Stability of Plane Poiseuille Flow of Casson Fluid Through a Porous Medium With Magnetic and Slip Effects

Abstract This study investigates the stability of plane Poiseuille flow of an electrically conducting Casson fluid through a homogeneous porous medium under a uniform transverse magnetic field. The flow, driven by a pressure gradient between two flat plates, is analyzed for the effects of the Casson parameter (β), permeability (M), Hartmann number (Ha), and slip length (I), under both symmetric and asymmetric slip conditions. A generalized eigenvalue problem is solved numerically using the Chebyshev spectral collocation method to determine the onset of instability. Results show that increasing the slip length l enhances flow stability for the Casson fluid, while Newtonian flow remains relatively unaffected within specific ranges of β, M, Ha, and I. Eigenspectrum analysis reveals that initial instabilities appear as wall modes, which diminish as β decreases, and M, Ha, and l increase. The neutral stability curves for various parameter values are extensions of the classical Tollmien–Schlichting instability in Newtonian fluids. An energy budget analysis identifies negative energy production from Reynolds stress as the key stabilizing factor. Meanwhile, viscous dissipation, porous medium effects, and magnetic field contribute positively to the energy balance, promoting stability throughout the flow.