Reliable treatments of differential transform method for two-dimensional incompressible viscous flow through slowly expanding or contracting porous walls with small-to-moderate permeability

In this article, 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 differential transform method (DTM). Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number on the velocity, normal pressure distribution and wall shear stress. The validity of our solutions is verified by the numerical results obtained by shooting method coupled with Runge–Kutta scheme. Since the transport of biological fluids through contracting or expanding vessels is characterized by low seepage Reynolds numbers, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.