Review of Falkner–Skan Transformation for Fluid Laminar Free Convection

  • De-Yi Shang
Part of the Heat and Mass Transfer book series (HMT)


In this chapter, the traditional Falkner–Skan type transformation for laminar free convection boundary layer is reviewed. The typical two-dimensional basic conservation equations for laminar free convection boundary layer are taken as example for derivation of the related similarity variables for Falkner–Skan type transformation. By means of the stream function and the procedure with the method of group theory, the similarity intermediate function variable \(f(\eta )\) is induced. Then, the velocity components are transformed to the related functions with the similarity intermediate function variable (\(f\eta )\). On this basis, partial differential momentum equation of the free convection boundary layer is transformed to related ordinary equation. At last, the limitations of the Falkner–Skan type transformation are analyzed in detail.


Stream Function Differential Momentum Equation Free Convection Boundary Layer Governing Partial Differential Equation Laminar Free Convection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    V.M. Falkner, S.W. Skan, Some approximate solutions of the boundary layer equations. Phil. Mag. 12, 865 (1931)Google Scholar
  2. 2.
    E.M. Sparrow, J.L. Gregg, The variable fluid property problem in free convection. Trans. ASME 80, 879–886 (1958)Google Scholar
  3. 3.
    B. Gebhart, Natural convection flow, instability, and transition. J. Heat Transfer 91, 293–309 (1969)CrossRefGoogle Scholar
  4. 4.
    E.R.G. Eckert, R.M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972)Google Scholar
  5. 5.
    H. Schlichting, Boundary Layer Theory (trans: J. Kestin) (McGraw-Hill, New York, 1979), pp. 316–317Google Scholar
  6. 6.
    D.D. Gray, A. Giogini, The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 19, 545–551 (1977)CrossRefGoogle Scholar
  7. 7.
    A.M. Clausing, S.N. Kempka, The influences of property variations on natural convection from vertical surfaces. J. Heat Transfer 103, 609–612 (1981)CrossRefGoogle Scholar
  8. 8.
    T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer (Springer, New York, 1984)Google Scholar
  9. 9.
    T. Fujii, Theory of Laminar Film Condensation (Springer, New York, 1991)Google Scholar
  10. 10.
    B. Louis et al., Convective Heat Transfer, 2nd edn. (Wiley, New York, 1993)Google Scholar
  11. 11.
    S. Kakac, Y. Yenner, Convective Heat Transfer, 2nd edn. (CRC Press, Boca Raton, 1995)Google Scholar
  12. 12.
    A. Bejan, Convection Heat Transfer, 2nd edn. (Wiley, New York, 1995)Google Scholar
  13. 13.
    I. Pop, D.B. Ingham, Convective Heat transferMathematical and Computational Modelling of Viscous Fluids and Porous Media (Elsevier, Amsterdam, 2001)Google Scholar
  14. 14.
    T. Cebeci, Convective Heat Transfer 2nd edn. (Springer, Heidelberg, 2002)Google Scholar
  15. 15.
    A.G. Hansen, Similarity analysis of boundary value problems in engineering (Presentice-Hall, Englewood Cliffts, 1964)Google Scholar
  16. 16.
    T.Y. Na, Computational methods in engineering boundary value problems (Academic, New York, 1979)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.OttawaCanada

Personalised recommendations