A new approach to the classical Stokes flow problem: Part II Series solutions and higher-order applications

AbstractThis is the second in a series of papers on the Stokes flow past an arbitrary axisymmetrical body. The truncated series solutions of the two infinite systems of simultaneous ordinary differential equations with variable coefficients are obtained for an arbitrary truncation order N. Each series solution together with logarithmic terms is shown to be convergent in the entire physical interval of interest. By the construction of the complete solutions of the systems, the corresponding hydrodynamical problem formulated in terms of the stream function has been solved. As a specimen numerical application, the drag on a prolate spheroid is computed and compared with the exact one. Highly accurate numerical results have been achieved depending on the b/a ratio of the spheroid