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 Incoming links: Oceanic heat flow: implications for global heat loss by Derrick Hasterok and others

Past exam of the plate tectonics course of the University of Oxford / 2022 / 3 / c / Solution 2026-10-25

The supplied plot gives surface heat flux, not a whole-crust mean temperature. At young ages its scatter is substantial. Representative readings suitable for an order-of-magnitude conductive calculation are

q_{J} ≃ 0.20 W m^{- 2}

near

5

Ma and

q_{N} ≃ 0.070 W m^{- 2}

near

50

Ma; plausible graphical ranges are roughly

0.12

–

0.23

and

0.06

–

0.09 W m^{- 2}

, respectively. These are approximate choices within the plotted population, not uniquely determined statistical means or a digitization of its red curve.

Assume the same normal oceanic crustal thickness

h_{c} = 7

km, seafloor temperature

T_{s} ≃ 0^{\circ} C

, negligible internal crustal heating and a linear conductive profile. These are additional assumptions; the paper supplies conductivity but not thickness. With depth

z

positive downward and

q

the magnitude of the upward flux, Fourier's law gives

T (z) = T_{s} + \frac{q z}{k}, \overline{T}_{c} = \frac{1}{h _{c}} \int_{0}^{h_{c}} T (z) d z = T_{s} + \frac{q h _{c}}{2 k} .

(1)

This is the crustal mean temperature from conductive heat flow, not the basal temperature, which is twice the excess above

T_{s}

. Substitution of

k = 1.3 W m^{- 1} K^{- 1}

gives

\overline{T}_{J} ≃ \frac{0.20 \times 7000}{2 \times 1.3} = 538^{\circ} C, \overline{T}_{N} ≃ \frac{0.070 \times 7000}{2 \times 1.3} = 188^{\circ} C .

(2)

A sensible rounded answer is therefore about $540^{\circ} C$ for the young crust and $190^{\circ} C$ for the old crust, with a representative contrast $Δ \overline{T}_{c} ≃ 350$ K. The corresponding basal values are about

1080

and

380^{\circ} C

. The quoted graphical ranges instead yield mean temperatures about

320

–

620

and

160

–

240^{\circ} C

, at the same assumed thickness.

Figure 1.
Original conductive temperature estimates and their crust-only thermal-buoyancy scaling; thickness, linear profiles and representative fluxes are explicit assumptions
. **Details**.

The temperatures scale linearly with

h_{c} / k

. Hydrothermal circulation can redistribute heat, especially in young permeable crust, and measurements through sediment need not equal the purely conductive cooling-model flux everywhere. The supplied study explicitly addresses the resulting oceanic heat-flow deficit.^[ref] Thus the calculation gives plausible incoming-crust averages under a stated model, not the entire plate's temperature or its later temperature at depth in the subduction zone.

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