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An approximate compact analytical expression for the Blasius velocity profile. (English) Zbl 1351.34026

Summary: A single-term, two-parameter, hyperbolic tangent function is presented to describe the flow profiles in the Blasius boundary layer, which reproduces the streamwise velocity profile within 0.003 (0.3% of free stream velocity) of its numerical exact solution throughout the flow. The function can be inverted for an implicit description of the velocity profile.

MSC:

34B40 Boundary value problems on infinite intervals for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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References:

[1] Blasius, H., Grenzschichten in flüssigkeiten mit kleiner reibung, Z math phys, 56, 1-37, (1908), [English translation NACA-TM-1256, 1950] · JFM 39.0803.02
[2] Schlichting, H., Boundary-layer theory, (1979), McGraw-Hill New York
[3] Liao, S.-J., An explicit, totally analytic approximate solution for blasius’ viscous flow problems, Int J non-linear mech, 34, 759-778, (1999) · Zbl 1342.74180
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[5] Howarth, M.A., On the solution of the laminar boundary layer equations, Proc R soc ser A, 164, 547-579, (1938) · JFM 64.1452.01
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