Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using the Padé approximation technique

Abstract

Following the asymptotic series solution of Seban & Bond [1], this paper evaluates the shear stress on the surface of a circular cylinder of radius a at rest in a fluid moving with steady velocity U0 parallel to the axis of the cylinder. The boundary layer builds up from the front of the cylinder and its thickness increases with increasing ξ, where ξ is a non‐dimensional variable representing axial distance from the front of the cylinder. The Seban & Bond solution is valid for small ξ only, near the front of the cylinder where the boundary layer thickness is small compared with a. Curle [2] extended the Seban & Bond results, thus making them valid for larger ξ. Glauert & Lighthill [3] used an asymptotic series to solve the problem in the region where ξ is large. They also used an approximate Pohlhausen method valid for small and large ξ. It is the purpose of this paper to extend the results given by the exact asymptotic series of Seban & Bond so that they are valid for both small and large ξ. This will be done using a Padé approximation technique, which will be compared with the historical results above. It will be seen that the region of validity of the series solution is extended without the need for Curle's extensive analysis and interpolation as in the other cases.