Is there an energy source in the Earth's core?

Yes, the earth houses a passive nuclear reactor. The evidence actually says all the earth's heating takes place in the mantle and crust, not the core. > All models of the inner Earth depend on indirect evidence. read more

Apparently there is a source of energy - heat generated by radioactive decay of the elements like Uranium that will be right at the core. About half of the heat is generated from this. The rest of the heat is left over from the formation of the earth. read more

Heavy, radioactive elements such as uranium sank to the Earth's core along with the Iron and Nickel early in Earth's history (when it was all molten) and these radioactive elements have been heating the core (rather like a nuclear power station) ever since. read more