Second order boundary-layer solutions for the stagnation flow of a circular cylinder

In case of finite Reynolds number, second-order solutions of the boundary-layer equation for the flow over a circular cylinder with separated wake are investigated in the vicinity of the stagnation point. The second-order effects for wall shear stress due to the curvature of the cylinder and the displacement of main flow are discussed by introducing the method for higher order boundary-layer solutions developed by Van Dyke (1962). As a result, it is shown that the wall shear stress decreases proportionally to the Reynolds number raised to the minus one-half power and that the effect of curvature amounts to 75 percent of the decreasing rate. Moreover, a new accurate method for solution of first order boundary-layer equation is proposed.