Power density
Power densities are covered in Nanosystems in the early chapter about scaling laws.
Lower bounds for maximally achievable power densities are explored in
later chapters covering electromechanical converters. They are very high.
Power-densities for mechanical energy transmission are explored here on this wiki a bit (follow the link).
(TODO: If possible get power densities from electromechanical converters and mechanical energy transmission in a form that is comparable. Despite different units ...)
Contents
SI Units
There are two kinds of power densities:
- aerial power density – W/m²
- volumetric power density – W/m³
- aerial power densities are relevant for transmission
- volumetric power densities are relevant for power conversion
(TODO: How & in how far can the two types be made comparable? And is there a way to get an intuitive grasp on them?)
Ultimate limits & cooling
While for
- small volumes and steady state
- big volumes and brief times (burst mode operation)
We already have lower bound conservative estimation numbers, for
- bigger volumes and longer operation times
waste heart removal becomes the limiting bottleneck.
Even with very high efficiencies given extreme power densities there will still be produce way too much waste heat.
To get a better handle on the ultimate limits of gem-gum systems
lower bounds for ultimate limits for power-densities for waste heat removal need closer investigation.
That is ultra high performance cooling systems. Likely based on solid state capsules in machine phase.
Math for onset of cooling limiting power density by system geometry
Nanosystems only covers:
- cooling systems sufficient for proposes the nanofactories – 11.5. Convective cooling systems
- cooling for nanomechanical computation – 12.8. Cooling and computational capacity
Questions: At which size scale does heat removal become the limiting factor for
- a volume (cube or sphere shape)
- a thin layer of specified thickness
Volumetric (cube) case:
- P_in = Q_V * V = Q_V * s³
- P_out = Q_A * 6A = Q_A * s²
- P_in = P_out
- s = 6Q_A / Q_V
This gives a maximal cube side-length.
Spherical case is left as exercise for the so inclined reader.
Thin layer case (s >> t):
- P_in = Q_V * (A*t) = Q_V * (s²*t)
- P_out = Q_A * (2*A + 4*s*t) ~ Q_A * (2*s²+0)
- P_in = P_out
- t = 2Q_A / Q_V
This gives a maximal layer thickness.
The layer side-length s can be arbitrarily large.
Related
- Energy conversion – There's an especially high lower bound for the maximal power density in electromechanical converters
- Energy density
High power energy transmission as a combination of:
- Chemical energy transmission
- Mechanical energy transmission
- Entropic energy transmission
- Thermal energy transmission – other quite different constraints here
External Links
Wikipedia
- Surface power density – W/m²
- Power density – W/m³
