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

0,1

Links

Table of n, a(n) for n=0..99.

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.

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).

Example

0.332057336215196298937180062010582966547093561412679818100447564...

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 *)

Crossrefs

Sequence in context: A114187 A016037 A106449 * A097278 A254411 A056223

Adjacent sequences: A256519 A256520 A256521 * A256523 A256524 A256525

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 01 2015

Extensions

Extended to 100 digits by Jon E. Schoenfield (private email) then confirmed with Mathematica by Jean-François Alcover, Sep 18 2016

Status

approved