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Passive sub-ambient cooling:
radiative sky cooling vs. evaporative cooling
Ablimit Ailia, Xiaobo Yina,b, Ronggui Yangc,d,*
a Department of Mechanical Engineering, University of Colorado, Boulder, CO
80309, United States b Materials Science and Engineering Program, University of Colorado, Boulder, CO
80309, United States
cSchool of Energy and Power Engineering, Huazhong University of Science and
Technology, Wuhan, Hubei 430074, China
dState Key Laboratory of Coal Combustion, Huazhong University of Science and
Technology, Wuhan 430074, China
* Corresponding authors: [email protected]
Abstract
Day-and-night radiative sky cooling has emerged as a potential alternative to
conventional cooling technologies such as refrigeration-based air conditioning and
evaporative wet cooling. Both radiative sky cooling and evaporative cooling can
passively achieve sub-ambient cooling. Although both cooling methods are subject to
impacts from various weather conditions, the extents of impacts under the same
conditions are not well understood. In this work, we both experimentally and
theoretically explore how a passive radiative cooler and a passive evaporative cooler
perform when exposed to a clear night sky. We show that evaporative cooling is better
suited for high-temperature and low-humidity weather conditions, with the
measured sub-ambient temperatures of the radiative and evaporative coolers being
−13.5℃ vs. −15.0℃ at a low relative humidity of 13% and a high ambient
temperature of 26℃. On the other hand, radiative cooling is relatively more resilient
than evaporative cooling under high-humidity and/or low-temperature weather
conditions, with the measured sub-ambient temperatures of the coolers being −11.5℃
vs. −10.5℃ at a slightly higher relative humidity of 32% and a slightly lower ambient
temperature of 17℃. Depending on water availability and weather conditions, both
evaporative cooling and radiative cooler can be adopted as mutually supplemental
cooling technologies.
Keywords: passive cooling, radiative sky cooling, evaporative cooling, sub-ambient
cooling
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1. Introduction
Developing environment-friendly, energy-efficient, and affordable sub-ambient
cooling technologies has become an increasingly important research endeavor as part
of the efforts to meet the ever-increasing energy demand,1 reduce greenhouse gas
emissions,2 combat climate change, tackle water scarcity,3 reduce thermal pollution,4
and address energy poverty.5 Conventional cooling technologies contribute to the
above-listed challenges in so many ways, directly or indirectly. For instance,
refrigeration-based air conditioning systems may directly leak hydrocarbons that are
considered harmful greenhouse gasses or ozone-depleting substances, although
refrigerants with reduced environmental damage are being developed.6 Another
drawback of current air conditioning systems is high power consumption and the
associated energy bill, which discourages households to turn on air conditioners, even
in developed countries.5 In many developing countries, a substantial number of
households have yet to install air conditioning systems because of their installation
and energy costs.7 Much more severe yet indirect impacts of air conditioning systems
come from the fact that fossil-fuel-burning thermal power plants account for most of
the electricity generation worldwide.8,9 Thermal power plants have at least three
major impacts on the environment. One is the release of greenhouse gases, mainly
CO2 into the atmosphere.10 Another impact is large water withdrawals and the
release of low-quality waste heat into water reservoirs, causing thermal pollution.4,11
Traditional one-through wet-cooled thermal power plants are often associated with
water reservoirs’ thermal pollutions.11 The third major impact is evaporative water
losses by cooling towers into the atmosphere. On one hand, the water evaporated
into the atmosphere must be resupplied by a water reservoir, which can otherwise be
used for other purposes such as agriculture and domestic applications, and especially
for alleviating water scarcity. On the other hand, this water vapor in the atmosphere
amplifies the greenhouse effect12 because it “cloaks” the atmospheric transmittance
window, trapping the outgoing thermal radiation from the Earth's surface and
increasing the downward radiation from the atmosphere.13 As the atmosphere gets
warmer, more electricity must be generated to meet the ever-growing demand for air
conditioning, thus forming a complex vicious cycle.14
Considering both cost and efficiency, evaporative cooling has been used in many
forms as an alternative to refrigeration-based air conditioning systems or to cool the
condensers in thermal power plants.15,16 The simplest form of evaporative cooling is
spraying water on surfaces, which is still widely used worldwide to cool ambient and
suppress dust on yards, roads, and construction zones. A more sophisticated form of
evaporative cooling is commercial portable swamp coolers used for space cooling.
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Swamp coolers work best in dry seasons and regions to achieve both humidification
and cooling. High humidity however severely affects the performance of swamp
coolers as the wet-bulb temperature approaches the dry-bulb (ambient) temperature.
The most vital and widest application of evaporative cooling is thermal power plant
cooling, mostly in the form of wet cooling towers and sometimes cooling ponds. In the
US alone, nearly 6 trillion liters of withdrawn water are evaporated into the
atmosphere by thermal power plants each year.17,18 Evaporative cooling in thermal
power plants indeed brings several challenges described above.
Radiative sky cooling has been proposed as an alternative cooling method.19,20,21
Without using much electricity or evaporating any water, radiative sky cooling
passively dumps waste heat through the atmospheric window into the deep space
instead of releasing it to the ambient air as in conventional cooling systems.22,23,24
Radiative sky cooling has the potential advantage of deep sub-ambient cooling due to
the ultra-cold Universe, given that little to no solar absorption occurs and parasitic
convective loss is minimized.25,26 With advancements in materials science and
engineering, highly solar reflective radiative cooling materials have recently been
developed in the form of solid photonic structures,27,28 thin films,29 paints,30,31 and
even wood.32 Radiative sky cooling systems with the capability of sub-ambient cooling
of water and cold generation have been demonstrated.33,34,35 Widespread adoption of
radiative sky cooling is possible if low-cost materials are available even though its
power density tends to be low (~100 W/m2).
In water-stressed and hot regions, radiative sky cooling can be a potential
alternative to evaporative cooling.36,37 Even though both evaporative cooling and
radiative sky cooling are reasonably well understood, it is not clear how these two
compare in terms of performance under similar environments. The two share several
similarities and differences. In addition to being able to passively achieve sub-
ambient cooling, both are adversely affected by humidity.34,38 An increase in humidity
(strictly speaking, precipitable water) results in a less transparent and more emissive
atmospheric window, thus increasing the downward radiation from the atmosphere
and diminishing the net radiative cooling power of an emissive surface.34,39,40 An
increase in humidity also results in reduced water uptake ability of the ambient air,
thus diminishing the rate and cooling power of evaporation.38 Other conditions affect
radiative cooling and evaporative cooling differently. Convection is considered purely
parasitic for achieving sub-ambient cooling by a radiative cooling surface.22 However,
the role of convection in evaporative cooling is two-fold: partially parasitic loss and
partially advective gain.38 An increase in the ambient temperature may reduce the
net cooling power of a radiative sky cooling surface because of increased atmospheric
downward radiation and increased convective parasitic loss. On the other hand, an
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increasing ambient temperature causes the atmosphere to uptake much more water
vapor and thus enhance the evaporative cooling power, even though convective
parasitic loss also increases. These similar yet different effects of weather conditions
on radiative sky cooling and evaporative cooling performance must be comparatively
evaluated to make an informative choice in applications.
In this work, we experimentally and theoretically compare the passive sub-
ambient cooling performances of a radiative sky cooler and an evaporative cooler. To
ensure the experiment variables were controllable, we carried out cooling tests during
the nighttime. The lack of solar irradiance, less windy ambient, as well as moderately
dynamic ambient temperature and humidity were helpful to achieve results with a
much better quality. Modeling was then used to study the effects of air heat transfer
coefficient, ambient temperature, and relative humidity on the sub-ambient cooling
performances of the coolers. Colormaps of net cooling power as a function of cooler
and ambient temperatures were created for extreme weather conditions: dry weather
with low humidity and wet weather with high humidity. Depending on weather
conditions, radiative sky cooling can perform better or worse than evaporative cooling.
Specifically, sub-ambient evaporative cooling is better suited for high-temperature
and low-humidity weather conditions, whereas sub-ambient radiative sky cooling is
more resilient than evaporative cooling under high-humidity and low-temperature
weather conditions.
2. Experiment setup
As shown in Fig. 1, a radiative cooling module and an evaporative cooling module
with an identical surface area of 0.3×0.3 m2 were made to carry out comparative
cooling experiments. On the radiative cooler (Fig. 1a), an emissive film made of
PETG with a thickness of 70 µm was laminated on a 1-mm thick aluminum plate. An
infrared transmissive PE windshield was added on the top to minimize parasitic heat
loss. On the evaporative cooler (Fig. 1b), a 70-µm thick hydrophobic film (PVDF) was
first laminated as a corrosion protection layer on an aluminum plate. A hydrophilic
cellulose fabric layer (~100 µm) was placed on top of the film to ensure the uniform
spreading of water. The initial layer thickness of water during the experiments was
around 3 mm. It was thin enough to make sure that the temperature gradient from
the water surface to the aluminum plate bottom surface was small ( Δ𝑇 = 𝑃𝑛𝑒𝑡 ∙
{𝜏𝑤 𝑘𝑤⁄ + 𝜏𝑓 𝑘𝑓⁄ + 𝜏𝑎𝑙 𝑘𝑎𝑙⁄ } ≈ 0 ~ 0.4 ℃ for the net cooling power range of 0 ~ 100 W).
The water was also sufficient to provide at least 12 hours of sub-ambient cooling
(𝑚𝑤 = 𝐴𝜏𝑤𝜌𝑤 ≈ 𝑃𝑒𝑣𝑎𝐴Δ𝑡 ℎℎ𝑓𝑔⁄ for Peva ≈ 100 W/m2). On both coolers, the back and the
four sides were insulated to ensure that heat transfer mainly occurred on the sky-
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facing top surface. Each cooler was equipped with three thermal couples to monitor
their temperature during experiments. Two thermocouples with a tip shielded with
non-emissive aluminum tape were used to monitor the ambient temperature.
The spectral emissivity of the radiative cooling surface (PETG film) and the
evaporative cooling surface (one layer of PVDF and one layer of cellulose fabric
without water) are given in Fig. 1c. The radiative cooling surface is wavelength-
selective, i.e., it mainly emits in the atmospheric transmittance window (8 – 13 µm).
The evaporative cooling surface, on the other hand, is nearly black, with a high
emissivity at wavelengths beyond 6µm. For sub-ambient cooling, a “selective”
radiative cooler is expected to perform better than a “black” radiative cooler.34,41
However, the addition of water evaporation can enhance the sub-ambient cooling
performance of the “black” radiative cooler.
Cooling experiments were carried out during clear-sky nighttime. There are
several advantages in conducting experiments during the nighttime than during the
daytime: avoiding complications due to different degrees of solar absorption by the
radiative cooling surface and the evaporative cooling surface with water, avoiding
frequently changing windy climate during the daytime, reducing frequent
fluctuations in air temperature and relative humidity, and most importantly,
achieving controllable and easily comparable cooling performances.
Since a change in one of the weather conditions was often accompanied by changes
in other weather conditions during the experiment, we also resort to theoretical
approaches in Section 5 to elucidate how radiative cooling and evaporative cooling
are affected by a single changing weather condition while other conditions remain
constant.
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Fig. 1. Experimental setup. (a) Passive radiative cooler. (b) Passive evaporative cooler.
On the radiative cooler, a radiative cooling film (PETG, ~70 µm thick) was laminated
on a 1-mm thick aluminum plate to ensure the surface temperature uniformity. An
infrared transmissive PE windshield was added to maximize the sub-ambient cooling
degree. On the evaporative cooler, a hydrophobic film (PVDF, ~70 µm thick) was also
laminated on an aluminum plate, and then a hydrophilic fabric (cellulose, ~ 100 µm
thick) was placed on top of the film to ensure the uniform spreading of water. The
initial water thickness during the experiment was around 3.0 mm. (c) The infrared
emissivity of the radiative cooling surface and evaporative cooling surface in its dry
form. The radiative cooling surface is “partially selective” and the evaporative cooling
surface is “nearly black”.
PE wind shield
Emissive film
Aluminum plate
Insulation
Thermocouple
Evaporative water
Hydrophilic fabric
Hydrophobic film
Aluminum plate
Insulation
Thermocouple
b
2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0
0.0
0.2
0.4
0.6
0.8
1.0
Em
issi
vity
Wavelength (mm)
Evap cooler
Rad cooler
Atmosphere
Radiative cooler Evaporative coolera
c
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3. Experiment results
Fig. 2 presents the measurement results of the nighttime cooling experiments
that continued from 8:30pm to 6:30am the second day (June 16-17, 2020). The relative
humidity and the wind velocity during the experiments are given in Fig. 2a. Except
for a gust of wind, the wind velocity was mostly within 0 ~ 1.0 m/s, implying rather
calm weather. Initially, the relative humidity was quite stable within the range of 10
~ 20 %. Upon the arrival of the wind gust, the relative humidity jumped to a range of
30 ~ 35% and remained relatively constant afterward. The ambient temperature (Fig.
2b) also evolved at a mostly steady rate, except for a sudden drop with the arrival of
the wind gust, gradually decreasing from a peak of 27°C near the beginning of the
experiment to a low of 17°C near the end of the experiment. Mostly stable but
occasionally dynamic weather conditions allowed us to observe interesting and
delicate changes in the temperatures of the coolers.
Temperatures of the coolers are presented in Fig. 2b. Initially, the coolers were
placed indoors at a temperature of 23oC and covered with opaque shields. The coolers
were then moved outdoors, with the covers immediately lifted triggering rapid
temperature drops. There was a lag in the evaporative cooler temperature because of
the larger thermal mass of water. However, the evaporative cooler temperature fell
below the radiative cooler temperature in less than an hour from the start of the
experiment, and it remained as such for at least 5 hours. The arrival of a wind gust,
a sudden jump in the relative humidity, and a slightly abrupt drop in the ambient
temperature all coincided with an inversion in the trend of the cooler temperatures.
The temperature of radiative sky cooler temperature now dropped below the
evaporative cooler temperature, which is explored further in the following sections.
We also plotted the sub-ambient cooling temperatures (Ts −Tamb) of the coolers in
Fig. 2c. Throughout the measurement duration, both coolers’ temperatures were well
below the ambient temperature. Two timepoints, t1 (10:30 pm) and t2 (05:45 am)
indicated by red arrows, are used to specify the sub-ambient temperature of the
coolers. At time t1, the sub-ambient temperatures of the radiative and evaporative
coolers were −13.5℃ and −15.0℃, respectively, demonstrating the excellent passive
cooling performance of both coolers. As the ambient temperature slowly dropped, the
sub-ambient temperatures of the coolers gradually increased but were still below
−12.0℃, until a flip in trend occurred with the occurrence of the wind gust and an
abrupt increase in the relative humidity from 15 ~ 20% to 30 ~ 35%. At time t2, the
sub-ambient temperatures of the radiative cooler and the evaporative cooler were
about −11.5℃ and −10.5℃, respectively. Although both coolers saw a deterioration
in their sub-ambient cooling performance as the relative humidity increased from
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13.0% at t1 to 32.0% at t2 and the ambient temperature decreased from 26.0℃ to
17.0℃, the degree of deterioration on the evaporative cooling was larger.
Next, we use theoretical approaches to elucidate how radiative cooling and
evaporative cooling are affected by individual changes in the convective heat transfer
coefficient, ambient temperature, and relative humidity (precipitable water).
Fig. 2. Sub-ambient cooling measurement results. (a) Relative humidity (red curve)
and wind velocity (blue curve) as a function of time. (b) Temperatures of the radiative
cooler (green curve), the evaporative cooler (blue curve), and the ambient (black curve).
(c) Sub-ambient temperatures of the radiative cooler (green curve) and the evaporative
cooler (blue curve). The two time points highlighted by red arrows, t1 = 10:30 pm and
t2 = 05:45 am, corresponds to the ambient weather conditions later used in modeling,
where Tamb-t1 = 26.0oC, RHt1 = 13, Vt1 = 0.50 m/s, and Tamb-t2 = 17.0oC, RHt2 = 32.0%,
Vt2 = 0.00 m/s.
4. Modeling
4.1. Radiative sky cooling and evaporative cooling models
On a sky-facing cooler (radiative or evaporative), the power density of upward
radiation from the cooler surface is given by
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𝑃𝑠 = ∫ ∫ ∫ 휀𝑠(𝜆, 𝜃)𝐼𝐵(𝑇𝑠, 𝜆) sin 𝜃 cos 𝜃
𝜋2
0
𝑑𝜃2𝜋
0
𝑑𝜑∞
0
𝑑𝜆, (1)
where 𝐼𝐵 is the blackbody spectral radiance (𝐼𝐵 =2ℎ𝑝𝑐2
𝜆5
1
exp[ℎ𝑝𝑐 (𝜆𝑘𝐵𝑇)⁄ ] −1), λ is the
wavelength, and 휀𝑠(𝜆, 𝜃) is the hemispherical spectral emissivity of the cooler
surface.
The atmospheric downward radiation absorbed by the cooler surface is given by
𝑃𝑎𝑡𝑚 = ∫ ∫ ∫ 휀𝑠(𝜆, 𝜃)휀𝑎𝑡𝑚(𝜆, 𝜃, 𝑃𝑊)𝐼𝐵(𝑇𝑎𝑡𝑚, 𝜆) sin 𝜃 cos 𝜃
𝜋2
0
𝑑𝜃2𝜋
0
𝑑𝜑∞
0
𝑑𝜆, (2.1)
where 휀𝑎𝑡𝑚(𝜆, 𝜃, 𝑃𝑊) is the effective hemispherical spectral emissivity of the
atmosphere, and 𝑇𝑎𝑡𝑚 refers to the ambient temperature 𝑇𝑎𝑚𝑏 . Our analyses show
that using zenith-0o atmospheric emissivity, which is the lowest over the hemisphere,
and 𝑇𝑎𝑚𝑏, which is the highest in the densest layer of the atmosphere, gives the lowest
error when the atmosphere is treated as if it is a solid body with an effective spectral
emissivity.
The effective atmospheric emissivity is mainly a function of the atmospheric
precipitable water (PW), which itself is a function of both relative humidity and
ambient temperature. For a location with a clear sky and a given altitude (~1600 m
in this work), PW (in mm) can be estimated by34,42
𝑃𝑊 ≈ 2.15𝑅𝐻3800 exp (
17.63𝑇𝑎𝑚𝑏
𝑇𝑎𝑚𝑏 + 243.04)
𝑝𝑎𝑚𝑏− 0.82. (2.2)
The atmospheric spectral emissivity can be computed as a function of the
precipitable water by using tools such as MODTRAN.43,44
The convective parasitic power density over the cooler surface is simply given by
𝑃𝑐𝑜𝑛𝑣 = ℎ𝑎𝑖𝑟(𝑇𝑎𝑚𝑏 − 𝑇𝑠), (3.1)
where ℎ𝑎𝑖𝑟 is air convective heat transfer coefficient. For horizontal rectangular
surfaces, it may be expressed as34,45
ℎ𝑎𝑖𝑟 = 𝑎 + 𝑏𝑉 (3.2)
where V is the wind velocity, and coefficients as a and b depend on if there is a
windshield or not. Without a windshield, ℎ𝑎𝑖𝑟 ≈ 8.5 + 2.5𝑉 .46,47 With a windshield,
ℎ𝑎𝑖𝑟 ≈ 2.5 + 2.0𝑉 .34 For 𝑉 ≈ 0~1.0 𝑚/𝑠 in the experiment, we estiamte ℎ𝑎𝑖𝑟 ≈
8.5~11.0 𝑊𝑚−2𝐾−1 for the evaporative cooler, and ℎ𝑎𝑖𝑟 ≈ 2.5~4.5 𝑊𝑚−2𝐾−1 for the
radiative cooler.
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For the evaporative cooler, the power density of evaporation is given by48
𝑃𝑒𝑣𝑎 =𝑑𝑚𝑤
𝑑𝑡∙ ℎ𝑓𝑔 = ℎ𝑚𝑎𝑠𝑠(𝜌𝑣,𝑠 − 𝜌𝑣,∞)ℎ𝑓𝑔, (4.1)
where hmass is the mass transfer coefficient, 𝜌𝑣,𝑠 and 𝜌𝑣,∞ are respectively the vapor
densities at the water surface and in the air far from the surface, and ℎ𝑓𝑔 is the latent
heat of vaporization of water.
The mass transfer coefficient is related to the convective heat transfer hair as48
ℎ𝑎𝑖𝑟
ℎ𝑚𝑎𝑠𝑠= 𝜌𝑎𝑖𝑟𝑐𝑝,𝑎𝑖𝑟𝐿𝑒1−𝑛, (4.2)
where 𝜌𝑎𝑖𝑟 is the air density, 𝑐𝑝,𝑎𝑖𝑟 is the air heat capacity, and Le is the Lewis number,
which is the ratio of the thermal and concentration boundary layer thicknesses
(𝛿𝑡 𝛿𝑚⁄ = 𝐿𝑒𝑛). For gasses, Le is on the order of unity (𝐿𝑒 ≈ 1). For the air-water
systems in this work, it is set 0.847.49 Here, the value of the exponent n is set ¼ since
the surface was horizontal and the wind velocity was small during the experiment.
The water vapor densities at the surface and in the air can be obtained from the
surface and air temperatures and the relative humidity, respectively, as
𝜌𝑣,𝑠 =𝑝𝑠𝑎𝑡
𝑅𝑣𝑎𝑝𝑜𝑟𝑇𝑠, 𝑎𝑛𝑑 𝜌𝑣,∞ =
𝑅𝐻 ∙ 𝑝𝑠𝑎𝑡
𝑅𝑣𝑎𝑝𝑜𝑟𝑇𝑎𝑚𝑏. (4.3)
Combining equations (1), (2.1), and (3.1) with their respective parameters and
properties, the net cooling power of the radiative cooler is then given as
𝑃𝑛𝑒𝑡− 𝑟𝑎𝑑 = 𝑃𝑠(𝑇𝑠,𝑟𝑎𝑑, 휀𝑟𝑎𝑑 ) − 𝑃𝑎𝑡𝑚(𝑇𝑠,𝑟𝑎𝑑 , 휀𝑠,𝑟𝑎𝑑 , 휀𝑎𝑡𝑚 )
− 𝑃𝑐𝑜𝑛𝑣(𝑇𝑠,𝑟𝑎𝑑 , 𝑇𝑎𝑚𝑏 , ℎ𝑎𝑖𝑟,𝑟𝑎𝑑). (5)
Similarly, combining equations (1), (2.1), (3.1), and (4.1) with their respective
parameters properties, the net cooling power of the evaporative cooler is then given
as
𝑃𝑛𝑒𝑡− 𝑒𝑣𝑎 = 𝑃𝑒𝑣𝑎(𝑇𝑠,𝑒𝑣𝑎, 𝑇𝑎𝑚𝑏 , 𝑅𝐻, ℎ𝑚𝑎𝑠𝑠) + 𝑃𝑠(𝑇𝑠,𝑒𝑣𝑎, 휀𝑒𝑣𝑎 ) − 𝑃𝑎𝑡𝑚(𝑇𝑠,𝑒𝑣𝑎 , 휀𝑠,𝑒𝑣𝑎 , 휀𝑎𝑡𝑚 )
− 𝑃𝑐𝑜𝑛𝑣(𝑇𝑠,𝑒𝑣𝑎, 𝑇𝑎𝑚𝑏 , ℎ𝑎𝑖𝑟,𝑒𝑣𝑎). (6)
The sub-ambient cooling temperature of the coolers at equilibrium is given by Pnet
= 0. Using the above models for radiative sky cooling and evaporative cooling, we
investigate next how air heat transfer coefficient, ambient temperature, and relative
humidity individually affect the net cooling power and the sub-ambient temperature
of the coolers.
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4.2. Effect of air heat transfer coefficient on sub-ambient cooling
In sub-ambient cooling, convection is a purely parasitic loss on the radiative cooler
(Eq.3), where its role on the evaporative cooler is two-fold: parasitic loss (Eq.3) and
advective removal of water vapor (Eq.4.1). Fig. 3 shows net cooling power (Pnet) vs.
non-equilibrium sub-ambient temperature (Ts− Tamb) for different values of air heat
transfer coefficient at Tamb = 25℃ and RH = 30%. On the radiative cooler (Fig. 3a),
the smaller the air heat transfer coefficient, the higher the net cooling power at any
sub-ambient cooling temperature. At equilibrium (Pnet = 0), the sub-ambient
temperature of the radiative cooler drops from −4.5℃ to −14.5℃ as the air heat
transfer coefficient hair decreases from 20 W/(m2K) to 2.5 Wm-2K-1. The transition
from convective loss to convective gain occurs only at (Ts− Tamb = 0) for all heat
transfer coefficient values.
In comparison, the case for the evaporative cooler is more complicated (Fig. 3b).
At Tamb = 25℃ and RH = 30%, a low air heat transfer coefficient is beneficial to
achieve a sub-ambient cooling temperature as low as possible at equilibrium (Pnet =
0): −15.4℃ vs. −11.2℃ for hair values of 20 Wm-2K-1 vs. 2.5 Wm-2K-1, respectively. As
the sub-ambient temperature increases to around −10℃, all cooling power curves for
different hair values intersect at an inversion point, where the gain from evaporation
overtakes the parasitic loss from convection. At an even higher sub-ambient
temperature above the inversion point, the larger the air heat transfer coefficient, the
higher the net cooling power.
Based on the analyses above, to achieve a low sub-ambient temperature alone, it
is preferable to keep the air heat transfer coefficient small for both coolers, implying
a windshield is beneficial to reduce the convective loss. For practical purposes,
however, a windshield was added only to the radiative cooler during the sub-ambient
cooling experiment.
It is important to point out that when there is no sub-ambient cooling (Ts− Tamb =
0), the net cooling power densities of the radiative and evaporative coolers are 115
W/m2 vs. at least 190 W/m2, implying evaporative cooling posses a much higher
cooling potential under hot and dry climates.
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Fig. 3. Effects of air heat transfer coefficient, hair, on the net cooling powers (Pnet), and
the sub-ambient temperatures (Ts− Tamb) of the coolers. (a) Radiative cooler and (b)
evaporative cooler. For both coolers, the lower the convective heat transfer coefficient,
the lower the sub-ambient cooling temperature at equilibrium (Pcool = 0) at the given
ambient conditions of Tamb = 25oC and RH = 30%. However, a larger convective heat
transfer coefficient is beneficial to the evaporative cooler when the sub-ambient cooling
degree is smaller than 10oC because of evaporative cooling power overcoming
convective parasitic loss.
4.3. Effects of ambient temperature and relative humidity on sub-
ambient cooling
Weather conditions such as relative humidity and ambient temperature naturally
affect the cooling performances of the radiative and evaporative coolers. As shown in
Fig.4, we separately modeled the effects of humidity and ambient temperature on
the coolers’ equilibrium sub-ambient temperatures when one of the conditions is fixed.
The specified relative humidity values, RH = 13% and 32%, as well as the two ambient
temperatures Tamb = 26℃ and 17℃, are respectively based on the weather conditions
at t1 = 10:30 pm and t2 = 05:45 am during the experiments. The air convective heat
transfer coefficients used in modeling are 4.5 Wm-2K-1 for the radiative cooler with a
windshield and 10.5 Wm-2K-1 for the evaporative cooler without a windshield, as
estimated from Eq.3.2 and the best agreement between the modeling and
experimental results. The corresponding atmospheric precipitable water (PW, Eq 2.1)
estimated from relative humidity and ambient temperature is given as the top x-axis.
The measured sub-ambient temperatures at the experimental conditions are
highlighted by open circles. The modeling and experimental results agree well with
less than 1℃ differences.
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Fig.4. Effects of ambient temperature and relative humidity on the sub-ambient
cooling temperatures of the radiative and evaporative coolers. (a & b) Effects of
ambient temperature on the cooler sub-ambient temperatures at equilibrium, for RH
= 13% and 32%, respectively. (c & d) Effects of relative humidity on the cooler sub-
ambient temperatures at equilibrium, for Tamb = 26℃ and 17℃, respectively. The
specified relative humidity values, RH = 13% and 32%, as well as the two ambient
temperatures Tamb = 26℃ and 17℃, are respectively based on the weather conditions
at t1 = 10:30 pm and t2 = 05:45 am during the experiments. The experimental sub-
ambient temperatures at the corresponding conditions are highlighted by open circles.
The atmospheric precipitable water (PW) given as the top x-axis was estimated from
the corresponding relative humidity and the ambient temperature. The air convective
heat transfer coefficients used in modeling are 4.5 Wm-2K-1 for the radiative cooler
with a windshield and 10.5 Wm-2K-1 for the evaporative cooler without a windshield,
as estimated from Eq.3.2.
As Fig.4a&b shows, the equilibrium sub-ambient temperatures (Ts− Tamb) of the
radiative and evaporative coolers are affected by the ambient temperature differently
at the two specified humidities. The sub-ambient temperature of the radiative cooler
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overall increases with the ambient temperature (except at low humidity and low
temperature in Fig.4a), whereas the sub-ambient temperature of the evaporative
cooler decreases with the ambient temperature. For the radiative cooler, even though
relative humidity is fixed, rising ambient temperature results in increasing
precipitable water at a growing rate (see top x-axes) and thus increasing atmospheric
emissivity. Rising ambient temperature and its consequent effect on the atmospheric
emissivity causes the atmospheric downward radiation to grow at a faster rate (Eq.2)
than the upward radiation from the cooler surface as it is only dependent on the
surface temperature (Eq.1). On the other hand, for the evaporative cooler, the
evaporative cooling power (Eq.3) is enhanced by the rising ambient temperature
much more than the convective loss (Eq.4), resulting in decreased sub-ambient
temperature.
The effect of relative humidity on the cooler sub-ambient temperatures at
equilibrium is presented in Fig.4c&d for the two specified ambient temperatures,
respectively. Both coolers are adversely affected, yet differently, by an increase in
relative humidity. The evaporative cooler sees a faster deterioration than the
radiative sky cooler. This is because the net cooling power of the radiative cooler is
only non-linearly and negatively correlated to relative humidity (Eqs.2) through the
atmospheric radiation. On the other hand, the net cooling power of the evaporative
cooler contains an evaporative term that is linearly and negatively proportional to
relative humidity (Eqs. 4) and the atmospheric radiation term that is non-linearly
and also negatively correlated to relative humidity (Eqs.2). It can be inferred further
that the radiative sky cooler may be a more resilient sub-ambient cooler under high
humidity conditions because of its relatively weaker dependence on humidity. On the
other hand, the evaporative cooler could perform better under high temperature and
low humidity conditions. In Fig.4, the measured sub-ambient temperatures (open
circles) of the radiative and evaporative coolers agree well with the modeled sub-
ambient temperatures: (−13.5℃ and −15.0℃) vs. (−13.8℃ and −15.8℃) at RH = 13%
and Tamb = 26℃, and (−11.5℃ and −10.5℃) vs. (−11.5℃ and −10.3℃) at RH = 32%
and Tamb = 17℃.
4.4. Net cooling power at low and high humidity
To investigate how extreme weather conditions, such as very low or very high
humidities, affect the passive net cooling power and the sub-ambient temperatures
of the coolers, we plotted in Fig. 5 net cooling power colormaps as functions of the
cooler and ambient temperatures for two humidity values: a low RH = 15% and a high
RH = 70%. In this figure, the regimes of sub-ambient cooling are bounded by two
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dashed curves: the equilibrium sub-ambient cooling temperature curve at Pnet = 0 and
the net cooling power curve at Ts− Tamb = 0. The horizontal width of the highlighted
regimes represents the sub-ambient cooling temperatures of the coolers. At RH = 15%,
both coolers have a large sub-ambient cooling potential at all temperatures plotted,
although the sub-ambient temperature of the radiative cooler does not change much
at high temperatures (Fig. 5a) while the evaporative cooler sees a noticeable increase
(Fig. 5b). At RH = 70%, however, the sub-ambient cooling potential of both coolers
diminishes at all temperatures (Fig. 5c&d), which is especially significant on the
evaporative cooler. The sub-ambient temperature of the radiative cooler also becomes
significantly small at high temperatures and this specified high humidity.
Fig. 5. Net cooling power color maps as functions of the cooler surface temperature and
the ambient temperature. (a) Radiative cooler and (b) evaporative cooler. The two
figures at the top are for a high-humidity condition (RH = 70%), and the two figures
at the bottom are for a low-humidity condition. The highlighted regions represent
passively achievable sub-cooling regimes defined by Ts – Tamb = 0 and Pnet cool = 0. The
horizontal width of the sub-ambient cooling regimes represents the sub-ambient
temperatures of the coolers.
Low
Humidity
(RH = 15%)
High
Humidity
(RH = 70%)
Radiative cooler Evaporative coolera b
c d
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The cooling power colormaps and the sizes of the sub-ambient cooling regimes
indicate that evaporative cooling is better suited for high-temperature and low-
humidity weather conditions, although radiative cooling also performs well under
these conditions. On the other hand, radiative cooling is positioned better than
evaporative cooling to work at high-humidity and low-temperature weather
conditions, where cold generation and storage for later use may be a more practical
approach. High-humidity and high-temperature weather conditions, unfortunately,
are detrimental to the performances of both coolers.
5. Conclusions
In this work, we have experimentally and theoretically investigated the passive
sub-ambient cooling performances of radiative cooling and evaporative cooling under
the same weather conditions. With sky-facing radiative and evaporative coolers with
the same surface, we experimentally observed the sub-ambient temperatures (Ts
−Tamb) of the coolers were −13.5℃ and −15.0℃, respectively, at a relative humidity
(RH) of 13% and an ambient temperature (Tamb) of 26℃. This shows the evaporative
cooler performs better than the radiative cooler at low-humidity but high-
temperature weather conditions. At a higher relative humidity of 32% and a lower
ambient temperature of 17℃, the observed sub-ambient temperatures of the
radiative and evaporative coolers were −11.5℃ and −10.5℃, respectively. This
indicates the radiative cooler is better positioned to work under low temperature or
high humidity conditions.
To elucidate the impacts of air convection, ambient temperature, and relative
humidity on the sub-ambient cooling performances of the coolers, we carried out
further theoretical analyses. We created net cooling power colormaps as functions of
the cooler and ambient temperatures for two humidity conditions: a low RH = 15%
and a high RH = 70%. The cooling power colormaps and the sizes of the sub-ambient
cooling regimes further confirm our experimental observations.
Our study validates and compares the passive sub-ambient cooling potential of
radiative cooling and evaporative cooling. In regions with high humidity or limited
water resources, radiative cooling can be a potential alternative to evaporative
cooling.
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