The process of turbulent natural convection in a vertical channel formed by two parallel plates maintained at constant temperatures is studied numerically. The objective is to obtain basic information needed to predict the rate of natural convection cooling of advanced passive reactor vessels under abnormal operating conditions. A low-Reynolds-number turbulence model is employed in the problem formulation and the governing system is solved by an implicit finite-difference method. The development of flow and heat transfer in the channel is investigated for both the symmetric and asymmetric heating cases. Numerical results are obtained showing the effects of various parameters on the pressure variation and heat transfer performance of the system. Based on the characteristics of the heat flux variation along the channel, the concept of critical channel length is developed which leads to the highest heat transfer per unit length of the channel. Comparison of the present results is made with those obtained under constant-wall-heat-flux conditions.