%I #29 May 20 2023 23:16:23
%S 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,
%T 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,
%U 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
%N 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.
%H Asaithambi Asai, <a href="http://dx.doi.org/10.1016/j.cam.2004.07.013">Solution of the Falkner-Skan equation by recursive evaluation of Taylor coefficients</a>, J. Comput. Appl. Math. 176 (2005), 203-214.
%H Heinrich Blasius, <a href="https://iris.univ-lille.fr/handle/1908/2024">Grenzschichten in Flüssigkeiten mit kleiner Reibung</a>, Z. Math. u. Physik 56 (1908), 1-37.
%H Heinrich Blasius, <a href="http://naca.central.cranfield.ac.uk/reports/1950/naca-tm-1256.pdf">Grenzschichten in Flüssigkeiten mit kleiner Reibung</a>, Z. Math. u. Physik 56 (1908), 1-37 [English translation by J. Vanier on behalf of the National Advisory Committee for Aeronautics (NACA), 1950].
%H John P. Boyd, <a href="https://projecteuclid.org/euclid.em/1047262359">The Blasius function in the complex plane</a>, Experimental Mathematics 8(4) (1999), 381-394.
%H Stephen Childress, <a href="http://www.math.nyu.edu/faculty/childres/fluidsbook.pdf">An Introduction to Theoretical Fluid Dynamics</a>, p. 124.
%H V. P. Varin, <a href="https://doi.org/10.1134/S096554251406013X">A solution to Blasius problem</a>, Computational Mathematics and Mathematical Physics 54(6) (2014), 1025-1036. [The author gives rational approximations to the constant.]
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Blasius_boundary_layer">Blasius boundary layer</a>.
%F 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).
%e 0.332057336215196298937180062010582966547093561412679818100447564...
%t 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 *)
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Apr 01 2015
%E Extended to 100 digits by _Jon E. Schoenfield_ (private email) then confirmed with Mathematica by _Jean-François Alcover_, Sep 18 2016