Numerical study of laminar convective cooling of ribs in a parallel plate channel is investigated. Single rib mounted on one channel wall in forced, mixed and free convection is analyzed. Furthermore, the series ribs array with in-line and staggered mounted on channel walls are considered. Through the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control volume method with non-uniform grid. The effects of the Reynolds number, thermal conductivity ratio of rib to fluid and rib¡¦s profile area on heat transfer rate of single rib and rib array are presented. In addition, the effects of the length from inlet to the first rib and the space between ribs for rib array are carried out. A correlation for single and rib array in forced convection is presented to estimate the optimum aspect ratio of rib with various Reynolds number, thermal conductivity ratio of rib to fluid, rib¡¦s profile area. Furthermore, the results of different Gr/Re2 and various channel inclination angle in mixed convection are also examined numerically. The results indicate that both in forced and mixed convection, the optimum aspect ratio of a rib corresponding to the rib with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed rib profile area. In forced convection the optimum aspect ratio of rib array increases with rib¡¦s space but decreases with the length from inlet to the first rib of channel. Then, numerical correlations to predict the optimum aspect ratio of single rib and rib array are developed for fixed rib¡¦s area with various Re, K and rib number. In mixed convection, the optimum aspect ratios of single rib and staggered rib array increase with not only the inclination angle but also Gr/Re2.