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Laminar forced-convection at small Prandtl numbers

Laminare erzwungene Konvektion bei kleinen Prandtl-Zahlen

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Summary

Through the direct use of displacement thickness a first-order correction to the general solution ofParlange, obtained for vanishing Prandtl number, is presented. The general solutions are applied to wedge flows with wall temperature or wall heat flux varying as a power of the distance from the leading edge. Data for some special cases are given. It is shown that the present small Prandtl number approximation is simple, explicit, and capable of yielding sufficiently accurate results for practical applications.

Zusammenfassung

Eine Korrektur der vonParlange für verschwindende Prandtl-Zahlen angegebenen allgemeinen Lösung wird durch direkte Verwendung der Verdrängungsdicke erzielt. Die allgemeinen Resultate werden auf die Strömung um einen Keil angewendet, wobei Wandtemperatur oder Wärmefluß an der Wand als Potenz des Abstandes von der Vorderkante angesetzt wird. Für einige Spezialfälle werden numerische Werte angegeben. Es wird gezeigt, daß diese Näherung für kleine Prandtl-Zahlen einfach ist und für praktische Zwecke hinreichend genaue explizite Ergebnisse liefert.

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References

  1. Schlichting, H.: Boundary-Layer Theory, 6th ed., p. 270, New York: McGraw-Hill. 1968.

    Google Scholar 

  2. Riley, N.: Unsteady heat transfer for flow over a flat plate. J. Fluid Mech.17, 97 (1963).

    Google Scholar 

  3. Boussinesq, J.: Calcul du pouvoir refroidissant des courant fluids. J. Math. Pures Appl.1, 285 (1905).

    Google Scholar 

  4. Morgan, G. W., A. C. Pipkin, andW. H. Warner: On heat transfer in laminar boundary-layer flows of liquids having a very small Prandtl number. J. Aero. Sci.25, 173 (1958).

    Google Scholar 

  5. Goddard, J. D., andA. Acrivos: Asymptotic expansions for laminar forced convection heat and mass transfer. J. Fluid Mech.24, 339 (1966).

    Google Scholar 

  6. Merk, H. J.: Rapid calculations for boundary-layer transfer using wedge solutions and asymptotic expansions. J. Fluid Mech.5, 460 (1959).

    Google Scholar 

  7. Evans, H. L.: Laminar Boundary-Layer Theory, p. 83. Reading, Mass.: Addison-Wesley. 1968.

    Google Scholar 

  8. Parlange, J.-Y.: Thermal boundary-layer similarity at limiting Prandtl numbers. AIAA J.8, 574 (1970).

    Google Scholar 

  9. Ince, E. L.: Ordinary Differential Equations, p. 188, New York: Dover. 1956.

    Google Scholar 

  10. Erdélyi, A., et al.: Tables of Integral Transforms, p. 139. New York: McGraw-Hill. 1954.

    Google Scholar 

  11. Elzy, E., andR. M. Sisson: Table of Similar Solutions to the Equations of Momentum, Heat and Mass Transfer in Laminar Boundary Layer Flow. Eng. Exp. Station Bulletin No. 40, Corvallis, Oregon: Oregon State Univ. 1967.

    Google Scholar 

  12. Chen, J. L. S., andB. T. Chao: Thermal Response Behavior of Laminar Boundary Layers in Wedge Flow. Int. J. Heat Mass Transfer13, 1101 (1970).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Pittsburgh, 15213, Pittsburgh, PA, USA

    J. L. S. Chen

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  1. J. L. S. Chen
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Chen, J.L.S. Laminar forced-convection at small Prandtl numbers. Acta Mechanica 17, 315–322 (1973). https://doi.org/10.1007/BF01183764

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  • DOI: https://doi.org/10.1007/BF01183764

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