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.


34B40 Boundary value problems on infinite intervals for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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[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
[4] Goldstein, S., Modern developments in fluid dynamics, (1938), Clarendon Press Oxford
[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
[6] He, J., Approximate analytic solution of blasius’ equation, Commun nonlinear sci numer simulat, 3, 260-263, (1998) · Zbl 0918.34016
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