A Fourth-order compact finite alternating direction implicit difference scheme on the nine-points 2D stencil is formulated for solving the unsteady-state streamfunction-vorticity formulation of the Navier-Stokes/Boussinesq(N-S/B) equations. The unconditional stable numerical method is provided by alternating direction implicit difference method. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature.