The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.