Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

doi:10.1007/s10483-011-1465-6

Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (7): 859-874.doi: https://doi.org/10.1007/s10483-011-1465-6

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

司新毅¹ 司新辉² 郑连存² 张欣欣³

1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, P. R. China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China;
3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China

收稿日期:2010-10-06 修回日期:2011-04-20 出版日期:2011-07-03 发布日期:2011-07-03
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 50936003 and 50905013) and the Open Project of State Key Laboratory for Advanced Materials (No. 2009z-02)

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

SI Xin-Yi¹, SI Xin-Hui², ZHENG Lian-Cun², ZHANG Xin-Xin³

1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, P. R. China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China;
3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China

Received:2010-10-06 Revised:2011-04-20 Online:2011-07-03 Published:2011-07-03
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 50936003 and 50905013) and the Open Project of State Key Laboratory for Advanced Materials (No. 2009z-02)

摘要/Abstract

摘要： The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method (HAM) is used to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu’s model, in the second case which
is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

Abstract: The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method (HAM) is used to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu’s model, in the second case which
is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

中图分类号:

76M99
76D10

司新毅司新辉郑连存张欣欣. Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(7): 859-874.

SI Xin-Yi;SI Xin-Hui;ZHENG Lian-Cun;ZHANG Xin-Xin. Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(7): 859-874.

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Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

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