A new multifold series general solution of the steady, laminar boundary layers. I - Theory of the multifold series expansion. II - Application theory of the Euler transformation

Consideration is given to a theory of multifold series expansion analysis for steady, laminar boundary layers. The theory treats the general case wherein the mainstream velocity varies arbitrarily. The truncated series solution consists of only four terms, although its accuracy surpasses that of conventional series solutions with 6-9 terms. It is shown that the narrow-sense Euler transformation is best suited to the series. Procedures are derived for determining the proper position of the leading term of the transformation as well as the proper number of repeating times. The application of the Euler transformation extends the series expansion analysis with accuracy comparable to a precise numerical solution.