Coupled thermal histories of layered mantle convection

Two separately mixed layers with an interfacial thermal bottleneck require separate energy budgets. For lower input $F$, interlayer transfer $J$, surface loss $E$, and per-area heat capacities $H_l,H_u$, these are $H_l{\dot{T}}_l=F-J$ and $H_u{\dot{T}}_u=J-E$. At equilibrium all three fluxes agree, but a finite interface resistance retains a temperature difference. Thus layer count alone does not specify the cooling rate.