Central European Journal of Physics

, Volume 7, Issue 4, pp 791–799 | Cite as

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

  • Saeed DinarvandEmail author
  • Mohammad Mehdi Rashidi
  • Ahmad Doosthoseini
Research Article


In this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.


expanding or contracting walls nondimensional wall dilation rate permeation Reynolds number homotopy analysis method (HAM) convergence 

PACS (2008)

68.37.Hk 68.37.Ps 78.68.+m 81.15.Ef 81.65.Cf 


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Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Saeed Dinarvand
    • 1
    Email author
  • Mohammad Mehdi Rashidi
    • 1
  • Ahmad Doosthoseini
    • 1
  1. 1.Mechanical Engineering DepartmentEngineering Faculty of Bu-Ali Sina UniversityHamedanIran

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