Open AccessThe analytical approximate solutions of capillary flow in circular tubes under microgravity
Author(s) -
Yongqiang Li,
Chenhui Zhang,
Ling Liu,
Duan Li,
Qi Kang
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.044701
Subject(s) - homotopy analysis method , series (stratigraphy) , capillary action , convergence (economics) , nonlinear system , flow (mathematics) , mathematics , homotopy , function (biology) , mathematical analysis , taylor series , rate of convergence , tube (container) , computer science , physics , geometry , materials science , thermodynamics , paleontology , channel (broadcasting) , computer network , quantum mechanics , evolutionary biology , pure mathematics , economics , composite material , biology , economic growth
The capillary flow in a circular tube under microgravity environment is investigated by the homotopy analysis method (HAM), and the approximate analytical solution in the form of series solution is obtained. Different from other analytical approximate methods, the HAM is totally independent of small physical parameters, and thus it is suitable for most nonlinear problems. The HAM provides us a great freedom to choose basis functions of solution series, so that a nonlinear problem can be approximated more effectively, and it adjusts and controls the convergence region and the convergence rate of the series solution through introducing auxiliary parameter and the auxiliary function. The HAM hews out a new approach to the analytical approximate solutions of capillary flow in a circular tube. Through the specific example and comparing homotopy approximate analytical solution with the numerical solution which is obtained by the fourth-order Runge-Kutta method, the computed result indicate that this method has the good computational accuracy.