= Half-space cooling model
{title2=$T(z,\tau)=T_s+(T_m-T_s)\operatorname{erf}[z/(2\sqrt{\kappa\tau})]$}
The <half-space cooling model> solves the one-dimensional <heat equation> for initially hot material cooled at a fixed-temperature surface. For constant <thermal diffusivity> $\kappa$, a fixed interior-temperature isotherm deepens proportional to $\sqrt\tau$. Applied to an oceanic <lithosphere>, it explains the leading age dependence of cooling; finite plate thickness and basal heat supply limit its extrapolation to old ages.
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