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Some perturbation solutions in laminar boundary layer theory Part 2. The energy equation

Published online by Cambridge University Press:  28 March 2006

Herbert Fox  and
Paul A. Libby
Herbert Fox
Affiliation:
Polytechnic Institute of Brooklyn
Paul A. Libby
Affiliation:
Polytechnic Institute of Brooklyn
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Abstract

Solutions for two types of problems involving the energy equation for flows with velocities described by the Blasius solution are presented. The first type arises in flows with arbitrary initial distributions of stagnation enthalpy and with surfaces downstream of the initial station either with constant wall enthalpy or with zero heat transfer. Exact solutions in these cases are obtained for constant ρμ, and Prandtl number of unity; they are given in terms of complete orthogonal sets of functions which can be used to obtain first- and higher-order corrections for the effects of variable ρμ, non-unity Prandtl number, and deviations of the velocity field from that described by the Blasius solution.

The second type of problem pertains to flows with power-law descriptions of the wall enthalpy. Again the basic solutions are obtained for Prandtl number of unity and the effect of non-unity Prandtl number is treated as a perturbation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 3 , July 1964 , pp. 433 - 451
Copyright
© 1964 Cambridge University Press

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References

Baron, J. R. 1956 The binary-mixture boundary layer associated with mass transfer cooling at high speeds. Massachusetts Institute of Technology, Naval Supersonic Lab. TR 160.
Chapman, D. R. & Rubesin, M. W. 1949 Temperature and velocity profiles in the compressible laminar boundary layer with arbitrary distribution of surface temperature. J. Aero. Sci. 16, 547.Google Scholar
Durgin, F. H. 1959 An experiment on the insulating properties of boundary layers. Massachusetts Institute of Technology DSR No. 7509, AFOSR TN 57-392, AD 132467.
Eckert, E. R. G. 1950 Introduction to the Transfer of Heatt and Mass, Ist Ed. New York: McGraw-Hill Book Company, Inc.
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory, Applied Mathematics and Mechanics, vol. 5. New York: Academic Press.
Howe, J. T. 1959 Some finite difference solutions of the laminar compressible boundary layer showing the effects of upstream transpiration cooling. NASA Memo, no. 2-26-59A.Google Scholar
Lees, L. 1956 Laminar heat transfer over blunt-nosed bodies at hypersonic speeds. Jet Propulsion, 26, 259.Google Scholar
Libby, P. A. & Fox, H. 1963 Some perturbation solutions in laminar boundary layer theory. Part 1. The momentum equation. J. Fluid Mech. 17, 433.Google Scholar
Libby, P. A. & Morduchow, M. 1954 Method for calculation of compressible laminar boundary layer with axial pressure gradient and heat transfer. NACA TN, no. 3157.Google Scholar
Lighthill, M. J. 1950 Contributions to the theory of heat transfer through a laminar boundary layer. Proc. Roy. Soc. A. 202, 359.Google Scholar
Low, G. M. 1955 The compressible laminar boundary layer with fluid injection. NACA TN, no. 3404.Google Scholar
Pallone, A. 1961 Non-similar solution of the compressible-laminar-boundary-layer equations with application to the upstream-transpiration cooling problem. J. Aero. Sci. 28, 449.Google Scholar
Schlichting, H. 1955 Boundary Layer Theory, pp. 264–268. New York: McGraw-Hill Book Company, Inc.
Tifford, A. N. & Chu, S. T. 1953 Heat transfer and frictional effects in laminar boundary layers. Part I. Wedge Analyses. WADC TR no. 53-288.Google Scholar
Tribus, M. & Klein, J. 1952 Forced convection from nonisothermal surfaces. Heat Transfer, pp. 211–235. Engineering Research Institute, University of Michigan.