Maximum density effects on the stability of thermal convection in a vertical Brinkman layer with uniform horizontal throughflow

This study examines the impact of the maximum density property on the instability of thermal convection in a vertical Brinkman layer under uniform horizontal throughflow. Deviating from the classical Boussinesq approximation, the density relationship is modified to a quadratic polynomial. The Navier–Stokes equations are converted to the Orr–Sommerfeld eigenvalue problem by linear stability analysis and solved numerically by the Chebyshev collocation method. The results show that the maximum density effect will cause the buoyancy to reverse, counteract some disturbances, and enhance the stability of the system. Moreover, the presence of throughflow has a significant impact on the basic state and instability. At low Pe, increasing throughflow enhances stability; however, beyond a critical range, further increase in Pe amplifies inertial effects and vertical temperature non-uniformity, which destabilize the stability. Meanwhile, PrD also has dual effect on system stability, with low PrD promoting instability and high PrD enhancing viscous diffusion to suppress instability. Particularly, the pure and modified quadratic density models exhibit similar stability behavior in certain regions.