I wonder, if we draw enough heat out... would the core cool enough to shrink? And if so, would the crust collapse to the new size?
Pure speculation of course, but did the first guy burning coal know the outcome?
Anyhow, I love geothermal, think you're right, but just got tweaked on the word "infinite".
Q = m c ΔT
m = mass of the crust (roughly 10^22 kg)
C = specific heat of crust (roughly 1000 J/kg·K)
ΔT = 1 K
Q = 10^25 joules would be needed to lower the earths crust by 1 degree K
About 10,000 years worth of today’s human energy consumption
Even at million+ year timescales, I can’t see any way the temperature of the upper crust could matter to the core at all - even if the crust was at absolute zero.
Dirt insulates relatively well, and the amount of thermal mass present is mindboggling.
Kind of joking: unless there are nonlinear effects near 300K? Fig 4 [1] seems to suggest that the thermal diffusivity of the mantle grows very fast as temperature declines past 300K... but the data stop at 200K.
Reason for initial comment: we could probably set up a spherical heat equation to guess how crust cooling would change heat conduction at the outer core. But I have absolutely no idea how to reason about changes in heat conduction affecting the convection dynamics that generate the field. I was silently hoping for one of the domain experts lurking this forum to see it and share wisdom. (But overall it was a silly question, I know).
[1] https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200...