Analysis of steady viscous flow in slender tubes

Abstract.

The computer extended perturbation series method is used to analyze the problem of steady viscous flow in slender tubes. The objective is to obtain an expansion in a power series of λ (= ɛ R, ɛ is a small parameter and $R = \frac{M}{{L\nu }}$ is a streamwise Reynolds number) and look for its analytic continuation. Such an expansion was usually terminated at the second or third order term and consequently they have a very limited utility. Sufficiently large number of terms in the series, representing physical quantities are, generated for the detail analysis which enables to get converging Pade’ sums for large λ. Domb-Sykes plot enables in finding singularity restricting the convergence of the series. Useful results valid up to λ = 15 are obtained for different derived quantities whereas in earlier findings [6], analysis could be done only up to λ = 10 resulting into a substantial improvement in the present study.