On creeping flow over a cylinder rotating in presence of translating plane boundary
The creeping flow over a cylinder rotating in the presence of translating plane boundary has been analysed by using conformal mappings. The problem reduces to the solution of biharmonic equation with conditions for fluid velocity posed on the two lines bounding the domain. A closed-form mapping function is obtained which transforms the original infinite domain of solution onto an annulus. The solution of the problem, represented by two Goursat functions, is derived in a general form, consisting of Laurent series supplemented by proper logarithmic terms. The system of linear equations for the unknown coefficients of these functions is obtained by requiring that the boundary conditions are satisfied on both circles bounding the annulus, and then a pseudospectral method is applied for the determination of coefficients. The author shows that all the coefficients of Goursat functions -- except seven -- vanish, so that the functions represent an exact solution in the annular domain. As the mapping function is exact, the solution is also exact in the original infinite domain. Finally, the author presents streamline patterns corresponding to four characteristic sets of boundary conditions.
scientific article; zbMATH DE number 1491326