2D‐ <scp>MHD</scp> Brinkman flow around circular cylinders inside a microchannel exhibiting wall roughness

Abstract This investigation focuses on the dynamic behaviour of the steady, pressure‐driven flow of a two‐dimensional viscous incompressible fluid around circular cylinders of equal diameter within a rectangular permeable microchannel featuring wall roughness. The wall roughness is modelled by implementing Navier's slip condition on the horizontal channel walls with a phase difference, examining both small and large‐patterned wall roughness scenarios. The flow, characterized by a low Reynolds number, is subjected to an inclined magnetic field, while the induced magnetic field effects are neglected under a low magnetic Reynolds number assumption. The Brinkman equations describing the flow are solved using the boundary element method (BEM) based on stream function and vorticity variables. The results indicate that increasing Darcy numbers enhances the permeability of the porous medium, reducing flow resistance, particularly away from the channel walls. The Lorentz force maximizes drag when perpendicular to the flow and becomes less effective as the magnetic field inclination increases. Shear stress is minimized at Navier's slip and no‐slip conditions interface. This investigation supports advancements in targeted drug delivery in microfluidic applications, optimization of lab‐on‐chip devices for diagnostics, and improvement of fluid dynamics in heat exchangers and filtration systems.