Creeping flow of Carreau fluid through a porous slit

We will investigate the creeping flow of a Carreau incompressible fluid through a slit with uniformly porous walls. Non-dimensionalization is used to represent the controlling two-dimensional flow equations and non-homogeneous boundary conditions. The resulting equations are solved using a recursive method. Equations are developed for the stream function, velocity components, volumetric flow rate, pressure distribution, shear and normal stresses on the slit wall as well as in general, fractional absorption, and leakage flux are also considered. Moreover, maximum velocity component points are noted. It is evident from the graphs that when porosity parameter (S) grows, the axial velocity decreases and backward flow is visible in the channel’s center. This is because the higher wall permeability allows more fluid to pass through the slit walls. Axial velocity rises toward the slit walls and decreases at the center as Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} grows due to the larger non-Newtonian parameter. This subject provides a mathematical basis for understanding the physical phenomena of fluid flows through slit walls, which arise in many problems, including gaseous diffusion, filtration, and biological systems.