Circular objects do not melt the slowest in water

Abstract

We report on the melting dynamics of ice suspended in fresh water and subject to natural convective flows. Using direct numerical simulations we investigate the melt rate of ellipsoidal objects for $2.32\times 10^4 \leq \text{Ra} \leq 7.61\times 10^8$, where \text{Ra} is the Rayleigh number defined with the temperature difference between the ice and the surrounding water. We reveal that the system exhibits non-monotonic behavior in three control parameters. As a function of the aspect ratio of the ellipsoidal, the melting time shows a distinct minimum that is different from a disk which has the minimum perimeter. Furthermore, also with \text{Ra} the system shows a non-monotonic trend, since for large \text{Ra} and large aspect ratio the flow separates, leading to distinctly different dynamics. Lastly, since the density of water is non-monotonic with temperature, the melt rate depends non-monotonically also on the ambient temperature, as for intermediate temperatures ($\unit{4}{\celsius}$--$\unit{7}{\celsius}$) the flow is (partially) reversed. In general, the shape which melts the slowest is quite distinct from that of a disk.