Assessment of Nusselt Number Correlations for Liquid Metals Applied in Alloying Processes in Turbulent Flows

There are many correlations for Nusselt numbers applied to calculate heat transfer between a fluid and a sphere. In all massive industrial processes of metal production, there is the need to calculate the melting times of metal additions during alloying operations. A multiphase mathematical model helps to assess the applicability of these correlations to actual industrial processes. This model simulates the heat transfer between solid particles and liquid steel under turbulence conditions during the tapping operation of steel with simultaneous argon bottom stirring. There are six recommendable correlations among the 16 most relevant available ones in the literature. These correlations apply to small Prandtl numbers (Pr = 0.01 to 0.2, i.e., metals) or medium magnitudes of Prandtl numbers (Pr = 1 to 10, air and water). Melting rates depend on the turbulence intensities and superheat of the metal. High superheats cause the hydrodynamic effects to have less influence on the melting time of alloying particles.