A plate cooling model for a mid-ocean ridge system has plate thickness

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth

Problem

A plate cooling model for a mid-ocean ridge system has plate thickness ap=90 kma_{\rm p} = 90\,\mathrm{km}, temperature contrast Tm−T0=1350 KT_m - T_0 = 1350\,\mathrm{K} and thermal conductivity k=3.2 W m−1 K−1k = 3.2\,\mathrm{W\,m^{-1}\,K^{-1}}. ((a)) Find the heat flow the plate model predicts for very old sea floor (t→∞t \to \infty). ((b)) State, in one sentence, what determines this asymptotic value within the model (as opposed to the falling 1/t1/\sqrt{t} heat flow of the half-space model).

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