In the study of fluid transport in biological organisms, we deal with the flow between permeable walls that may expand or contract, this type of flow has a great importance in medical and biological sciences. In this article, the laminar flow of an incompressible viscous fluid is considered in a semi-infinite rectangular domain. It is bounded by two moving porous walls that enable the fluid to enter or exit during successive contractions or expansions. The solution of the problem is approximated by using Variation of Parameters Method (VPM). To investigate the effect of non-dimensional wall expansion/contraction rate and permeation Reynolds number, on the flow field, the graphical results are presented. A couple of graphs, highlighting the effects of involved parameter on the normal pressure distribution, are also included. The analytical solution obtained by (VPM) is also supported by numerical results and both show an excellent agreement. A comparison among the current solution and some already existing solutions is also presented. The study of the flow between dilating or squeezing porous walls is drastic simplification of the transport of biological fluids through dilating or squeezing vessels.
Syed Tauseef Mohyud-Din, Naveed Ahmed, Umar Khan