Linear Stability Analysis of MHD Flow Through a Porous Channel with Wall Slip and Surface Roughness

This study investigates the linear stability of magnetohydrodynamic (MHD) flow in a porous channel with Navier-slip boundary conditions and lower-wall surface roughness to clarify the combined effects of these mechanisms on flow transition. A modified Orr–Sommerfeld eigenvalue model incorporating the Reynolds number, Hartmann number, Darcy number, slip parameter, and roughness wavenumber is formulated and solved using the Chebyshev spectral collocation method. The results demonstrate that surface roughness has a negligible effect on the base-flow profile, while increasing the roughness wavenumber enhances disturbance attenuation and promotes flow stability. Wall slip increases the base-flow velocity and further suppresses disturbance growth. The Hartmann number provides strong magnetic damping, significantly enhancing flow stability. In contrast, increasing the Darcy number reduces porous-medium resistance and promotes instability, leading to a transition from stable to unstable behaviour within the investigated parameter range. The numerical results closely match established benchmark solutions, demonstrating the accuracy and robustness of the proposed approach. These findings provide new insights into the coupled influence of wall slip, surface roughness, porous permeability, and magnetic effects on hydrodynamic stability, with potential applications in MHD transport systems, porous channels, microfluidic devices, and advanced thermal management technologies.