“Stokes’s Problem With Melting”, Steven H. Emerman, D. L. Turcotte1983-11-01 (self-sinking waste disposal)⁠:

[Stokes problem] In this paper we solve for the drag experienced by a hot rigid sphere which melts its way through a cold medium.

The temperature of the sphere is maintained by internal heat generation. The cold medium is solid and deforms only when the hot sphere heats it above its melting point.

We find that the flow is confined to a thin layer about the forward hemisphere when the Péclet number is much greater than a known function of the Stefan number.

We apply our results to the China Syndrome problem and show that in about 2000 years a nuclear reactor core could melt its way through the solid earth to the earth’s core.