This paper describes the fundamentals of melting when a shell of phase
-change material rides on a heated horizontal cylinder. In the first p
art of the paper, contact melting theory is used to predict the histor
y of the melting process and, in particular, the time when the remaini
ng ice falls off the cylinder. It is shown that the melting process co
nsists of two distinct regimes, first, an early regime when the cylind
er is surrounded by ice and, second, a late regime when the cylinder c
uts through the top of the ice shell. The second part describes labora
tory measurements that validate the theory. The third part of the pape
r shows that in the complete cycle that starts with freezing the shell
and ends with the contact-melting removal of the shell, there exists
an optimal frozen shell thickness such that the cycle-averaged product
ion of ice is maximized.