The limits of cooling

Disclaimer: This page is …

• … not about feasibility analysis of advanced productive nanosystems.
• … not about exploratory engineering
• about having some fun collecting ideas on how to the boundaries of the possible could be pushed to the limit

Application cases may include:

• Hyper high throughput microcomponent recomposition
• Carriage particle accelerators (for space rockets)
• Nuclear fusion
• ... military horrors :(

Strategies that could be employed include:

• Choice of best materials as the thermal mass (this is beyond metamaterial emulatability)
• Choice of best materials as the thermal conductors (this is beyond metamaterial emulatability)
• Choice of best materials for applying eventual tricks (this is beyond metamaterial emulatability)
• Thermal mass capsules transported on tracks providing good thermal contact.
• Trick: Active squeeze-out of degrees of freedom from the perspective of the equipartitioning theorem

(wiki-TODO: discuss these in detail)

Choice of materials

• Best for thermal conduction seems diamond
• Best for thermal resilience/refractoryness (and still very good for conduction) seems moissanite (gem quality silicon carbide)
• Best for thermal mass seems water high pressure can be easily safely contained by nanoencapsulations

Cooling by capsule transport & its optimization

Thermal energy transport via heat conduction can be very fast.
Especially across short distances. But longer macroscale distances is slows down. Nonlinearly.
One way to counter that is to physically transport thermal masses.
There are some interesting tradeoffs/optimizations to make.
Thus there should be:

• some optimal cooling transport speed depending on details of design choices.
  
• some optimal scale of thermal-mass-transport-capsules

Optimizing speed:

• PRO: Higher speed means faster heat removal. Trivial.
• CON: Speeding up to high speeds means higher dissipative losses from (wearless) friction
  leading to even more heat needing removal.
  Unfortunately very low friction suspension (like means of levitation) are not an option at the hot side
  due to them providing insufficient thermal contact.
  

Optimizing scale:

• PRO: Bigger thermal-mass-capsules means less thermally conductive bearing area per thermal mass
• CON: Bigger thermal-mass-capsules means (nonlinear) increase in charge-up-time of these capsules

Squeezeout of degrees of freedom of thermal energy

See related topic: entropomechanical converter

Note: The following is wasteful as it actively increases the devaluation of energy (irreversibly converting free to bond energy).
This seems only useful for boosting performance (not efficiency) while keeping system volume small.

Basically the idea is to accelerate the dumping of heat on the cold side.

• thermal-mass-capsules contain bundles of chain molecules attached to two end-plates
• hot side: bundle-capsules arrive stretched out thermal – normal suck-up
• hot side: end plates are released (leaving machine phase) further thermal suck-up => loss of potentially recuperable free energy
• transport: bundles-capsules are transported to cold side
• cold side: bundles-capsules are pulled apart by force (injection of free energy) accelerating the release of stored thermal energy due to further elevated temperature
• transport back and repeat

By pulling the chain molecules straight they loose degrees of freedom (equipartitioning theorem).
With conservation and fast adiabatic pulling the same energy concentrate in fewer DOFs. Temperature rises accordingly.
Higher temperature means higher thermal gradient means higher speed of thermal flow.
As desired and as is the point of the whole exercise.
Another alternate way to look at the chain molecule stretching process is to interpret it as a forcing of disorder from position space into impulse space.

Limits:
The chain molecules need to be both

• thermally resilient and
• highly flexible.

This is only possible to a limited degree.
Silicones might be the best bet allowing temperatures to about ~600K or ~300°C

Unfortunately emulation by mechanical metamaterials is not viable.
While chains made of moissanite (SiC) crystolecules would be superbly resistant against very high temperatures,
they would likely not provide a sufficient volumetric density of mechanically squeezable thermal degrees of freedom
due to the size of the individual chain-links being at least several dozens or rather hundreds atoms each.

Related

• Cooling
• The challenge of high speeds near nanoscale