Analytical investigation of laminar flow through expanding or contracting gaps with porous walls

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 investigated analytically using optimal homotopy asymptotic method (OHAM). OHAM is a powerful method for solving nonlinear problems without depending to the small parameter. The concept of this method is briefly introduced, and it׳s application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of OHAM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate (αα) and permeation Reynolds number (ReRe) on the velocity, normal pressure distribution and wall shear stress. 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.