Dimensionless correlations for forced convection in liquid metals: Part I. single-phase flow

Abstract

Two main objectives were addressed in this article. First, a dimensionless heat-transfer correlation for single-phase flow forced convection in liquid aluminum has been derived using a novel experimental method. An aluminum sphere was rotated with a specific tangential velocity in liquid aluminum. Its melting time was measured and correlated with the convective heat-transfer characteristics. The resulting correlation has the following form:The second objective of the study was to assess the accuracy of various correlations using an annular channel, which was available at an independent setting, at the Alcan Research and Development Laboratory. The correlations investigated were those derived from the current experimental work as well as those derived by other investigators, as presented in their respective published work. Results indicated that when applied to liquid metals, theoretically derived equations as well as equations developed for fluids with a Prandtl number greater than 0.7 exhibit a very large error. As such, these equations are unsuitable for liquid metals. A considerably smaller error is exhibited by equations derived experimentally, specifically for liquid metals, thereby attesting to the careful consideration that must be exercised in the choice of correlations that are employed.This study also provides a critical assessment of various exponents used in dimensionless equations for convective heat transfer in liquid metals. While there is a general consensus that the exponent of the Reynolds number is around 0.5, the exponent for the Prandtl number varies considerably.

Macroscopic Models for Gas Stirred Ladles

“…Liquid [38][39][40][41][42][43][44][45][46][47][48] Solid and liquid interactions and the resultant transport of heat and/or mass are characteristics of many processes (viz., alloying addition, powder injection and so on) that are carried out in refining ladles. Over the years, numerous investigations of the subject have been carried out wherein significant efforts were made to develop reliable mathematical models for the estimation of heat and mass transfer rates.…”

“…Over the years, numerous investigations of the subject have been carried out wherein significant efforts were made to develop reliable mathematical models for the estimation of heat and mass transfer rates. A number of these studies were specifically concerned with gas agitated melts/baths in which, either previously reported 38,39) or newly developed [44][45][46][47][48] correlations were applied to estimate heat or mass transfer rates between solid and bulk liquid. A summary of the correlations applied/developed by various groups of investigators is presented in Table 6.…”

“…47,48) These authors argued that the Prandtl number in metallic melts is significantly smaller than those of the equivalent aqueous or air systems. Thus, classical correlations applicable to higher values of Prandtl numbers are likely to be inadequate for equivalent metallic systems because of the very different nature of the thermal boundary layer thickness in these systems.…”

“…In addition to this, classical correlations which are essentially valid under steady state conditions may not be directly applicable to metallic systems because the mode of heat transfer between solid and liquid there is transient (the solid dimension together with the thickness of the thermal boundary layer are truly transient and these change with time). Thus, Argyropoulos and coworkers 47,48) carried out melting experiments in a high temperature, laboratory scale melt and developed correlations between average Nusselt number and Reynolds number (Prandtl number was constant as the solid-liquid types were fixed) for both single phase as well as two phase flow systems (see Table 6). It was shown by these authors 47,48) that the measured melting rates can be characterized solely in terms of the object Reynolds number, for both single phase as well as two phase flow systems.…”

“…Thus, Argyropoulos and coworkers 47,48) carried out melting experiments in a high temperature, laboratory scale melt and developed correlations between average Nusselt number and Reynolds number (Prandtl number was constant as the solid-liquid types were fixed) for both single phase as well as two phase flow systems (see Table 6). It was shown by these authors 47,48) that the measured melting rates can be characterized solely in terms of the object Reynolds number, for both single phase as well as two phase flow systems. Interestingly, the exponents on the Reynolds number in their correlations (see Table 6) were significantly different from the ones applied by various previous investigators to infer melting/dissolution rates in metallic melts.…”