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 $2.32\times {10}^4\le \text{Ra}\le 7.61\times {10}^8$, where Ra is the Rayleigh number defined with the temperature difference between the ice and the surrounding water. We reveal that the system exhibits nonmonotonic behavior in three control parameters. As a function of the aspect ratio of the ellipsoid, the melting time shows a distinct minimum that is different from a disk which has the minimum perimeter. Furthermore, also with Ra the system shows a nonmonotonic trend, since for large Ra and large aspect ratio the flow separates, leading to distinctly different dynamics. Lastly, since the density of water is nonmonotonic with temperature, the melt rate depends nonmonotonically also on the ambient temperature, as for intermediate temperatures $(4{}^{\circ }\mathrm{C} – 7{}^{\circ }\mathrm{C})$ the flow is (partially) reversed. In general, the shape which melts the slowest is quite distinct from that of a disk.