INSTABILITY OF POISEUILLE FLOW IN A POROUS MEDIUM WITH COUPLE STRESSES EFFECT

This study explores the impact of couple stresses on the stability of Poiseuille flow through a Brinkman porous medium saturated with a non-Newtonian fluid. It involves numerically solving the Orr-Sommerfeld eigenvalue problem, which mirrors the stability analysis. The stability eigenvalue issue is resolved through the use of two Chebyshev collocation methods. Challenges associated with determining the spectrum for the porous Orr-Sommerfeld equation are addressed. Additionally, findings relevant to the clear fluid scenario are derived from this research as a specific instance, showing that, unlike in the porous scenario, couple stresses invariably have a stabilizing effect. Furthermore, the numerical solutions offered here will serve as a benchmark for evaluating the precision and effectiveness of other numerical approaches.