Use of a Transcendental Approximation in Laminar Boundary Layer Analysis

Abstract

The usefulness of an approximate boundary layer velocity profile which is an exponential function of an exponential function is examined. The momentum and energy integral equations for two-dimensional incompressible boundary layers are used to determine the parameters of the assumed profile for the classic example of wedge flows. The integrals involved are reduced to the exponential integral, which can be evaluated from existing tables. Comparison of the wall shear stress with Hartree's solution is remarkably good except near separation, and the agreement of the minimum critical Reynolds number with comparable results based upon Hartree's profiles is also very good. The profile function described here can be applied to further examples.

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