Extending the utility of perturbation series in problems of laminar flow in a porous pipe and a diverging channel. (English) Zbl 0956.76074

Makinde, O. D.

J. Aust. Math. Soc., Ser. B 41, No. 1, 118-128 (1999).

The author applies Taylor series to obtain approximate solutions for steady inviscid incompressible flows first in a porous pipe, and then in an exponentially diverging asymmetric channel (in boundary-layer approximation). Using the symbolic algebra package Maple, the author calculates in the former case the first 54 coefficients, and in the latter case 44 coefficients, which allows to determine the radii of convergence and, employing a recent technique developed by P. G. Drazin and Y. Tourigny [SIAM J. Appl. Math. 56, No. 1, 1-18 (1996; Zbl 0858.65048)], to investigate the bifurcation diagrams and the position of flow separation.

Reviewer: Oleg Titow (Berlin)

MSC:

76M45	Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76S05	Flows in porous media; filtration; seepage
76D10	Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

perturbation series; Taylor series; steady inviscid incompressible flows; porous pipe; exponentially diverging asymmetric channel; boundary-layer approximation; symbolic algebra package Maple; radii of convergence; bifurcation diagrams; position of flow separation

Citations:

Zbl 0858.65048

Software:

Maple