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The Blasius problem has been used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past a flat plate moving at a constant speed β and it is well known that there exists the critical value β ≥ β* and has no positive solution for β < β*. The known numerical result showsβ*. In this paper, by the study of the integral equation equivalent to the Blasius problem, we obtain the relation between the velocity function f′and the shear stress functions f′, upper and lower bounds of || f′||and a new lower bound of β*. In particular, 4√27/9 ≤||f′|| ≤ √3/3, β* > -045. Regarding β*, previous results presented a lower bound -0.5 and an upper bound -0.18733. © 2012 Yang et al.; licensee Springer.

On the shear stress function and the critical value of the Blasius problem