On the polynomial approximation of boundary-layer flow profiles

The behaviour of the polynomial approximation to the boundary layer velocity profile is investigated. Various orders of polynomials and 4 different schemes of “reasonable” boundary conditions are examined for applicability as approximate solutions to the Blasius flow over a flat plate. A variational formulation, based upon the local potential is used to obtain the solution. It is found that the best and most consistent results are obtained when a symmetric distribution of auxiliary boundary conditions on the wall and outer edge of the boundary layer is used. The 6th order polynomial of this type, for example, already gives a wall friction factor within 0.5% of the exact solution.