Nusselt number correlations are presented for tall, square and shallow cavities heated from one side and cooled from other side, while its horizontal surfaces are insulated. Transient and steady-state patterns of stream function and temperature are presented. Energy, continuity and momentum equations need suitable time step in order to reach steady-state solution. A two-dimensional time-dependent numerical computation method has been developed to determine laminar free convection in closed cavities. The transport equations are solved with the implicit method. The resulting implicit method remains stable up to a Rayleigh number of 1012 . A transformation relation is proposed for sufficiently accurate determination of thermal and hydrodynamic boundary layers near the vertical side walls in cavities.