A Numerical Modeling of Rayleigh-Marangoni Steady Convection in a Non-Uniform Differentially Heated 3D Cavity

摘要

A numerical study of a buoyancy driven convection flow in presence of ther-mocapillarity has been developed. The fluid is a silicone oil (Prandtl number equal to 105) contained in a three-dimensional box bounded by rigid and impermeable walls with top free surface exposed to a gaseous phase. At the lateral box walls a different non-uniform temperature distribution is assumed so to induce horizontal convection and to keep separated thermocapillary and buoyancy effects. The vorticity-velocity formulation of the time-dependent Navier-Stokes equations for a non-isothermal incompressible fluid is used. A procedure based on a linearized fully implicit finite difference second order scheme has been adopted. We obtained very complex steady configurations for several values of the temperature difference at the lateral walls, ΔT = 30, 40 and 50 ℃. Along the direction perpendicular to the lateral walls, for ΔT increasing, we observe a physically meaningful growth of heat transfer. Confidence in these results is supported by a comparison with recent experimental and numerical observations.