This paper presents numerical simulations of the convection and diffusion of heat or a contaminant released from a source in a ventilated two-dimensional room with one inlet and one or two outlets. Besides the influential factors on the air flow characteristic such as the Reynolds number (Re) and Grashof number (Gr) as well as the geometrical arrangement of the inlet and outlets, the effect of imposing boundary conditions particularly the condition at the outlet upon the air flow is studied numerically in this paper. By imposing an adequate condition for heat/contaminant on the outlet, the steady and near steady solutions of the problem are firstly computed. These solutions allow to evaluate the removal efficiency as well as show the different influence of the zero-value condition from that of the zero-flux one on the air flow characteristic. As shown in this raper, these two boundary conditions have quite different effects on the heat/mass transfer capability of the air flow.