A256522 Decimal expansion of the dimensionless Blasius coefficient 0.332... in the formula for the shear stress on a flat plate in a boundary layer flow.
3, 3, 2, 0, 5, 7, 3, 3, 6, 2, 1, 5, 1, 9, 6, 2, 9, 8, 9, 3, 7, 1, 8, 0, 0, 6, 2, 0, 1, 0, 5, 8, 2, 9, 6, 6, 5, 4, 7, 0, 9, 3, 5, 6, 1, 4, 1, 2, 6, 7, 9, 8, 1, 8, 1, 0, 0, 4, 4, 7, 5, 6, 4, 0, 1, 9, 8, 7, 2, 4, 1, 7, 4, 0, 1, 8, 0, 6, 4, 4, 0, 5, 0, 7, 0, 4, 9, 0, 7, 3, 1, 8, 5, 5, 1, 4, 6, 3, 6, 8
Offset: 0
Examples
0.332057336215196298937180062010582966547093561412679818100447564...
Links
- Asaithambi Asai, Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients, J. Comput. Appl. Math. 176 (2005), 203-214.
- Heinrich Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. u. Physik 56 (1908), 1-37.
- Heinrich Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. u. Physik 56 (1908), 1-37 [English translation by J. Vanier on behalf of the National Advisory Committee for Aeronautics (NACA), 1950].
- John P. Boyd, The Blasius function in the complex plane, Experimental Mathematics 8(4) (1999), 381-394.
- Stephen Childress, An Introduction to Theoretical Fluid Dynamics, p. 124.
- V. P. Varin, A solution to Blasius problem, Computational Mathematics and Mathematical Physics 54(6) (2014), 1025-1036. [The author gives rational approximations to the constant.]
- Wikipedia, Blasius boundary layer.
Programs
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Mathematica
m = 24; digits = 100; g = NDSolveValue[1/2*G[eta]*G''[eta] + G'''[eta] == 0 && G[0] == 0 && G'[0] == 0 && G''[0] == 1, G, {eta, 0, m}, WorkingPrecision -> 2 digits, Method -> "StiffnessSwitching"]; b = g'[m]^(-3/2); RealDigits[b, 10, digits][[1]] (* updated Sep 18 2016 *)
Formula
b = g'(oo)^(-3/2) where g is the solution to the o.d.e. (1/2)*g*g'' + g''' = 0, with g(0) = g'(0) = 0 and g''(0) = 1 (a variant of the Blasius equation (1/2)*f*f'' + f''' = 0).
Extensions
Extended to 100 digits by Jon E. Schoenfield (private email) then confirmed with Mathematica by Jean-François Alcover, Sep 18 2016