This study examines the linear stability of two-dimensional incompressible viscous flow through a parallel channel embedded in a porous medium under the influence of a transverse magnetic field and various slip boundary conditions. Employing the Brinkman model, the analysis integrates Navier-slip boundary formulations, including general, symmetric, and asymmetric configurations, to capture realistic surface-fluid interactions relevant to modern sustainable technologies. The modified Orr-Sommerfeld equation is solved using the Chebyshev spectral collocation method to determine velocity distributions, eigenvalues, and critical flow parameters with high numerical precision. The findings reveal that wall slip, particularly under symmetric conditions, tends to destabilise the flow by reducing wall shear stress, whereas porous resistance and asymmetric slip enhance hydrodynamic stability. An approximate 20-30% decrease in wall shear stress is related to the effect of increasing wall slope. However, the presence of a transverse magnetic field partially reduces this decrease, resulting in a 10-15% increase in wall shear stress due to magnetic damping. The role of magnetic influence and porous drag is systematically explored, offering valuable insights into optimising flow control for efficient resource utilisation, energy conservation, and environmentally responsive fluid systems. Overall, this work advances sustainable and resilient design in magnetohydrodynamic (MHD) energy systems, microfluidic devices, and porous transport technologies. Maintaining flow stability supports cleaner industrial operations and the development of energy-efficient technologies.
P et al. (Thu,) studied this question.