Amplified radiative cooling via optimised combinations of aperture geometry and spectral emittance profiles of surfaces and the atmosphere

Abstract

Net thermal radiation cooling, from surfaces at sub-ambient temperatures, to the night sky is amplified if the aperture to the sky is partially blocked with heat mirrors. The temperature at which radiation loss stagnates (the effective sky temperature) falls continuously as the aperture closes and is derived in terms of the aperture size and the spectral properties and temperatures of the atmosphere and of the emitting surface. Cooling surfaces must have high absorptance between 7.9 μm and 13 μm where the atmosphere is most transparent. The best response for the remainder of the Planck radiation spectrum surprisingly switches between two spectral extremes at a temperature which falls as the aperture gets smaller. A perfect absorber is best above this switch, while surfaces which reflect all of this radiation are best below it. A simple formula is presented for the cross-over temperature as a function of aperture size. With known material properties plus representative non-radiative heat gains a high emittance surface is generally better except when heat mirrors are not used. A known high emittance roof paint at 10° C below ambient, under a 45° aperture lined with shiny aluminium, can achieve a net output power near 135 W m −2 under a clear sky.