A Karman-Pohlhausen type approximate method for solving second order boundary layer equations

In this paper a Karman-Pohlhausen type method is developed for approximately solving the incompressible two-dimensional second order boundary layer equations, by expanding all the variables (momentum and displacement thickness, etc.) in an asymptotic series in powers of inverse square root of Reynolds number. To the first order we recover back the well known Karman-Pohlhausen method. Solutions are worked out for a few particular cases in longitudinal curvature problem corresponding to which similarity solutions exist. The results obtained thus not only compare well with the exact solutions but also are fairly insensitive to the order of polymonial approximation adopted for the velocity profiles. It is shown finally, but taking a simple example, that depending on its gradient even a positive curvature can lead to a positive increment to skin friction (in contrary to the usual notion).