When a heated plate is exposed to ambient room air without an external source of motion, a movement of air is experienced as a result of density gradients near the plate. This process is known as natural convection. The main objective of this paper is the computational study of the flow initiated by natural convection. We investigate the colliding boundary layer in a rectangular enclosure. The solution procedure in this problem involves the transformation of the dimensional governing equations to non-dimensional equations whose purpose is to reduce the effort required to make a study over a range of variables. In this study a non-dimensional scheme is chosen which leads to improved iterative convergence for faster transients. The three dimensional analogue of the stream function- vorticity formulation was used in which the scalar vorticity was replaced by a vector and the scalar stream function by a vector potential. The equations were then solved using the method of variable false transients in which the elliptic equations for the components of the vector potential were replaced by parabolic equations by insertion of false transient terms. The insertion of these multiplying factors before each time derivative effectively enabled different time steps to be used for each equation. The results of the numerical simulation showed that the flow region was stratified into three regions; a warm lower region, a cold upper region and a hot region in the area of the confluence of hot and cold streams.