Energy Budget: Is the Earth's magnetic field slowly decaying?

Earth's magnetic field is maintained by the dynamo effect, and I have no doubt that this effect could sustain Earth's magnetic field for a very long ("infinite") time.

It's my understanding that the energy flow is as follows. Thermal gradients in the liquid metal and differential rotating inner iron core and inner mantle yield kinetic liquid metal energy, which results in viscous dissipation losses, and magnetic energy, which results in joule heating.

The differential rotating inner iron core and inner mantle is fueled by the conserved angular momentum of the rotating earth. The same side of our moon always faces us due to (I think) tidal locking (water tides on the moon slowly stripped its angular momentum).

Here's my question:

1. Can we lose the energy source from differential rotating inner iron core and inner mantle over time by losing the differential rotation?

2. If the answer to 1. is "yes", then will the other input energies be enough to maintain Earth's dynamo?

3. If the answer to 2. is "no" or "maybe", then can we compute a time estimate of how long that will take? How long will it take?

Any help is greatly appreciated!

• Angular momentum is only conserved for a point mass in a perfectly symmetric radial potential. This is not given, there are tidal forces by the other planets. There are radioactive decays inside the earth that heat it up. Energy is dissipated into the universe. I think it is hard to make an estimate on the relative sizes of the effects out of the blue. Commented Oct 1, 2016 at 12:57
• The dynamo is driven by convection, not differential rotation.The core is at 5,700 K and cooling about 100 degrees Celsius per billion years. Commented Oct 2, 2016 at 1:47
• This answer over at Earth Science StackExchange suggests the earth's core has cooled by about 250 K over the last 4 billion years, so I doubt that the losses you mention in the 2nd paragraph are particularly strong. Commented Nov 24, 2016 at 16:56