= 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.
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