Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Abstract

The current study examines the features of a two-dimensional steady incompressible flow of creeping couple stress fluid across a permeable channel with uniform reabsorption. The mathematical model that governs this flow is composed of linear partial differential equations and homogeneous boundary constraints. The Inverse method approach, an analytical technique, is used to find solutions to the problem. By converting the momentum equations to stream functions, the inverse approach helps derive all the relevant physical quantities, including the longitudinal and transverse velocities, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. Using MATLAB software, the dependent functions such as stream function, pressure, and volume flow are evaluated for different parameter values. The findings indicate that the longitudinal velocity is affected by the initial flow rate, while the transverse velocity shows no change in its profile. The streamlines become more straight and identical as the flow rate increases. Backward flow occurs at the end of the slit due to the porosity parameter. However, the initial flow rate does not impact the transverse velocity of the fluid in the permeable channel. This study fully describes a mathematical foundation for understanding fluid movement across permeable boundaries, which have practical applications in areas such as gaseous diffusion, filtration, and biological mechanisms.