Laminar boundary layer in low Prandtl number flows with variable thermal properties on a flat plate
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The laminar boundary layer flow of a low Prandtl number fluid with arbitrary thermal properties past a flat plate is studied by the method of matched asymptotic expansions. By assuming power law relations for the viscosity, density and Prandtl number, the first order results for the skin friction, the recovery factor and the heat transfer rate at the wall are obtained. It turns out that the outer flow in the thermal boundary layer is governed by a simple nonlinear differential equation of second order, which is correct to all orders in Prandtl number. Exact and approximate solutions to this outer equation are obtained. Further, it is shown that the first order terms for the recovery factor are independent of the thermal properties, while the heat transfer terms have a complicated dependence. The skin friction result shows the dependence on thermal properties, Mach number and heat transfer rate.
KeywordsMach Number Prandtl Number Skin Friction Flat Plate Heat Transfer Rate
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- K. Stewartson,The Theory of Laminar Boundary Layer in Compressible Fluids, Oxford University Press (1964).Google Scholar
- P. A. Lagerstrom, Laminar Flow Theory,Theory of Laminar Flows, in High Speed Aerodynamics and Jet Propulsion, Vol. 4 edited by F. K. Moore, Princeton University Press (1964).Google Scholar
- C. F. Hansen,Approximations for the thermodynamic and transport properties of high temperature air, NASA Tech. Rep. R-50 (1959).Google Scholar
- M. Van Dyke,Perturbation Methods in Fluid Mechanics, Academic Press (1964).Google Scholar
- D. K. Edward and D. M. Tellep, Heat transfer in low Prandtl number flow with variable thermal properties,Am. Roc. Soc. jl., 31 (1961) 652–654.Google Scholar
- G. Kuerti, The Laminar boundary layer in compressible flow,Advances in Applied Mechanics, Vol. II, edited by R. Von Mises and T. Von Karman pp. 23–91. Academic Press, New York (1950).Google Scholar