Improved perturbation solution for viscous flow in a dilating–contracting permeable channel with velocity slip

Abstract

Recently, Mandal and Ghosh [“Lie-group method solutions for a viscous flow in a dilating-squeezing permeable channel with velocity slip,” Phys. Fluids 35, 047121 (2023)] constructed perturbation solutions for viscous flow in porous channels with a slip condition and moving walls restricted to slow wall dilation–contraction rates. Herein, we show that this “slowness” assumption may be completely removed. In doing so, we develop a more widely applicable and more accurate perturbation scheme for all dilation–contraction rates. Our strategy involves generating new and exact solutions to the linear, inviscid problem with slip condition, and then we draw on this precise form to construct more accurate perturbation expansions for solutions to the nonlinear flow model than are currently available.