Hydrodynamical study of couple stress fluid flow in a linearly permeable rectangular channel subject to Darcy porous medium and no-slip boundary conditions

Abstract

In this paper, the study investigates the problem of the creeping flow of a non-Newtonian couple stress fluid through a linearly porous walled slit within a Darcy porous medium. The well-established approach, the Inverse Method approach, was employed to attain the precise solution of the governing equations. The inverse technique is utilized to transform the momentum equations into stream functions. The physical parameters are all computed: longitudinal velocity, transverse velocity, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. The data was also graphed, indicating that the initial flow rate affects longitudinal velocity but not transverse velocity. The streamlines are greatly affected by the initial flow rate, resulting in straighter and more uniform patterns as the flow rate increases. Parameters like permeability and the couple stress parameter also have an impact on physical quantities. Because of the porosity parameter, backward flow occurs at the slit's end. The novelty of this research lies in the investigation of couple stress fluid flow within both linear channel walls and a porous medium. The present research focuses on how kidney disease affects fluid flow in renal tubules. It's critical because fibers, lipids, and waste particles can clog or disrupt these channels, lowering kidney performance. Understanding this helps in the management of kidney disease and provides insights for better biomedical engineering in the development of improved renal medicines.