The UM (p. 97) says that radioactivity can’t be keeping the center of the Earth hotter than the surface, because radioactive elements are most concentrated in the crust. This is wrong.
It’s true that the most abundant radioactive isotopes tend to concentrate most in the crust of the Earth, but that really doesn’t matter. Suppose you have a sphere with heat sources spread throughout, but especially near the surface. Heat energy is generated, and spreads out. Some of it flows toward the surface and is radiated out into space, and some of it flows toward the center, because heat tends to flow, on average, in the direction of colder temperatures. When the heat energy gets to the center, where does it go? The only way to flow is toward the surface, but if the temperature is still warmer on the outside of the sphere, the net heat flow will still be toward the center. Therefore, the center will keep heating up until it is hotter than the outside of the sphere and heat can flow back the other way.
Think about this, UMers. If the Earth is actually colder in the center, then there must be some kind of black hole sucking heat out of there.
