The Prandtl Number Effect on Melting Dominated by Natural Convection

In a recent paper, Gobin and Benard considered the task of correlating the heat transfer data for melting in the presence of natural convection when the Pr value of the liquid phase is considerably smaller than 1. To correlate the low-Pr data is an important and timely task, especially in view of the voluminous work that has been dedicated to situations in which Pr is greater than 1. For the convection-dominated regime known also as quasi-stationary melting, Gobin and Benard correlated their low-Pr numerical data with the formula: Nu=0.29 Ra[sup 0.27]Pr[sup 0.18] They noted that this correlation does not agree with the Nu[approximately](RaPr)[sup 1/4] trend that might be expected from the single-phase natural convection scales for low Prandtl numbers. They concluded that: (1) The relevance of the group (RaPr) is not verified by their numerical results for convection-dominated melting, and (2) further work is required to determine the scaling laws that govern the transition from the initial (conduction) regime to the final (convection) regime of the process of melting by side heating. These two conclusions defined the work presented in this note. In it is reported that the correct scales of natural convection melting when the Prandtl number is small.more » Then construct a scaling-correct heat transfer correlation that spans the entire range of Prandtl numbers.« less