Asymptotic solution of a boundary layer suction problem

Abstract

The theory of the boundary layer on a flat plate in a uniform stream with a velocity of suction proportional to xpower-1/2 (x being the distance from the leading edge of the plate), has been developed by Thwaites a in a report which contains numerical solutions of the problem obtained on the differential analyser. The behaviour of the solution when the rate of suction is large is investigated here, and it is found that the velocity distribution in the boundary layer approximates to the Griffith-Meredith or asymptotic suction profile. The solution is developed in the form of a series of descending powers of the suction velocity and the coefficients of this series are obtained successively by the so1ution of linear differential equations. The first four coefficients are obtained explicitly and numerical values are given in Table 1. Series are also obtained for the displacement and momentum thicknesses and for the skin friction and form parameter H. Comparisons are made with Thwaites's solutions, and good agreement is found when the rate of suction is large.