Ice penetration by a bluff-body melting probe

We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by lubrication theory. The resulting Stefan problem is solvable in closed form. The solution determines the dependence of the penetration speed on the temperature differential between the probe and the surrounding ice, the size, shape and weight of the probe, the viscosity of liquid water and the thermal properties of solid ice.