Rayleigh-benard convection during solidification of an eutectic solution cooled from the top
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NTRODUCTION
IT is well known that when a homogeneous, motionless fluid layer is cooled from the top, thermal instabilities can give rise to the Rayleigh–Benard type of convective-flow patterns when a critical value of the Rayleigh number is exceeded. Heat extraction through the upper boundary is also likely to promote solidification once the fluid temperature at a particular location falls below the local liquidus temperature (i.e., the temperature below which the liquid starts crystallizing). Convection in the liquid, in turn, enhances heat transfer from the melt and influences the rate of solidification, as well as the evolution of the solidifying interface. This interaction between the solidification interface and the Rayleigh–Benard type of convection is of particular significance to fields such as geological sciences, oceanography, crystal growth, materials processing etc. It can be noted that when a melt is cooled from below, the fluid layer is always thermally stable, and hence, a thermal-buoyancy driven flow does not occur. Numerous theoretical, experimental, and numerical studies have been devoted toward understanding fluid mechanics during solidification, and a comprehensive review is presented by Huppert.[1] Many of the previous experimental investigations pertaining to solidification along the vertical direction have addressed the influence of convection on solidification of binary systems cooled from below.[2–5] A pioneering work regarding solidification from the top was first reported by Turner et al.[6] In their investigation, the authors described a number of laboratory experiments and supplemented the same with the theoretical analysis of solidification of a pure (or eutectic) melt cooled and solidified P. KUMAR and S. CHAKRABORTY, Graduate Students, K. SRINIVASAN, Professor, and P. DUTTA, Associate Professor, are with the Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India. Contact e-mail: [email protected] Manuscript submitted June 29, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS B
from above. Their theory has elucidated the changing balances between heat conduction through the solid, the latent heat released by solidification of the melt, and the heat transfer from the convecting fluid below. A significant outcome of the experimental work undertaken by Turner et al.[6] and those performed by Brandeis and Jaupart[7] illustrates an important concept that under certain conditions, cooling at the top of a container may lead to crystallization at the floor, remote from the site of cooling. These preliminary studies have greatly been extended by Kerr et al.[8,9,10] In all the articles, theoretical models have been developed to describe new observations, which have enabled the authors to compare the quantitative predictions of the analysis successfully against the results of laboratory experiments with aqueous solutions of isopropanol and sodium sulphate. The aim of the present study is to investigate the effects of convection on solidification of a
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