Semi-theoretical correlations of melting process driven by Rayleigh–Bénard convection suitable for low melting point metal

Abstract

This paper studies the melting process of low melting point metal (LMPM) in a square cavity heated from bottom in the presence of Rayleigh–Bénard convection. Existing research focuses on high–Pr PCM melting process, and the difference between low and high-Pr PCM melting process needs to study. Scale analysis and numerical investigation are applied to analyze low-Pr LMPM melting process. Scale analysis tries to research the LMPM melting rate and obtain basic theoretical relationships of liquid fraction and Nu with Fo, Pr, Ras and Ste. A numerical model is established to elaborate dynamic melting heat transfer characteristics of low–Pr LMPM. The numerical results show that different from high-Pr PCM, the flow cell morphology presents obvious changes for low-Pr LMPM, and the time needed to completely melt is much shorter and the average heat flux is higher. The Rayleigh–Bénard convection causes oscillation of Nu in the convection dominated regime, and the average Nu for LMPM increases from 5.11 to 13.77 with the Ra from 5.0×105 to 1.25×107. Finally, the semi-theoretical correlations for liquid fraction and Nu are developed by scale analysis and numerical investigation, and the accuracy is numerically validated.