zbMATH — the first resource for mathematics

Boundary layer growth on a flat plate with suction or injection. (English) Zbl 1230.76017
Summary: Exact solutions of the Navier-Stokes equations are obtained for the boundary layer growth on an infinite flat plate with uniform suction or injection (with velocity $$V$$ normal to its plane) which is started at time $$t=0$$ (with velocity $$U$$ along its plane), for the two cases: i) $$U=$$arbitrary, $$V=$$const and ii) $$U\propto t^{\alpha}$$, $$V\propto t^{-1/2}$$. i) gives simple relations between the cases of suction and injection and ii) gives similar velocity profiles. Rayleigh’s problem ($$U=$$const) is investigated in detail, and the resulting solutions show the same qualitative natures as the corresponding steady flow solutions for an semi-infinite flat plate so far obtained.

MSC:
 76D10 Boundary-layer theory, separation and reattachment, higher-order effects
Full Text: