 Similarity solution for a sink-flow boundary layer

ID: similarity-solution-for-a-sink-flow-boundary-layer

Near a radial wall, let

x

measure distance from the sink along the wall and

y

point into the fluid. With

δ = x \frac{ν}{Q}, η = \frac{y}{δ}, ψ = ν Q f (η),

f^{'''} = 1 - (f^{'})^{2}, f (0) = f^{'} (0) = 0, f^{'} (\infty) = - 1.

One physical solution has

f^{'} (η) = \frac{5 - c o s h ( 2 η + c )}{1 + c o s h ( 2 η + c )}, c = arcosh 5.

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