Two-dimensional Viscous Flow through Permeable Walls with Expanding or Contracting Gaps

Abstract: In this study, 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 using a series of based analytical techniques named Homotopy Perturbation Method (HPM), Differential Transformation Method (DTM) and Optimal Homotopy Analysis Method (OHAM). The concepts of these methods are briefly introduced and their application for this problem is studied. These methods are very useful and applicable for solving nonlinear problems. Then, the results are compared with numerical results and the validity of these methods are shown. Comparison between obtained results shows that HPM is more accurate and acceptable than two other methods. After this verification, we analyze the effects of some physical applicable parameters on velocity profile, pressure drop and shear stress to show the efficiency of HPM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate (α) and permeation Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. The obtained results, in comparison with the numerical solution results, 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.