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

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Abstract

A numerical study of a buoyancy driven convection flow in presence of thermocapillarity 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°C. 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.

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Bucchignani, E., Mansutti, D. A Numerical Modeling of Rayleigh–Marangoni Steady Convection in a Non-Uniform Differentially Heated 3D Cavity. Journal of Scientific Computing 20, 115–136 (2004). https://doi.org/10.1023/A:1025850513781

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  • DOI: https://doi.org/10.1023/A:1025850513781

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