A., Bassom A.P.: New similarity solutions of the unsteady incompressible boundary-layer equations. Q. J. Mech. Appl. Math. 53, 175–206 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Pop, I.: Transient heat transfer in boundary-layer flows. In Padet, J., Arinç, F. (eds), Proc. Int. Symposium on Transient Convective Heat Transfer, Cesme, Turkey, August 19–23, pp. 3–17. Begell House, New York (1996)

  9. Watkins C.B. Jr: Unsteady heat transfer in impulsive Falkner–Skan flows. Int. J. Heat Mass Transfer 19, 395–403 (1976)

    Article  MATH  Google Scholar 

  10. Tsay S.-Y., Shih Y.-P.: Laminar forced convection in wedge flow with separation. J. Chinese Inst. Eng. 2, 53–7 (1979)

    Google Scholar 

  11. Bhattacharyya S., Gupta A.S.: Transient compressible boundary layer on a wedge impulsively set into motion. Arch. Appl. Mech. 66, 336–42 (1996)

    MATH  Google Scholar 

  12. Harris S.D., Ingham D.B., Pop I.: Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall temperature case. Eur. J. Mech. B Fluids 21, 447–68 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Stewartson K.: On the impulsive motion of a flat plate in a viscous fluid. Q. J. Mech. Appl. Math. 4, 182–98 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  14. Smith S.H.: On the impulsive flow of a viscous liquid past a semi-infinite flat plate. SIAM J. Appl. Math. 22, 148–54 (1972)

    Article  MATH  Google Scholar 

  15. Lin H.-T., Lin L.-K.: Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int. J. Heat Mass Transfer 30, 1111–18 (1987)

    Article  Google Scholar 

  16. Heeg R.S., Dijkstra D., Zandbergen P.J.: The stability of Falkner–Skan flows with several inflection points. Z. Angew. Math. Phys. (ZAMP) 50, 82–93 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Stewartson K.: Further solutions of the Falkner–Skan equation. Proc. Camb. Phil. Soc. 50, 454–65 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hartree D.R.: On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer. Proc. Camb. Phil. Soc. 33, 223–39 (1937)

    Article  Google Scholar 

  19. Banks W.H.H., Drazin P.G.: Perturbation methods in boundary-layer theory. J. Fluid Mech. 58, 763–75 (1973)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rock Deformation Research, School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK

    S. D. Harris

  2. Centre for Computational Fluid Dynamics, University of Leeds, Leeds, LS2 9JT, UK

    D. B. Ingham

  3. Faculty of Mathematics, University of Cluj, CP 253, 3400, Cluj, Romania

    I. Pop

Authors
  1. S. D. Harris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. B. Ingham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Pop
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. D. Harris.

Additional information

Dedicated to Professor Wilhelm Schneider on the occasion of his 70th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Harris, S.D., Ingham, D.B. & Pop, I. Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall heat flux case. Acta Mech 201, 185–196 (2008). https://doi.org/10.1007/s00707-008-0081-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-008-0081-z

Keywords

Search

Navigation