In the current paper, we examine the flow of immiscible bi-viscous Bingham and Newtonian fluids through a composite porous channel. It consists of two porous regions, which are saturated with a non-Newtonian bi-viscous Bingham fluid, with a Newtonian fluid region sandwiched between them. The porous regions have anisotropic permeability and are governed by the Brinkmann model, while the Stokes equation governs the fluid region. To evaluate the hydrodynamic quantities, the continuity conditions of shear stress and velocity are assumed at both the fluid–porous interfaces, and the no-slip conditions are imposed at the upper and lower plates. The graphical and tabular results demonstrate that the permeability ratio, anisotropic angle, and bi-viscous Bingham parameters significantly influence velocity profiles and skin friction. The rate of fluid motion is greater when the permeability ratios are less than unity, and there is no deviation in the principal direction of permeability. Interestingly, the results show that fluid motion is greater when porous regions are saturated with a bi-viscous Bingham fluid than with a Newtonian fluid. The skin friction at upper and lower plates is greater in a bi-viscous Bingham fluid than in a Newtonian fluid, and is also affected by the permeability ratio and anisotropic angle. The limiting cases of the present work perfectly matched the previous work. The present investigation enhances our understanding of the role of immiscibility at the porous–fluid interface and anisotropic porous media, indicating potential applications in reservoir rocks of oil field and blood flow in arteries.
Kumar et al. (Thu,) studied this question.