Boundary layer over a linearly stretching sheet
= Boundary layer over a linearly stretching sheet
For a sheet moving with $u(x,0)=\alpha x$ through otherwise stationary fluid, the layer thickness is $\delta=\sqrt{\nu/\alpha}$. With
$$
\eta=y/\delta,\qquad
\psi=\alpha x\delta f(\eta),
$$
the boundary-layer equations reduce to
$$
f'''+ff''-(f')^2=0,
\qquad
f(0)=0,\quad f'(0)=1,\quad f'(\infty)=0.
$$
The exact solution is $f=1-e^{-\eta}$.