A finite-difference technique of numerically integrating the time dependent Boussinesq equations with variable fluid diffusion properties is introduced.

The technique uses the primitive variables for the flow equations, i.e. the velocities and pressure, and though it has been so far applied to two-dimensional problems, it appears to lend itself to an easy extension for those in three-dimensions. The equations are integrated with respect to time by a marching process, together with the iterative solution for the pressure. A suitable form of the finite difference equation gives a computa- tionally-stable long term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow. For the cavity flows driven by buoyancy a systematic study on the determining flow parameters is presented.

Also the influence of the ratio Gr/Re² on the combined forced and natural convection effects in channel flows is analysed.