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Asymptotic expansions for laminar forced-convection heat and mass transfer Part 2. Boundary-layer flows

Published online by Cambridge University Press:  28 March 2006

J. D. Goddard  and
Andreas Acrivos
J. D. Goddard
Affiliation:
University of Michigan
Andreas Acrivos
Affiliation:
Stanford University
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Abstract

This is the second of two articles by the authors dealing with asymptotic expansions for forced-convection heat or mass transfer to laminar flows. It is shown here how the method of the first paper (Acrivos & Goddard 1965), which was used to derive a higher-order term in the large Péclet number expansion for heat or mass transfer to small Reynolds number flows, can yield equally well higher-order terms in both the large and the small Prandtl number expansions for heat transfer to laminar boundary-layer flows. By means of this method an exact expression for the first-order correction to Lighthill's (1950) asymptotic formula for heat transfer at large Prandtl numbers, as well as an additional higher-order term for the small Prandtl number expansion of Morgan, Pipkin & Warner (1958), are derived. The results thus obtained are applicable to systems with non-isothermal surfaces and arbitrary planar or axisymmetric flow geometries. For the latter geometries a derivation is given of a higher-order term in the Péclet number expansion which arises from the curvature of the thermal layer for small Prandtl numbers. Finally, some applications of the results to ‘similarity’ flows are also presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 2 , February 1966 , pp. 339 - 366
Copyright
© 1966 Cambridge University Press

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References

Acrivos, A. & Goddard, J. D. 1965 J. Fluid Mech. 23, 27.
Boussinesq, J. 1905 J. Math. Pures Appl. 1, 28.
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. (eds.) 1954 Higher Transcendental Functions, 3 vol. and Tables of Integral Transforms, 2 vol., Bateman Manuscript Project. New York: McGraw-Hill.
Levich, V. G. 1962 Physicochemical Hydrodynamics (translated from the Russian). Englewood Cliffs, New Jersey: Prentice-Hall.
Lighthill, M. J. 1950 Proc. Roy. Soc., A 202, 269.
Meksyn, D. 1961 New Methods in Laminar Boundary Layer Theory. New York: Pergamon Press.
Merk, H. J. 1959 J. Fluid Mech. 5, 46.
Morgan, G. W., Pipkin, A. C. & Warner, W. H. 1958 J. Aero. Sci. 25, 17.
Proudman, I. & Pearson, J. R. A. 1957 J. Fluid Mech. 2, 23.
Schlichting, H. 1955 Boundary Layer Theory. New York: Pergamon Press.
Sutton, W. G. L. 1943 Proc. Roy. Soc., A 182, 48.
Taylor, T. D. & Acrivos, A. 1964 J. Fluid Mech. 18, 46.