Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2013 / Paper 1 / 1 / a / iii / Solution

At the bottom, $T(0,t)=T_1$. Convecting mantle is treated as maintaining the basal temperature and supplying heat to the plate. This is a prescribed thermal boundary at fixed thickness, not a claim that the real mechanical base is an impermeable material interface.