An exact solution to the problem of creeping flow around circular cylinder rotating in presence of translating plane boundary

Abstract

The problem of determination of steady, plane creeping flow around circular cylinder rotating with constant angular velocity in presence of plane boundary, translating with constant linear velocity — is investigated and solved in the paper by means of aspectral method. The original domain of solution is mapped conformally onto an auxiliary, annular one, wherein flow velocity, pressure, and other components of stress tensor are represented by twoGoursat's functions, which are sought for in form ofLaurent's series provided with the necessary logarithmic terms. It is shown, that all coefficients of these series-except seven-must vanish, if boundary conditions expressing impermeability and absence of slip have to be satisfiedsimultaneously at the cylinder and at the plane boundary. Finally, closed formulae for these coefficients are presented — as depending on two velocities defining the problem, and on three constants of the mapping function. The paper can be considered as a counterpart to a former one [1], wherein the problem was solvednumberically by means of apseudospectral method.