JOUL, Volume 3

Supplemental Information

Subambient Cooling of Water: Toward

Real-World Applications
of Daytime Radiative Cooling
Dongliang Zhao, Ablimit Aili, Yao Zhai, Jiatao Lu, Dillon Kidd, Gang Tan, Xiaobo
Yin, and Ronggui Yang
Table of Contents

Supplementary Information 1: Transient Heat Transfer Model for the RadiCold Module
Supplementary Information 2: Measurement of Water and Ambient Temperatures
Supplementary Information 3: Cooling Performance of RadiCold Module in 72
Continuous Hours
Supplementary Information 4: Measurement Method for Net Radiative Cooling Power
Supplementary Information 5: Effect of Cloud Cover on Radiative Cooling Power
Supplementary Information 6: Comparative Test of the 4 Water Modules under
Scattered Cloud Conditions
Supplementary Information 7: Validation of Overall Heat Transfer Coefficient
Supplementary Information 8: Operation Strategy of the RadiCold system
Supplementary Information 9: Optical Transmission of 3M Vikuiti ESR Film
Supplementary Information 10: Building-integrated RadiCold System and its Annual
Performance
Supplementary Information 1: Transient Heat Transfer Model for the RadiCold

Module

The heat transfer processes for a RadiCold module under the sun, as shown in

Figure 1 of the main text are represented by the following quantities: radiative cooling

power density (W/m2) emitted from the RadiCold metafilm surface (𝑃𝑟𝑎𝑑 ), the absorbed

power density of atmospheric radiation on the RadiCold metafilm surface (𝑃𝑎𝑡𝑚 ), the

absorbed power density of solar irradiance on the RadiCold metafilm surface (𝑃𝑠𝑜𝑙𝑎𝑟 ), and

convective and conductive heat fluxes between RadiCold module and ambient air

(𝑃𝑐𝑜𝑛𝑣+𝑐𝑜𝑛𝑑 ).

The radiative cooling power density of the RadiCold metafilm can be obtained by

integrating the spectral radiance over the whole spectrum and the hemisphere:

𝜋/2 ∞
𝑃𝑟𝑎𝑑 (𝑇) = 2𝜋 ∫ ∫ 𝐼𝐵𝐵 (𝑇, 𝜆)𝜖𝑓𝑖𝑙𝑚 (𝜆, 𝜃) sin 𝜃𝑐𝑜𝑠𝜃 𝑑𝜆𝑑𝜃 (S1)
0 0

2ℎ𝑐 2 1
where, 𝐼𝐵𝐵 (𝑇, 𝜆) = is the spectral radiance of blackbody at radiative
𝜆5 exp(ℎ𝑐 ⁄(𝜆𝑘𝐵 𝑇)−1

surface temperature T, λ is the radiation wavelength, and 𝜖𝑓𝑖𝑙𝑚 (𝜆, 𝜃) is the spectral

emissivity (absorptivity) of the RadiCold metafilm.

Similarly, the power density of absorbed thermal radiation from the atmosphere,

depending on both the RadiCold metafilm and atmospheric emissivity, is given by:

𝜋/2 ∞
𝑃𝑎𝑡𝑚 (𝑇𝑎𝑚𝑏 ) = 2𝜋 ∫ ∫ 𝐼𝐵𝐵 (𝑇𝑎𝑚𝑏 , 𝜆)𝜖𝑓𝑖𝑙𝑚 (𝜆, 𝜃)𝜖𝑎𝑡𝑚 (𝜆, 𝜃, 𝐻2 𝑂) 𝑠𝑖𝑛𝜃𝑐𝑜𝑠 𝜃𝑑𝜆 𝑑𝜃 (S2)
0 0
where 𝑇𝑎𝑚𝑏 is the ambient temperature and 𝜖𝑎𝑡𝑚 (𝜆, 𝜃, 𝐻2 𝑂) is the atmospheric emissivity,

which is a function of humidity and is represented by precipitable water,1 defined as the

depth of water in a column if all the water vapor in that column were precipitated as rain.

The atmospheric emissivity 𝜖𝑎𝑡𝑚 is calculated using ATRAN – an online software

provided by SOFIA Science Center.2 It is important to point out that most of the

atmospheric thermal radiation comes from the atmosphere near the ground, so the

ambient temperature (𝑇𝑎𝑚𝑏 ) is used in the calculation, which is a common practice in

estimating atmospheric radiation.3 Note that spectral atmospheric emissivity instead of

an averaged constant value is used in this work. Therefore, we do not need to use the

so-called effective sky temperature which is derived by assuming a constant sky

emissivity.4

The power density of absorbed solar irradiance is given by:

∞
𝑃𝑠𝑜𝑙𝑎𝑟 = 𝑐𝑜𝑠 𝜑 ∫ 𝜖𝑓𝑖𝑙𝑚 (𝜆, 𝜑)𝐼𝑠𝑜𝑙𝑎𝑟 (𝜆)𝑑𝜆 (S3)
0

where 𝐼(𝜆) is the solar spectral irradiance, and φ is the angle between the normal

directions of the RadiCold metafilm and the solar irradiance.

The convective and conductive heat transfer between RadiCold module and

ambient air are simply given by:

𝑃𝑐𝑜𝑛𝑣+𝑐𝑜𝑛𝑑 = (𝑇 − 𝑇𝑎𝑚𝑏 )ℎ𝑎𝑖𝑟 (S4)

where ℎ𝑎𝑖𝑟 , is the overall heat transfer coefficient between RadiCold module and ambient

air.
 To evaluate the convective heat transfer coefficient for flow over a flat surface with

steady state flow conditions, either theoretical method based on dimensionless

parameters (e.g., Reynolds and Nusselt number) can be used, or experimental method

based on wind tunnel measurements can be employed. 5 In outdoor conditions, as wind

constantly changes both its speed and blowing directions, air flow keeps transitioning

between natural convection, laminar flow, and turbulent flow, which makes it difficult to

obtain those non-dimensional parameters. Fortunately, there have been a large body of

work available in literature. Earlier experimental studies suggest that the effect of wind

speed on heat transfer coefficient from a flat surface can be quantified by a linear form of

correlation.6–10

ℎ𝑎𝑖𝑟 = 𝑎 + 𝑏𝑣 (S5)

where 𝑣 is the local wind speed, and 𝑎 and 𝑏 are fitted parameters. This is a generally

accepted correlation that used to quantify convective heat transfer coefficient on a flat

plate, such as solar thermal collectors11 and solar cells.12

By fitting parameters a and b to match the predicted water temperature with the

measured water temperature as shown in Figure 3A, the effect of wind on heat transfer

coefficient is quantified. In our experiments, the heat transfer coefficients change with

wind are ℎ = 2.5 + 2𝑣 and ℎ = 8.3 + 2.5𝑣 for a RadiCold module with and without PE film

on top, respectively. Note that the heat transfer coefficient here is the overall heat transfer

coefficient between ambient air and RadiCold module. These correlations are then further

validated by using more experimental data (see Supplementary Information 7).

Apparently, at sub-ambient operating conditions, the employment of a PE film on top of

the RadiCold module could substantially reduce thermal loss.

With all the heat transfer data from and into the RadiCold module as shown above

given, the net cooling power, which equals to the rate of cold gain in the water and

polycarbonate water container (assuming water and polycarbonate have the same

temperature since they are in direct contact and the polycarbonate container has a wall

thickness of only 0.5 mm while the radiative cooling process is slow), can be expressed

as:

(𝑐𝑤 𝑚𝑤 +𝑐𝑝 𝑚𝑝 ) 𝜕𝑇
= 𝑃𝑟𝑎𝑑 − 𝑃𝑎𝑡𝑚 − 𝑃𝑠𝑜𝑙𝑎𝑟 − 𝑃𝑐𝑜𝑛𝑣+𝑐𝑜𝑛𝑑 (S6)
𝐴 𝜕𝑡

where 𝑐 and 𝑚 are heat capacity and mass, subscripts 𝑤 and 𝑝 denote water and

polycarbonate panel, respectively, 𝐴 is the radiative surface area. 𝑇 is the temperature of

the RadiCold module, The above equation is not directly solvable because all the

parameters except for the surface area are not constants. Rearranging the above

equation and using a reasonably short time step, Δ𝑡, and index notation gives

𝐴[𝑃𝑟𝑎𝑑 − 𝑃𝑎𝑡𝑚 − 𝑃𝑠𝑜𝑙𝑎𝑟 − 𝑃𝑐𝑜𝑛𝑣+𝑐𝑜𝑛𝑑 ]

𝑇𝑡(𝑖+1) = 𝑇𝑡(𝑖) − ∙ Δ𝑡 (S7)
𝑐𝑤 𝑚𝑤 + 𝑐𝑝 𝑚𝑝

where i is the index of time t. Just using an initial surface temperature, the net cooling

power and temperature of the module at any later time can be calculated.
Supplementary Information 2: Measurement of Water and Ambient Temperatures

Figure S1. Measurement of water temperature in the modules. (A) Top view of the locations

of the thermocouples (red dots) that measure water (W1-W5) and ambient air temperatures (A1-

A3). (B) Cross-sectional view of the locations of the thermocouples that measure water

temperatures. The thermocouples are submerged in the polycarbonate water container to directly

measure water temperature. The yellow line on the top represents a polyethylene (PE) film. By

building an air gap between the PE film and the water container, convection heat loss of the water

module is reduced. (C) An example measurement of water temperatures inside the RadiCold

module. (D) An example measurement of ambient air temperatures.

 For each water module, there are 5 K-type thermocouples submerged inside the

water container to measure the water temperature. All thermocouples are pre-calibrated

to have 0.3°C accuracy for the measurement range of 0-50°C by using a standard

calibration method.13 Figure S1A and S1B shows the location of the 5 thermocouples (W1

– W5). There are also 3 thermocouples (A1 – A3) distributed around the water modules

(within 1-meter distance) to measure the ambient air temperature. The 3 thermocouples

that measure ambient air temperature are placed at sun-shielded locations but the air can

freely pass by. All thermocouples are connected to a National Instruments cDAQ-9174

system and temperature recordings were made every 5 s. Figure S1C shows a typical

measurement of water temperatures in the module. The temperature difference among

different thermocouples are within ±1°C. Figure S1D shows the measured ambient air

temperatures surrounding the RadiCold module during the same period. It can be see

that the measured ambient air temperatures have more fluctuation during the day, which

is due to the higher local wind speed during the day.

Comparison of ambient temperature measured using thermocouple with the data

from weather station

To show the accuracy of our measurement on ambient temperature using

thermocouples, we compared the thermocouple measured ambient temperature (at CU

Engineering Center Rooftop in Boulder, Colorado) to the data obtained from our weather

station (shown in Figure 2A). Figure S2A shows that good agreement between these two

measurements has been achieved.

Figure S2. Comparison of ambient temperature measurement from our thermocouples and

data obtained from our weather station. (A) The measured ambient temperatures from

thermocouples and our weather station are in good agreement. (B) The Boulder Municipal

Airport weather station is located 5 kilometers away from CU Engineering Center. Within

a few kilometers range, the highest temperature is 33°C and the lowest temperature is

27°C, which clearly indicate that one has to carefully track the temperature locally. (C) A

local weather station is generally located a few meters above the ground in a large open

space far from buildings and city center.

Here, we wanted to note that it is not very meaningful to compare our measured

ambient temperature to the online data reported from a regional weather station. For

example, in Boulder, Colorado, online ambient temperature is available

(https://www.wunderground.com/history) for a regional weather station located at the

Boulder Municipal Airport, ~5 kilometers away from CU Engineering Center as depicted

in Figure S2B. However, Figure S2B also shows that ambient temperature varies

dramatically from place to place even in a short distance during the day under the sun
(especially with different types of ground cover). It can be observed that within a few

kilometers range, the highest temperature is 33°C and the lowest temperature is 27°C,

which clearly indicate that one has to carefully track the temperature locally. The

difference in measured ambient temperatures is because that the ambient temperature is

strongly affected by the objects surrounding it due to the absorption of sunlight. The

regional weather stations are generally located in a large open space far from buildings

and city center (see Figure S2C), and usually placed a few meters above the ground. Our

RadiCold modules and the measuring thermocouples for the ambient temperature are

only 1-meter high from the building roof (see Figure 2A in the main text). Due to the close

proximity, we believe that the ambient temperature measured by us is accurate to

represent the local ambient temperature for the RadiCold modules.

Test of the four water modules using the same surface material

A test has been carried out to show the four water modules are truly identical when

the same surface material (i.e., the RadiCold metafilm) is applied to all the four modules.

Figure S3A shows water temperature variation in those four water modules during a 24-

hour period with clear sky condition. Figure S3B gives the precipitable water, wind speed,

and solar irradiance during the test period of the same day. It is observed that the average

temperatures inside the four modules are almost identical throughout the test, with a

maximum deviation of ±0.3°C at night, and a maximum deviation of ±0.5°C during the

day.
Figure S3. Test of four water modules when the same surface material is applied. (A)

temperature change of ambient (black curve) and four modules during a 24-hour test. (B)

Precipitable water (red curve), wind speed (black dots), and solar irradiance (orange filled area)

change during the test.

Supplementary Information 3: Cooling Performance of RadiCold module in 72

Continuous Hours

Test of the RadiCold module has been carried out in three consecutive days (June

1 to June 3, 2018) to show the consistency of the experimental results. Figures S4A and

S4B show the measurement results and weather conditions respectively. The sky was

clear on June 1 and June 2, while there were scattered clouds present on June 3. At noon

time (12pm - 2pm), average sub-ambient temperature differences between ambient and

water in the RadiCold module for the three consecutive days were 10.5°C, 8.2°C, and

6.2°C, respectively. Sub-ambient temperature difference obtained on June 1 is in

consistent with the results presented in Figure 2C in the main text. Sub-ambient

temperature difference on June 2 is smaller than that on June 1 because the precipitable

water at the daytime of June 2 is higher. Sub-ambient temperature difference on June 3

is the lowest due to the presence of scattered clouds.

Figure S4. Performance of RadiCold module in three consecutive days. (A) temperature

change of ambient (black curve) and water in RadiCold module (blue curve) during a 3-day

consecutive test. (B) Precipitable water (red curve), wind speed (black dots), and solar irradiance

(orange filled area) change during the test.

Supplementary Information 4: Measurement Method for Net Radiative Cooling

Power

2
March 7, 2018
1
Temperature (oC)
Ambient air
Water
0

-1

-2

-3

-4
23:00 23:10 23:20 23:30 23:40
Time (hh:mm)

Figure S5. A typical radiative cooling test to obtain the net radiative cooling power.

Temperatures of ambient air (black curve) and water (red curve) are plotted. We begin the

measurement when water temperature in the RadiCold module is about 2°C higher than the

ambient air, and end it when water temperature is about 2°C lower than ambient air. The effect

of convective and conductive thermal losses are ruled out since water temperature is close to the

ambient air temperature. The rate of the water temperature drop represents a close approximation

of net radiative cooling power.

To rule out the convective and conductive heat exchanges (𝑃𝑐𝑜𝑛𝑣+𝑐𝑜𝑛𝑑 ) between

RadiCold metafilm and ambient air, the net radiative cooling powers were calculated

under the condition that the radiative surface temperature is close to ambient air

temperature. Therefore, energy balance of the RadiCold module becomes 𝑃𝑛𝑒𝑡 = 𝑃𝑟𝑎𝑑 −
𝑃𝑎𝑡𝑚 − 𝑃𝑠𝑜𝑙𝑎𝑟 . One example of the net radiative cooling power measurement is shown in

Figure S5. The test began at when water temperature in the RadiCold module was about

2°C higher than ambient air, and was ended when water temperature was about 2°C

lower than ambient air. Net radiative cooling power (W/m2) was calculated through the

(𝑐𝑤 𝑚𝑤 +𝑐𝑝 𝑚𝑝 )∆𝑇

change of water temperature in the RadiCold module by using the equation ,
𝐴∆𝑡

where 𝑐 is heat capacity, 𝑚 is mass, subscript 𝑤 and 𝑝 denotes water and polycarbonate

water container respectively. 𝐴 is the radiative surface area. Water and polycarbonate

are assumed to have the same temperature. ∆𝑇 is the water temperature change during

the short time period ∆𝑡. The slope of water temperature change represents a close

approximation of net radiative cooling power.

Supplementary Information 5: Effect of Cloud Cover on Radiative Cooling Power

Cloud, which contains small water droplets, has an emissivity close to 1 in the

atmospheric transmission window (8-13 μm).14 The presence of cloud blocks the

atmospheric transmission window. It is therefore expected to have detrimental impact on

radiative cooling power. In this work, the cloud conditions are estimated in terms of how

many eighths of the sky are covered by the cloud, ranging from 0 (clear sky) to 8

(overcast), which is a common practice in meteorology.15 The human observations of

cloud amount are usually reported in five categories: clear (0/8), few (1/8 – 2/8), scattered

(3/8 – 4/8), broken (5/8 – 7/8), and overcast (8/8).

Figure S6. Radiative cooling test on one day with changing cloud conditions. (A)

Temperatures of the water inside RadiCold module (blue curve) and ambient air (black curve). (B)

Precipitable water (red curve), wind speed (black dots), and solar irradiance (filled in yellow)

conditions during the test day.

 We first tested the effect of cloud cover on one day that has cloud conditions

change from clear (0/8) to broken (5/8 – 7/8). Figure S6 shows that ambient air

temperature (between 7 and 11°C), local wind speed (0-3 m/s), and precipitable water

(between 4.5 and 6 mm) are all stable during the test period. When the sky is clear in the

morning between 9 am – 10:30 am, water in the RadiCold module (without PE film) is

about 7°C below the ambient air. As cloud accumulates, the temperature difference

between water and ambient air decreases. At broken cloud conditions between 1 pm – 4

pm, temperature difference dropped to around 3°C. The increase of cloud cover

decreased radiative cooling power.

Figure S7. Test of radiative cooling power at different days with different cloud cover

conditions. (A) Radiative cooling power at different cloud cover conditions. (B) Pictures show

sky conditions during the test periods.

 We also tested the cloud effect on different days with different cloud conditions as

depicted in Figure S7B. All tests were conducted at late afternoon around 5 pm to 6 pm

without direct solar irradiance on the RadiCold metafilm. The precipitable water are from

7.4 mm (clear) to 16.7 mm (overcast). Figure S7A shows that the highest cooling power

is close to 100 W/m2 when the sky is clear, while the lowest cooling power is even close

to 0 W/m2 under the overcast condition. The decrease of the cooling power is nearly

proportional to the increase of cloud cover. We also conducted the test on the effect of

cloud with solar irradiance at noon. A similar conclusion can be drawn about the effect of

cloud on radiative cooling power.

Supplementary Information 6: Comparative Test of the 4 Water Modules under

Scattered Cloud Conditions

Clouds have an adverse impact on radiative cooling performance due to their high

absorptivity in the atmospheric transmission window (8-13μm). We measured the

temperature change of the 4 water modules under scattered clouds conditions. The test

began at 11am, with clouds scattered and occupied about 40% area of the sky, as can

be seen from Figure S8B-D. Figure S8A shows that the water in the RadiCold module

can still be cooled to 5.6°C below ambient.

Figure S8. Day-time radiative cooling performance with scattered clouds. (A) Water

temperatures in the four modules along with ambient air temperature. Water in the RadiCold

module (blue curve) can stay 5.6°C below ambient air (black curve). (B) Pictures show cloud

cover change during the test period.

Supplementary Information 7: Validation of Overall Heat Transfer Coefficient

Figure S9. Validation of overall heat transfer coefficient. (A) Comparison of the change of

modeled water temperature (blue curve) and measured water temperature (red curve) with time

over a 24-hour clear sky test period. (B) precipitable water (red curve), wind speed (black dots),

and solar irradiance (yellow filled area) change during the test period.

The overall heat transfer coefficient as a function of wind speed is further validated

by our experiments. Figure S9A shows the comparison of modeling and measured water

temperatures inside the RadiCold module. During the test, water is stationary in the

RadiCold module. Temperature measurements take place every 5 seconds. At each time

point, the measured local wind speed, relative humidity, solar irradiance are inputs into

the model to calculate water temperature inside the RadiCold module in the next time

point. The modeling results and experimental data are in good agreement. Figure S9B

gives the weather conditions (precipitable water, wind speed, and solar irradiance) during

the 24-hour test period.

 Figure S10 shows the total thermal losses vary with different wind speeds and sub-

ambient temperature differences. Apparently, at sub-ambient operating conditions, the

employment of a PE film substantially reduced thermal loss.

250
Solid line - With PE film
Thermal Losses (W/m2)

Dashed line - Without PE film

200 DT=10oC
DT=5oC
DT=3oC
DT=2oC
150

100

50

0
0 1 2 3 4 5 6 7 8
Wind Speed (m/s)

Figure S10. Overall thermal losses as a function of local wind speed under a variety of sub-

ambient temperature differences. Solid are dashed lines are for RadiCold module with and

without the employment of a PE film respectively. ΔT is sub-ambient temperature difference

between water and ambient air.

Supplementary Information 8: Operation Strategy of the RadiCold system

Active use of radiative cooling could involve the production of cold water at a

specific temperature. However, in our approach, since water stays stationary in each

RadiCold module for most of the cooling time, an operation strategy needs to be

implemented to obtain continuous production of cold water. Figure S11 shows a proposed

RadiCold system that consists of many RadiCold modules to meet real-life cooling

demands that are generally continuous. Depending on the size of the entire system, a

subsystem can have a single RadiCold module or multiple modules. Each of the

subsystem is controlled and operated separately. Once the temperature in one RadiCold

subsystem reaches the targeted temperature, the cold water in that subsystem is

replaced with warm water coming from the mainstream. While fluid flow in one particular

substream is intermittent, the fluid flow in the mainstream is continuous.

Figure S11. A RadiCold system consists of multiple RadiCold subsystems connected in

parallel to achieve continuous cold water production. (The drawing of a RadiCold subsystem

may represent single to multiple RadiCold modules depending on RadiCold system size)
Supplementary Information 9: Optical Performance of 3M Vikuiti ESR film

One of the recent work by Stanford group (Goldstein et al., Nature Energy, 2,

2017)16 used a commercially available 3M Vikuiti ESR film to demonstrate sub-ambient

daytime cooling of water using radiative cooling. Although the company claimed that the

3M Vikuiti ESR film has a reflectance > 98% across the visible spectrum, the optical

performance across the entire solar spectra is not available. Here, we measured the

transmittance of the 3M Vikuiti ESR film and presented below in Figure S12. Indeed, the

3M Vikuiti ESR film has high solar reflectance in the visible spectrum range (0.4 -0.7µm)

only. When considering the entire solar spectrum, the film has very high transmittance in

the wavelength range of 1-3µm, which inevitably heats up any object underneath it when

placed under the sun. To increase the solar reflectance, Stanford group placed a silver

layer underneath the 3M Vikuiti ESR as reported in Nature Energy paper.

Spectrum Irradiance (W/m2/nm)

1.0 2.0
AM 1.5
0.9 1.8
Transmittance
0.8 1.6
Transmittance

0.7 1.4
0.6 1.2
0.5 1.0
0.4 0.8
0.3 0.6
0.2 0.4
0.1 0.2
0.0 0.0
0.3 0.7 1 1.5 2.5 5 8 13 25
Wavelength (mm)

Figure S12. Transmittance of 3M Vikuiti ESR film. The 3M Vikuiti ESR film has high solar

reflectance in the visible spectrum range (0.4 -0.7µm) only. When considering the entire solar

spectrum, the 3M Vikuiti ESR film has very high transmittance in the range of 1-3µm, which

inevitably heats up any object underneath it when placed under the sun.
Supplementary Information 10: Building-integrated RadiCold System and its

Annual Performance

Figure S13. Building-integrated RadiCold system to provide day-and-night continuous

cooling. (A) Schematic of a building-integrated RadiCold system that can provide continuous

day-and-night cooling. The nighttime cold storage loop (pink lines) is used for cold storage, and

daytime radiative cooling loop (green lines) is used to directly cool the condenser to improve air

conditioner’s efficiency. Cold water stored in the cold storage unit is used to pre-cool heat transfer

fluid in the radiant cooling loop (red lines) before in enters air conditioner’s evaporator during the

day. (B) An example test showing nighttime cold storage performance on the kw-scale RadiCold

system. An average of 86.7 W/m2 cooling power is achieved, which include the contribution from

both convection and radiation heat transfer. When temperature of the water tank is higher than

ambient (at 7pm – 2am), convection is beneficial. However, when temperature of the water tank

is lower than ambient (after 5am), convection is detrimental.

Figure S13A outlines a building-integrated RadiCold system that can provide

continuous day and night cooling. The RadiCold modules experience two working loops,

the daytime radiative cooling loop (green lines) and nighttime cold storage loop (pink
lines). During the day, the sub-ambient temperature heat transfer fluid, as demonstrated

in Figure 6C, is used to directly cool the condenser to improve the efficiency of an air

conditioner. At night, the nighttime cold storage loop stores the cooling energy in a storage

unit. Figure S13B shows nighttime cold storage performance of the kW-scale RadiCold

system. The test was performed without PE film on top of RadiCold modules. From 6pm

to 7am, cold storage unit temperature dropped to 11.4°C from 24.5°C in 13 hours, which

corresponding to an average of 86.7 W/m2 nighttime cooling power. The cold water stored

in the unit is then used to pre-cool heat transfer fluid in the radiant cooling loop (red lines)

before it enters air conditioner’s evaporator. The system efficiency can be significantly

enhanced with the day-and-night continuous cooling.

A modeling tool based on EnergyPlus and MATLAB has been developed for

evaluating the monthly electricity saving for cooling a commercial office building. The

whole building simulation software EnergyPlus developed by US Department of Energy17

is used to obtain the 8760-hour cooling load for a 3-floor building with a total floor area of

5000 m2. To meet the hourly cooling load requirement, models of the RadiCold module,

cold storage unit, and air conditioning system are developed in MATLAB to calculate

hourly electricity consumption. The building model used was originated from the building

energy codes program (DOE 2015), which has a rectangular shape with an aspect ratio

of 1.5 (length to width).18 Windows are distributed evenly in continuous ribbons around

the perimeter of the building. The window fraction of the overall façade area is 33%. The

performance values of the exterior envelope meet the minimum requirement of ASHRAE

Standard 90.1-2013 (ASHRAE 2013).19 Surface area of the RadiCold system is specified
as 810 m2 (half of the building roof area), corresponding to an area ratio of 1:6.2 (radiative

cooling surface area to building total floor area).

Figure S14. Annual energy saving of a RadiCold system that functions day-and-

night continuously. (A) Monthly electricity consumption of a commercial office building

located in Phoenix, Arizona with and without the RadiCold system. (B) Monthly electricity

saving by the RadiCold system at three different locations, Phoenix, Houston, and Miami.

The model is then used to evaluate the annual performance of the RadiCold

system in three different locations in the United States (Phoenix, Houston, and Miami)

using TMY3 weather data. Figure S14A shows the monthly electricity consumption for

building cooling with and without the RadiCold system at Phoenix, Arizona. Significant

electricity saving has been achieved, especially in the summer. Figure S14B shows the

monthly electricity saving by using the RadiCold system at Phoenix, Houston, and Miami.

For different locations, the RadiCold system could save 64-82% of the electricity

consumption for cooling in winter (from November to February), and save 32-45% of the
electricity consumption for cooling in summer (from May to August). Miami has the lowest

electricity saving percentage in winter, which is because Miami has the highest ambient

temperature in winter. Also, Phoenix has the lowest electricity saving percentage in

summer, which is because Phoenix is the hottest place in summer among the three

locations.
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