Low Reynolds number flow due to a rotating finned shaft in a cylinder
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A longitudinally finned shaft rotates inside a larger cylinder. At minute Reynolds numbers, the flow is governed by the biharmonic equation with mixed boundary conditions. The stream function is expressed in terms of the complete set of real eigenfunctions in cylindrical coordinates. The series coefficients are partially determined by collocation at the boundary. The flow and the torque are found as a function of the geometric parameters. The method illustrated would be useful for other problems (Stokes flow, plane elasticity, theory of plates) involving the biharmonic equation in cylindrical coordinates.
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