Efficient heat dissipation during braking is crucial for maintaining the performance and reliability of brake systems in heavy-duty vehicles. Although CFD has been widely applied to brake thermal analysis, the isolated influence of brake cooling duct cross-sectional geometry on airflow characteristics and convective cooling performance has received limited attention. This study numerically evaluated the influence of duct cross-sectional geometry on the flow characteristics and cooling performance of a heavy-duty bus brake system using two consecutive computational fluid dynamics (CFD) models implemented in ANSYS CFX. First, circular and square cross-section ducts were analyzed for vehicle speeds of 60, 90, and 120 km/h to determine the outlet flow conditions. Subsequently, these flow conditions were used as inlet boundary conditions for the thermal analysis of a brake disc subjected to surface temperatures of 600, 700, and 800 K. The numerical reliability of the simulations was verified through mesh independence analyses, where successive mesh refinements produced variations below 0.5% in the monitored variables. The results showed that the circular duct generated higher exit velocities than the square duct under all analyzed conditions, reaching 51.88 m/s and 39.52 m/s, respectively, at 90 km/h. Although this improvement was accompanied by greater pressure losses, the circular configuration increased the brake disc heat dissipation by approximately 51% at a surface temperature of 600 K. These findings demonstrate that duct geometry plays a decisive role in brake cooling performance and provide useful engineering guidelines for designing more efficient brake cooling systems for heavy-duty buses operating under severe thermal conditions.