Numerical simulations are presented for transient and steady laminar buoyancy-driven flows and heat transfer in a square cavity open on one side. Computations were performed within the domain of the cavity. Vorticity transport and energy equations were solved using the alternating direction implicit scheme, and a successive overrelaxation method was employed to obtain solutions for the streamfunction. A range of values were considered for Gr and Pr. The results indicate that natural convection in the cavity does not depend on the computational domain or on the boundary conditions at the open side, which influence only a small region nearby. Heat transfer from the cavity is calculated, and flow and transport characteristics are discussed