POLYNOMIAL APPROXIMATION OF THE LAMINAR BOUNDARY LAYER ON A FLAT PLATE ON THE BASIS OF THE KARMAN MOMENTUM INTEGRAL

A new approach to the polynomial approximation of the laminar boundary layer on the surface of a fl at plate on the basis of the Karman momentum integral with the use of additional optimum constraints is proposed. The polynomial coeffi cients of a solution of the problem on this layer were determined for the fi rst time with the use of the system of zero boundary conditions for the surface of the plate and defi nite boundary conditions for the outer side of the boundary layer on it. Optimum polynomial solutions of the problem in the zero to twentieth approximations have been obtained. A solution of the problem obtained in the seventeenth approximation is almost identical to the high-accuracy numerical solution of the Blasius equation, obtained by B. D. Ganapol, with a maximum deviation of 6∙10^–7.
   
Author:  V. A. Kot
Keywords:  boundary layer, Blasius equation, integral methods, Karman momentum integral, Karman–Pohlhausen method
Page:  438