Flow dynamics in a wavy channel filled with anisotropic porous material under the effect of wall slip

Abstract

In this study, a theoretical and graphical analysis is conducted to examine the effects of wall-velocity slip, anisotropic ratio, and porosity parameter on a two-dimensional, viscous, laminar, and incompressible flow through a wavy channel filled with anisotropic porous media. The flow is assumed to be steady and symmetric, with a constant volumetric flow rate imposed along the channel walls. The governing equations are described using the Darcy-Brinman model coupled with the continuity equation, while the tangential velocity at the wavy boundaries is represented through Navier slip conditions. An analytical solution is obtained using a perturbation approach under physically consistent boundary conditions. The effects of key parameters, including anisotropic ratio, Darcy number, and slip parameter, on flow characteristics such as axial velocity, pressure gradient, shear stress, and streamline patterns are examined in detail and presented graphically. The results indicate that wall velocity slip significantly reduces flow reversal, enhances near-wall velocity, and decreases the center-line velocity. For a fixed non-zero slip, a decrease in the Darcy number leads to a pronounced modification in the velocity profile, while increased slip further strengthens near-wall flow and weakens the core flow. Additionally, the streamline analysis reveals that velocity slip plays an important role in controlling flow separation near the crest of the wavy wall. In the case of isotropic porous media with a large amplitude wavy channel, flow separation can also be effectively regulated. Overall, the study demonstrates that velocity slip provides a powerful mechanism for controlling flow behavior by altering the shear distribution within the perturbed flow, with potential applications in technological, geophysical, and biophysical transport systems.