Prediction of Conjugate Heat Transfer in a Solid–Liquid System: Inclusion of Buoyancy and Surface Tension Forces in the Liquid Phase

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Abstract
Numerical predictions have been obtained for steady-state conjugate heat transfer in an open rectangular cavity. For the geometry considered, fluid motion is driven by augmenting buoyancy and surface tension forces. Predictions of the steady-state solid volume fraction and various solid thicknesses were obtained for a high Prandtl number fluid characterized by various Rayleigh and Marangoni (Ma) numbers. Due to numerical difficulties associated with large surface tension effects, a limited range of Ma was investigated (Ma≤250). The predictions show that surface tension induced flow can affect the solid geometry and, ultimately, freezing or melting rates. Specifically, the solid–liquid interface shape is altered, the steady-state solid volume fraction is decreased, and the solid thickness at the top surface is smaller, compared to the pure buoyancy-driven case. The dimensionless solid volume fraction and solid thicknesses are related to the governing dimensionless parameters of the problem. Finally, predictions are made for high Marangoni number flows (Ma>>250) to demonstrate the potential governing influence of surface tension effects in phase-change systems.

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