Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 38C / a

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- Solution a

Solution

With streamwise and normal velocities

u, v

, zero exterior pressure gradient gives the steady boundary-layer equations

u_{x} + v_{y} = 0, u u_{x} + v u_{y} = ν u_{yy} .

At the organism,

v (x, 0) = 0, ρ ν u_{y} (x, 0) = S x^{- 1/2},

and matching to the quiescent exterior requires

u (x, y) \to 0

y \to \infty

.

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