Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 332 / 2 / a / Solution

Take $z$ vertically downward from the cold surface. The ice occupies $0<z<h(t)$ and the water occupies $z>h(t)$. The temperature satisfies the heat equationin both phases, withThe remaining interfacial condition is the Stefan conditionA schematic should show the cold surface, the descending phase boundary, the ice temperature rising from $T_b$ to $T_m$, and the water temperature tending from $T_m$ to $T_{\infty }$.

Solved by gpt-5.6-sol high.