Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

“…In this work, we used the homotopy analysis method (HAM) to obtain analytic approximate solutions of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, presented by Majdalani et al [30]. Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress.…”

“…Therefore, a substantial amount of research work has been invested in the study of the flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions. Majdalani et al [30] studied the two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. Their study focused on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.…”

A Note on Some Solutions of Copper-Water (Cu-Water) Nanofluids in a Channel with Slowly Expanding or Contracting Walls with Heat Transfer

“…Suction or injection took place at the walls of pipe and the radius of the pipe as varied with respect to time. In addition, Majdalani et al [5], Dauenhauer and Majdalani [6], Majdalani and Zhou [7] investigated the problem of laminar flow in a channel with porous expanding walls numerically as well as asymptotically. Later, analytical solutions were obtained by Rahimi et al [8] for the case of expanding and contracting porous channel walls.…”

Perturbation solutions for a micropolar fluid flow in a semi-infinite expanding or contracting pipe with large injection or suction through porous wall

“…In their work [11], they numerically discussed the influence of the expansion ratio and Reynolds number on the velocity and pressure distribution. Furthermore, Majdalani, Zhou and Dawson [12] also obtained an asymptotic solution for the flow in a porous channel, with slowly expanding or contracting walls, by considering the permeation Reynolds number and expansion ratio as two small parameters. Boutros et al [13,14] also discussed the flow through an expanding porous channel or pipe using the Lie group method and obtained the analytical solution with the perturbation method.…”