The “missing” similarity boundary-layer flow over a moving plane surface

Abstract.

The m = -1 case of the 2-D boundary-layer flows induced by continuous permeable plane surfaces issuing from a linear slot at x = 0 and stretching towards $x = + \infty$ with a power-law velocity $U_w(x) = C \cdot x^m$ is considered. The characteristics of this self-similar flow which, according to the usual reduction procedure of pseudo-similarity to full similarity, should not exist at all, are analyzed in detail. It is shown that the flow only exists if a lateral suction with a sufficiently large suction parameter $\gamma\ge\gamma_{\min} = 1.079131$ is applied. For the threshold value $\gamma_{\min}$ the solution is unique but above it multiple solutions are encountered for every given value of $\gamma$.