Homotopy Analysis Solution for Micropolar Fluid Flow Through Porous Channel With Expanding or Contracting Walls of Different Permeabilities

SI Xin-yi; SI Xin-hui; ZHENG Lian-cun; ZHANG Xin-xin

doi:10.3879/j.issn.1000-0887.2011.07.005

Volume 32 Issue 7

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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, 2011, 32(7): 807-820. doi: 10.3879/j.issn.1000-0887.2011.07.005

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Homotopy Analysis Solution for Micropolar Fluid Flow Through Porous Channel With Expanding or Contracting Walls of Different Permeabilities

doi: 10.3879/j.issn.1000-0887.2011.07.005

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, P. R. China;
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, P. R. China;
Department of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China

Received Date: 2010-12-06
Rev Recd Date: 2011-04-20
Publish Date: 2011-07-15

Abstract

Abstract

The flow of amicropolar fluid through a porous channel with expanding or contracting walls of different permeability was investigated. Two cases were considered in which the opposing walls undergoeither uniformor nonuniform motion. In the first case, homotopy analysis method (HAM) was employed to obtain the expressions for velocity and micro-rotation fields. Graphs were sketched for some values of the param eters. The first conclusion can be made that expan sion ratio and different perm eability have miportant effects on the dynamic characteristics of the fluid. Following Xu. smodel, the second and more general case is that the wall expansion ratiovaries with time. Under this assumption, the govern ing equations were transformed in to non linear partial differential equations that also are solved analytically using HAM procedure. In the process, both algebraic and exponen tialmodels were considered to describe the evolution of a (t) from the initial a₀ to a final state a₁. As a result, it is found that the tmie-dependent solutions approach very rapidly to the steady state behavior. The second important conclusion can be made that the time-dependent variation of the wall expansion ratio plays a secondary role which maybe justifiably ignored.
- homotopy analysis method,
- micropolar fluid,
- expanding or contracting walls,
- porous channel,
- different permeability

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References(43)

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