A numerical simulation of two-dimensional laminar natural convection in a fully open tilted square cavity with an isothermally heated back wall is conducted. The remaining two walls of the cavity are adiabatic. Steady-state solutions are presented for Grashof numbers between 10(2) and 10(5) and for tilt angles ranging from -60 degrees to 90 degrees (where 90 degrees represents a cavity with the opening facing down). The fluid properties are assumed to be constant except for the density variation with temperature that gives rise to the buoyancy forces, which is treated by the Boussinesq approximation. The fluid concerned is air with Prandtl number fixed at 0.71. The governing equations are expressed in a normalized primitive variables formulation Numerical predictions of the the velocity and temperature fields are obtained using the finite-volume-based power law (SIMPLER: Semi-implicit Method for Pressure-Linked Equations Revised) algorithm. For a vertical open cavity (alpha = 0 degrees), the algorithm generated results that were in good agreement with those previously published. Flow patterns and isotherms are shown in order to give a better understanding of the heat transfer an flow mechanisms inside the cavity. Effects of the controlling parameters-Grashof number and tilt angle-on the heat transfer (average Nusselt number) are presented and analyzed. The results also revealed that the open-cavity Nusselt number approaches the flat-plate solution when either Grashof number or tilt angle increases. In addition, a correlation of the Nusselt number in terms of the Grashof number and tilt angle is developed and presented; a comparison is made with available data from other literature.