Insight into Hydrodynamics Behavior of Creeping Flow of Couple Stress Fluid Through Uniformly Porous Rectangular Channel under the Influence of Walls Slip; An analytical approach.

In this paper, we have obtained the exact solution for the slip effects on the creeping flow of a couple stress fluid through a uniformly porous walled channel. The momentum equations have been transformed into a stream function using the inverse method. Expressions for important physical quantities such as longitudinal velocity, transverse velocity, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure have been derived. Results have been presented graphically, demonstrating that the longitudinal velocity is influenced by the initial flow rate while the transverse velocity remains unaffected by the initial flow rate. Moreover, it has been shown that there are no detectable slip effects on the physical quantities studied. Notably, the initial flow rate significantly impacts the streamlines; an increase in flow rate straightens and aligns the streamlines, whereas a decrease leads to backward flow. The volume flow rate exhibits a substantial impact on longitudinal velocity, but no influence on transverse velocity is observed. This study holds the potential to assist bioengineers in designing medical tools with required pressure and flow rate specifications. The application of this model is particularly relevant to hemodialyzers.