Numerical study of three-dimensional low-pr buoyancy and thermocapillary convection

The problem of combined buoyancy and tkermocapillary convection in an upright cube with a top free surface is solved numerically. All other walls are considered to be solid and impermeable. The side walls are at uniform but different temperatures, while all other surfaces are adiabatic. The top surface deformation and interactions with the gaseous phase above are neglected. The Navier-Stokes, continuity, and energy equations are cast in the velocity-vorticily formulation and are discretized by using finite difference approximations. The solution procedure is of a three-level alternating direction implicit scheme. In order to save on computational cost, the equations were marched in time using the false transient technique. A typical 81 X 81 X 61 uniform staggered mesh has been used in the numerical compulations, which were performed in double precision on a workstation. Results will be presented for a typical fluid with a low Prandtl number (Pr = 0.01). The effects of positive and negative Marangoni numbers on the three-dimensional convection at different Grashof numbers will be considered and discussed.