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Technical Brief

# Modeling Radiative–Convective Panels for Nighttime Passive Cooling Applications

[+] Author and Article Information
Ana R. Dyreson

Solar Energy Laboratory,
Department of Mechanical Engineering,
1337 Engineering Research Building,
1500 Engineering Drive,

S. A. Klein

Solar Energy Laboratory,
Department of Mechanical Engineering,
1343 Engineering Research Building,
1500 Engineering Drive,
e-mail: saklein@wisc.edu

Franklin K. Miller

Solar Energy Laboratory,
Department of Mechanical Engineering,
1341 Engineering Research Building,
1500 Engineering Drive,
e-mail: fkmiller@wisc.edu

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received December 16, 2016; final manuscript received July 10, 2017; published online August 22, 2017. Assoc. Editor: Jorge Gonzalez.

J. Sol. Energy Eng 139(5), 054503 (Aug 22, 2017) (8 pages) Paper No: SOL-16-1515; doi: 10.1115/1.4037379 History: Received December 16, 2016; Revised July 10, 2017

## Abstract

Passive cooling by combined radiation–convection from black panels at night is a potential source of significant energy-efficient cooling for both homes and industry. Assessing the technology requires system models that connect cooling load, passive cooling technology performance, and changing weather conditions in annual simulations. In this paper, the performance of an existing analytical model for a passive cooling panel is validated using a full two-dimensional finite differences model. The analytical model is based on a solar hot water collector model but uses the concept of adiabatic surface temperature to create an intuitive, physically meaningful sink temperature for combined convection and radiation cooling. Simulation results are reported for cooling panels of different sizes and operating in both low temperature (comfort cooling) and high temperature (power plant) applications. The analytical model using adiabatic minimum temperature agrees with the high-fidelity finite differences model but is more practical to implement. This model and the validations are useful for the continued study of passive cooling technology, in particular, as it is integrated into system-level models of higher complexity.

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## References

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## Figures

Fig. 1

The cross section of an example radiative–convective panel using a roll bond type construction where plates are bonded together. The panel is painted black for maximum emissivity and is uncovered to allow convection cooling.

Fig. 2

A cross section of a radiative–convective panel (bottom left). The temperature is lowest in the midpoint between tubes (top left). The temperature of the fluid in the tubes decreases along the panel length (right).

Fig. 3

For 17 different radiator designs, the flux at typical conditions is calculated using three different models. The numerical model is always within ±1% of the analytical model using the adiabatic temperature reference, while the sky temperature model can be off by as much as 20% depending on the geometry of the panel.

Fig. 4

For 17 different radiator designs, the error in the heat transfer compared to the numerical model is plotted against the ratio FR

Fig. 5

The three different models were tested for a one radiator design in an hourly annual simulation. Treating the numerical model as the baseline, the analytical model using the adiabatic temperature reference is always within ± 0.2% except when wind speed is zero and the differences in free convection models result in differences of about 1%. The percentage error in the analytical model with reference to the sky temperature is up to 15%. Note that there are two operation conditions for the radiator system (taking inlet water from cold storage or warmer storage), making the error versus FR plot appears separated into two regions.

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