KARMAN–POHLHAUSEN METHOD: CRITICAL ANALYSIS AND NEW SOLUTIONS FOR THE BOUNDARY LAYER ON A PLANE PLATE

A generalized critical analysis of the main known polynomial solutions obtained for the velocity profi le of the fl uid fl ow in the laminar boundary layer on a plane plate with the use of the integral Karman–Pohlhausen method has been performed. The main reasons for the low accuracy of these solutions were revealed and ways of its increasing were determined. Effi cient schemes of calculating the parameters of the indicated boundary layer with minimum errors, in particular, a new trinomial polynomial, defi ning the velocity profi le of the fl uid fl ow in this layer, are proposed. A new solution of the problem on the boundary layer fl ow over a plane plate in the form of the fourth-degree (Sutton) polynomial gives an almost exact value of the friction stress of this fl ow with small errors in determining its displacement thickness (0.12%) and shape parameter (0.12%), and an analogous solution in the form of the seventhdegree (Mughal) polynomial provides a very high accuracy of approximation of the friction stress of the indicated fl ow with an almost zero error at negligible small errors in calculating its displacement thickness (0.04%) and shape parameter (0.03%) of this layer.
   
Author:  V. A. Kot
Keywords:  Karman–Pohlhausen method, boundary layer, Blasius equation, fl uid fl ow, plane plate, polynomial solutions, integral methods
Page:  1063