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Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities
Authors:Xin-yi Si  Xin-hui Si  Lian-cun Zheng  Xin-xin Zhang
Institution: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
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.
Keywords:homotopy analysis method  micropolar fluid  expanding or contracting wall  porous channel  different permeability
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