The heat flow crossing the core-mantle boundary is estimated to be

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

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

Problem

Q_c=9\,\mathrm{TW}

. The core's adiabatic temperature gradient follows

(\mathrm{d}T/\mathrm{d}z)_{\rm ad}=\alpha_VgT/c_p

with

\alpha_V=10^{-5}\,\mathrm{K^{-1}}

g=10.7\,\mathrm{m\,s^{-2}}

T=4000\,\mathrm{K}

and

c_p=750\,\mathrm{J\,kg^{-1}\,K^{-1}}

; take the core's thermal conductivity to be

k_{\rm core}=40\,\mathrm{W\,m^{-1}\,K^{-1}}

and its surface area to be

4\pi r_c^2=1.52\times10^{14}\,\mathrm{m^2}

. Someone argues: "the whole

9\,\mathrm{TW}

leaves the core, so the whole

9\,\mathrm{TW}

is available to drive the geodynamo." ((a)) Compute the heat conducted down the adiabat, in TW. ((b)) Say whether the argument is correct, and if not, how much of the

9\,\mathrm{TW}

can actually drive thermally driven convection, and what becomes of the rest.

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