The turbulent boundary layer with variable Prandtl number

  • E. R. van Driest


The general theory for the solution of the energy equation for laminar boundary layers with variable Prandtl number is applied directly to the turbulent case in order to extend the von Kàrmàn analogy between heat transfer and fluid friction to include a turbulence Prandtl number other than unity and a realistic shear distribution other than constant across the turbulent portion of the boundary layer.

The calculation of heat-transfer coefficients for high and low speeds is discussed. The general heat-transfer theory is compared with data for the supersonic flow of air over a flat plate in a wind tunnel.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Van Driest, E. R.: The Laminar Boundary Layer with Variable Fluid Properties. Presented at the 1954 Heat Transfer and Fluid Mechanics Institute, Berkeley, June 30, July 1–2, 1954.Google Scholar
  2. [2]
    Van Driest, E. R.: Turbulent Boundary Layer in Compressible Fluids. Jour. Aero. Sci., Vol. 18, No. 3, March, 1951.Google Scholar
  3. [3]
    Nikuradse, J.: Gesetzmäßigkeiten der turbulenten Strömung in glatten Rohren, VDI Forschungsheft 356, 1932.zbMATHGoogle Scholar
  4. [4]
    von Kármán, Th.: The Analogy Between Fluid Friction and Heat Transfer. Trans. ASME, Vol. 61, No. 11, November, 1939.Google Scholar
  5. [5]
    Schubauer, G. B., and Klebanoff, P. S.: Investigation of Separation of the Turbulent Boundary Layer. NACA TN 2133, August, 1950.Google Scholar
  6. [6]
    Stine, Howard A., and Scherrer, Richard: Experimental Investigation of the Turbulent Boundary Layer Temperature Recovery Factor on Bodies of Revolution at Mach Numbers from 2.0 to 3.8. NACA TN 2664, March, 1952.Google Scholar
  7. [7]
    Ross, Albert O.: Determination of Boundary Layer Transition Reynolds Numbers by Surface-Temperature Measurement of a 10° Cone in Various NACA Supersonic Wind Tunnels. NACA TN 3020, October, 1953.Google Scholar
  8. [8]
    Shoulberg, R. H., Hill, J. A. F., and Rivas, Jr., M. A.: An Experimental Determination of Flat Plate Recovery Factors for Mach Numbers Between 1.90 and 3.14. Wind Tunnel Report No. 36, Naval Supersonic Laboratory, Massachusetts Institute of Technology, May, 1952.Google Scholar
  9. [9]
    Coles, Donald: Direct Measurement of Supersonic Skin Friction. Readers’ Forum, Jour. Aero. Sci., Vol. 19, No. 10, October, 1952.Google Scholar
  10. [10]
    NBS-NACA Tables of Thermal Properties of Gases. National Bureau of Standards, U.S. Department of Commerce.Google Scholar
  11. [11]
    Wilson, Robert E.: Turbulent Boundary-Layer Characteristics at Supersonic Speeds-Theory and Experiment. Jour. Aero. Sci., Vol. 17, No. 9, September, 1950.Google Scholar
  12. [12]
    Shoulberg, R. H., et al: An Experimental Investigation of Flat Plate Heat Transfer Coefficients at Mach Numbers of 2, 2.5, and 3 for a Surface Temperature to Stream Total Temperature Ratio of 1.18. Wind Tunnel Report No. 39, Naval Supersonic Laboratory, Massachusetts Institute of Technology, June, 1953.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1955

Authors and Affiliations

  • E. R. van Driest
    • 1
  1. 1.North American Aviation, Inc.DowneyUSA

Personalised recommendations