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

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: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{gathered} \overline {Nu_D } = 2 + 10^{2.811} \times \operatorname{Re} _D^{0.585} \times \Pr ^{2.386} \hfill \\ 5162 \leqslant \operatorname{Re} _D \leqslant 21,273, \Pr \approx 0.014 \hfill \\ \end{gathered} $$ \end{document} 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.