Boundary element analysis for MHD Brinkman flow around circular cylinders inside a microchannel exhibiting wall roughness

Inspired by the dynamics of blood flow around clots, emboli, and drug capsules in blood vessels, this study introduces a hydrodynamic model describing the steady, pressure-driven flow of a viscous, incompressible fluid past multiple equally sized circular cylinders within a rectangular microchannel. To create a permeable environment, the microchannel is embedded with a uniform, isotropic porous medium. To simulate roughness on the permeable walls, alternating Navier slip and no-slip boundary conditions are imposed, maintaining the same phase configuration. The system operates at a low Reynolds number and is influenced by an external magnetic field. The Brinkman equations, which govern the flow through the porous domain, are solved using the boundary element method (BEM). The hydrodynamics of the proposed model, with two instances of slip-periodicity, are studied extensively. Increasing Darcy number induces a more permeable porous medium, causing a significant reduction in flow resistance, particularly in regions farther from the channel boundaries. The Lorentz force, which is most effective at generating drag when perpendicular to the flow, becomes less impactful as the inclination angle of the magnetic field increases. The shear stress is minimized at the points at which Navier's slip and no-slip boundary conditions coincide. The proposed model enhances microfluidic systems for precise drug delivery, optimizes lab-on-chip devices for diagnostics, and improves fluid dynamics in porous systems like heat exchangers and filtration processes. It also supports the development of medical devices that better simulate natural blood flow, advancing the efficiency of artificial organs and implants.