Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 39C / b / iii / Solution

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 $f=1-e^{-\eta}$.


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 Incoming links: Boundary layer over a linearly stretching sheet