Buoyancy and thermocapillary three-dimensional convection at moderate Pr: Numerical study

In the present study we consider the problem of the combined buoyancy and thermocapillary convection in an upright cube with a top free surface. All other walls are considered to be solid and impermeable. The side walls are at uniform but different temperatures, which 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-vorticity formulation. The governing equatons are discretized by using finite difference approximations. The solution procedure consists of a three level Alternating Direction Implicit (ADI) 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 computations. All computations were performed in double precision on a workstation. Results will be presented for a typical fluid with a moderate Prandtl number (Pr = 7). The effects of positive and negative Marangoni number on the three-dimensional convection at different Rayleigh numbers will be considered and discussed.