Circular objects do not melt the slowest in water
arxiv(2023)
摘要
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.
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