[burlesona]

The core of the earth is essentially a fission reactor with quite a lot of fuel available. While this heat source is technically finite, so is the sun, and the universe itself. If you somehow live to see the heat death of the universe, you’re probably SOL.

But for humans living on earth today, and in timescales we care about (millions of years), the Earth’s core won’t run out of heat.

[kragen]

Not the core, which is made of stable elements like iron, but the crust. You'd think that uranium and thorium would settle to the core because they're heavy, but they're not siderophilic, so most of them stays in the crust. About two thirds of the geothermal heat flux is from fission in the crust: https://en.wikipedia.org/wiki/Geothermal_gradient

Non-sustainable heat extraction is much more likely, because the sustainable resource is only about 44 TW, while world marketed energy consumption is already 18 TW (https://en.wikipedia.org/wiki/World_energy_supply_and_consum...). By contrast, there are about 100 000 TW of solar energy available. There are billions of years of fossil heat locked up in the crust, amounting to conservatively many millions of times the total oil supply, and by extracting it faster than it was produced you can get much higher power.

Like (above-ground) nuclear energy, this is not currently an economically competitive source of exergy because of the cost of the heat engines required, except in unusual cases. It was until only a few years ago, but PV has gotten much cheaper since then. It probably won't be again until a revolution in manufacturing technology.

[burlesona]

Thanks for the clarification! I was under the impression that the heavier elements would be found toward the center. I appreciate the links :)