Mantle thermal budget ($C_m\dot{\overline{T}}=H_m+Q_{\mathrm{cmb}}-Q_m$)

An energy balance for heat stored in the mantle. Here $C_m$ is its effective heat capacity, $H_m$ internally generated radioactive power, $Q_{\mathrm{cmb}}$ power entering across the core-mantle boundary and $Q_m$ power leaving the mantle. The sign of the right-hand side determines warming or secular cooling in this reduced model. Different reservoirs and latent heat may require additional terms. Surface heat loss includes crustal contributions and should not be substituted for $Q_m$ without specifying the partition.

The ratio of radiogenic heating to heat loss for a stated planetary reservoir, named for Harold Urey. A convective mantle Urey ratio uses mantle radioactive production and heat leaving the mantle; a bulk-silicate or surface ratio uses a different reservoir and heat budget. It must be labeled accordingly. A ratio below one is consistent with drawing on stored heat, but core heat or other inputs must also be included before inferring the sign of the mantle's temperature change.