Calculation of the axisymrnetric boundary layer on a long thin cylinder

Abstract

The laminar boundary layer in axial flow along a long thin cylinder is investigated, following Seban & Bond (1951), by expanding in powers of a variable £ that represents the ratio of the boundary layer thickness to the cylinder radius. The resulting series for the skin friction r, of which 20 terms are calculated, is analysed, and, by working in terms of the inverse series, for r _1, the radius of convergence is estimated to be £ = 0.37416. An Euler transformation then yields a more convergent expansion in terms of a new variable By using the known asymptotic expansion of r for large £, we deduce how t—1 behaves near 2 = 1 , and extraction of the leading terms leaves an even more convergent residual series. Although neither the original series nor the asymptotic expansion give very accurate results over the substantial range 0-2 < £ < 100, the present analysis gives r to about six, or more, significant figures throughout the range. Similar success is achieved in calculating the displacement area.