MELTING FROM BELOW OF A HORIZONTAL ICE PLATE IN A RECTANGULAR CAVITY

Abstract

This paper is concerned with the melting of a horizontal ice plate from below. The bottom hot plate is fixed at the temperature $T_h$ higher than $5^{\circ} \mathrm{C}$ and lower than $25^{\circ} \mathrm{C}$ and an initial ice temperature $T_{i n i}$ is the melting point $\left(0^{\circ} \mathrm{C}\right)$. The ice plate melts after the onset of natural convection based on the maximum density at $4^{\circ} \mathrm{C}$. The average heat transfer coefficient $\alpha_{a v}$ in the melting by natural convection is obtained by means of the numerical calculations on the PHOENICS Code. Melt thickness $X$ can be predicted by the Neumann's solution in the beginning of the melting. After the natural convection appeared, the transient melt thickness is predicted approximately by a simple closed form analytical solution including optimal average heat transfer coefficient $\alpha_{a v}$ determined by the numerical solutions. The average heat transfer coefficient in the range of $T_h>25^{\circ} \mathrm{C}$ can be estimated by the experimental results of the Nusselt number $(\mathrm{Nu})$ and the Rayleigh number $(R a)$ in the common liquids without the maximum density. Received: March 6, 2023Revised: July 27, 2023Accepted: August 2, 2023