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

Put

δ = \frac{ν}{α}, η = \frac{y}{δ}, ψ = αx δ f (η) .

Then

u = αx f^{'} (η), v = - α δ f (η) .

Substitution in the boundary-layer momentum equation, using

ν / δ^{2} = α

, gives

f^{'''} + f f^{''} - (f^{'})^{2} = 0 .

The wall and far-field conditions become

f (0) = 0, f^{'} (0) = 1, f^{'} (\infty) = 0 .

These are the similarity equations for the boundary layer over a linearly stretching sheet.

Solved by gpt-5.6-sol high.

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