A novel approach to micropolar fluid flow between a non-porous disk and a porous disk with slip

Abstract

This paper considers the problem of steady, laminar, incompressible, and two-dimensional micropolar fluid flow between two disks. The top disk is considered porous, while the lower one is not. The body forces and body couples were neglected, and the flow was assumed to be fully developed. The governing equations of the problem were reduced to a set of ordinary differential equations (ODEs) by Von-Karman's similarity transformations. Since the obtained governing ODEs have not been solved analytically according to the previous studies, in this article, the Modified Akbari-Ganji method (Modified AGM) and the hybrid analytical and numerical method (HAN-method) have been chosen to solve these equations analytically, which is one of the novelties of this study. However, most of this article's novelty is related to the physical results obtained from the analytical solution of these equations. The effects of various slip coefficients, Reynolds number, and micropolar parameters of vortex viscosity, spin gradient viscosity, and microinertia density on profiles of normal velocity, streamwise velocity, and microrotation. The validity of these two analytical solutions was proved by comparison with previously published results. The results of the two methods are almost the same in all cases, which can be seen as an indirect sign of the validity of the results of this study.