Instability of double-diffusive natural convection in a vertical Brinkman porous layer

The extended Brinkman model is employed in this study to investigate the instability of double diffusion natural convection in porous layers caused by vertical variations in boundary temperature and solute concentration. The stability of fluid flow is determined by discussing the temporal evolution of normal mode disturbances superposed onto the fundamental state. The linear dynamics problem is formulated as an Orr–Sommerfeld eigenvalue problem and solved numerically using the Chebyshev collocation method. The effects of thermal/solute Darcy–Rayleigh number (Ra_T/Ra_S), Lewis number (Le), and Darcy–Prandtl number (Pr_D) on system instability are analyzed. Growth rate curves indicate that solute Darcy–Rayleigh numbers can induce flow instability. Neutral stability curves show that increasing Ra_T/Ra_S promotes instability. There is a critical threshold for Le, exceeding this amplifies instability, while falling below suppresses it. For large Ra_T values, varying Pr_D leads to different effects of increasing Ra_S on flow stability. The stability of the system is significantly dependent on Ra_T and Ra_S, with the critical value of the Le playing a decisive role in system stability. Additionally, Pr_D significantly affects system instability under certain conditions.