Radiative imbalance with the sky → Mechanical work

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.12 × C.20 · Radiative imbalance with the sky × Photothermalfamily: PhotothermalD.12 × C.34 · Radiative imbalance with the sky × Marangonifamily: MarangoniD.12 × C.24 · Radiative imbalance with the sky × Turbomachineryfamily: Turbomachinery

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Radiative cooling power bound · resource-bound · listed, never decisive
  net cooling power ≲ 100–150 W/m² under a clear sky
• Carnot limit · formula-bound · hard, applies to this route
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c
• Betz limit · upper-bound · hard, filtered out by its applicability
  C_p ≤ 16/27 ≈ 59.3% of the kinetic power through the rotor disc

Steps

1. 01
   Radiative imbalance with the sky —drives→ Radiative sky coolingreplicatedclaim record

   radiative → thermal

   • an emitter with high emissivity in the 8–13 µm window and high solar reflectance
   • a clear sky; humidity and cloud close the window

   refs [1] [2] [3]
2. 02
   Radiative sky cooling —produces→ Temperature gradientreplicatedclaim record

   thermal → thermal

   • the cooled surface sits a few kelvin below ambient air

   refs [1] [4] [3]
3. 03
   Temperature gradient —drives→ Marangoni effectestablishedclaim record

   thermal → kinetic · loss to thermal

   • thermocapillary case: surface tension falls with temperature, so a temperature gradient along the interface drives flow toward the cold side

   liquid · temperature gradient required

   refs [5] [6]
4. 04
   Marangoni effect —produces→ Fluid flowestablishedclaim record

   kinetic → kinetic

   refs [5] [6]
5. 05
   Fluid flow —drives→ Aerodynamic and hydrodynamic liftestablishedclaim record

   kinetic → mechanical · loss to thermal

   • a rotor or vane in the produced stream at a working angle of attack; the driven flow must carry a directed momentum flux for a blade to load

   bulk flow required

   refs [7] [8]
6. 06
   Aerodynamic and hydrodynamic lift —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [8]
7. 07
   Mechanical motion —converts into→ Mechanical workestablishedclaim record

   mechanical → mechanical · loss to thermal

   refs [9]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 9

1. [1]
   A. P. Raman et al.. Passive radiative cooling below ambient air temperature under direct sunlight (2014)

   Nature 515, 540–544 · doi:10.1038/nature13883 · crossref ✓ 2026-09-19 · record
2. [2]
   Y. Zhai et al.. Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling (2017)

   Science 355, 1062–1066 · doi:10.1126/science.aai7899 · crossref ✓ 2026-09-19 · record
3. [3]
   J.-l. Kou et al.. Daytime radiative cooling using near-black infrared emitters (2017)

   ACS Photonics 4, 626–630 · doi:10.1021/acsphotonics.6b00991 · crossref ✓ 2026-09-19 · record
4. [4]
   A. P. Raman, W. Li, S. Fan. Generating light from darkness (2019)

   Joule 3, 2679–2686 · doi:10.1016/j.joule.2019.08.009 · crossref ✓ 2026-09-19 · record
5. [5]
   L. E. Scriven, C. V. Sternling. The Marangoni Effects (1960)

   Nature 187, 186-188 · doi:10.1038/187186a0 · crossref ✓ 2026-09-20 · record
6. [6]
   Q. Dai et al.. Directional interfacial motion of liquids: Fundamentals, evaluations, and manipulation strategies (2021)

   Tribology International 154, 106749 · doi:10.1016/j.triboint.2020.106749 · crossref ✓ 2026-09-20 · record
7. [7]
   A. Betz. Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren (1920)

   Zeitschrift für das gesamte Turbinenwesen 26, 307–309 · paper, no DOI · record
8. [8]
   S. L. Dixon, C. A. Hall. Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.) (2014)

   Butterworth-Heinemann · doi:10.1016/C2011-0-05059-7 · crossref ✓ 2026-09-19 · record
9. [9]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record