Study on Stokes Flow Past Circular Cylinder in Two-Dimensional Channel

A two-dimensional Stokes flow past a circular cylinder in a channel is analyzed. The circular cylinder is located at the center of the channel, and a plane Poiseuille flow exists upstream and downstream far from the circular cylinder. The Stokes approximation is used, and the flow is investigated analytically by using the eigenfunction expansion and the least square methods. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the circular cylinder and channel wall are calculated. The additional pressure drop induced by the circular cylinder and the force exerted on it are calculated as functions of the length of the radius of the circular cylinder. For a typical length of the radius of the circular cylinder, the streamline pattern and pressure distribution are shown