Flow in a slowly deforming channel with weak permeability: An analytical approach

The analytical solution of the Navier–Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls is developed in the present paper. The numerical solution of the resulting problem has been studied by Dauenhauer and Majdalani [E.C. Dauenhauer, J. Majdalani, Exact self-similarity solution of the Navier–Stokes equations for a deformable channel with wall suction or injection, AIAA 3588 (2001) 1–11]. However, for small RR (the permeation Reynolds number) and αα (the wall expansion ratio), the respective analytical solutions are presented by Majdalani et al. [J. Majdalani, C. Zhou, C.A. Dawson, Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, J. Biomech. 35 (2002) 1399–1403] and Boutros et al. [Y.Z. Boutros, M.B. Abd-el-Malek, N.A. Badran, H.S. Hassan, Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, Appl. Math. Modelling (in press)]. The small RR and αα may well arise in biomechanics. The Adomian decomposition method (ADM) is used to obtain the solution. The results so obtained are compared with the existing literature (namely, the last two references cited above) and a remarkable improvement leads to an excellent agreement with the numerical results.