Solar Energy Vol. 73, No. 6, pp. 403–417, 2002
 2003 Elsevier Science Ltd
doi:10.1016 / S0038–092X(03)00019–7 All rights reserved. Printed in Great Britain
0038-092X / 03 / $ - see front matter
Pergamon
www.elsevier.com / locate / solener
A STUDY OF A POLYMER-BASED RADIATIVE COOLING SYSTEM
M. G. MEIR† , J. B. REKSTAD and O. M. LØVVIK
University of Oslo, Department of Physics, P.O. Box 1048, Blindern, N-0316 Oslo, Norway
Accepted 6 January 2003
Communicated by BRIAN NORTON
Abstract—A radiative cooling system consisting of unglazed flat plate radiators, water as heat carrier and a
reservoir is presented. The radiators are twin-wall sheets made of a modified PPO (polyphenylenoxid) resin,
which are proposed as low cost roof integrated modules. The thermal performance of a system with a radiator
aperture area of 5.3 m 2 and reservoir volume of 280 l has been investigated in experiments for Oslo climate. A
parameterisation for the cooling performance of a tilted radiator surface for clear and cloudy atmospheres is
proposed and applied to model the experimental results. The impact of the tilt angle, the aperture area and the
reservoir volume on the cooling performance has been studied in simulations. The feasibility of a radiative
cooling system designed for a single-family house at southern latitudes has been modelled. Except for
mid-summer ambient temperature and high relative humidity, the simulations show that the radiative cooling
system seems to cover the demand.
 2003 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
The energy consumption related to cooling of
buildings is steadily increasing as a consequence
of the world-wide industrialisation and increasing
living standard. The debate on global warming
and the demand of reducing CO 2 emissions
suggests alternative cooling methods with the
potential to substitute or partly replace traditional
(active) air conditioning systems.
Radiative cooling is one passive cooling technique utilising the transmittance of the Earth’s
atmosphere for thermal radiation in the wavelength interval from approximately 8–14 mm. The
thermal radiation of a black body at ambient
temperature on the earth’s surface interacts with
higher and colder atmospheric layers and may
cool down below the ambient air temperature
under optimal conditions. The maximal cooling
power of a body at ambient temperature with high
infrared emittance is in the range of 100 W m 22
for clear night sky and low air humidity. Different
approaches have been made to design applicable
systems and to find suitable materials for utilising
this effect. Numerous studies with air as heat
carrier have been carried out, among others by
†
Author to whom correspondence should be addressed. Tel.:
147-22-85-6469;
fax:
147-22-85-6422;
e-mail:
mmeir@fys.uio.no
Argiriou et al. (1993), Mihalakakou et al. (1998),
Al-Nimr et al. (1999). Water-based systems are
mainly related to the roof pond concept, e.g.
(Chen et al., 1988) or to flat plate radiator
systems with a storage reservoir (Hamza et al.,
1995; Erell and Etzion, 1996, 2000). Solar heating
systems have often been modified for radiative
cooling applications, or systems were designed in
order to serve both solar heating and radiative
cooling (Bliss, 1961; Matsuta et al., 1987). Focus
has been given to find appropriate selective
radiator materials (Catalanotti et al., 1975; Berdahl et al., 1983; Matsuta et al., 1987; Martin,
1989; Granqvist and Eriksson, 1991), and the
effect of glazing or wind screening has been
studied, e.g. by Mostrel and Givoni (1982).
The present work investigates the performance
of unglazed polymer flat plate radiators with
water as heat carrier and a large storage mass. It is
the continuation of experiments carried out in
˚ 1997) and it lays to a certain
small scale (Storas,
extent in the line of studies carried out by Erell
and Etzion (1992, 2000) and Etzion and Erell
(1991). The motivation was not only to design a
system which, under normal conditions, meets the
cooling demand, but it should also be economically feasible and have a potential for architectural
integration. Experimental and theoretical studies
of the cooling system under different climatic
conditions are presented.
403
404
M. G. Meir et al.
2. SYSTEM DESCRIPTION
2.1. General concept
The radiative cooling system investigated, is a
modified solar heating system with PPO and PC
twin-wall sheets as major collector components
(Henden, 2000). The relatively low costs for these
materials motivated the design of a radiative
cooling system based on the same materials.
Hence, aspects as metal coatings, selective coatings and cover foils were not investigated for
enhancing the performance.
The system utilizes water as heat carrier and
consists of a radiator roof, a reservoir, connecting
pipes, a pump and a control unit. The radiators are
mounted as integrated modules on the roof of a
building, normally under a small tilt angle, and
replace conventional roof cover materials. The
heat carrier is lifted by pump power in the upper
part of the radiator. Driven by the force of gravity
the liquid trickles through the radiator’s intrinsic
channels, releases heat and returns to the reservoir. The system is a drain-back system and the
store represents the drain-back reservoir for the
heat carrier when the system is not operative. The
heat carrier circulates freely between the radiator
loop and the storage tank without intermediate
heat exchangers. When no net cooling power is
obtained, the circulation is stopped by the controller, the water drains back in the reservoir and
unwanted heat gains are avoided.
The aim of the present experiments is to
determine the cooling power of the radiators. In
order to simplify the analysis, a simultaneous load
is avoided when the radiative cooling system is
operative. Hydronic radiant distribution systems
with large surfaces such as ceilings or floors are
proposed for transporting the cooling energy from
the store to the building. Although the performance of a radiant distribution system might have
limitations, it has advantages in cases where it
also will be used for heating in the winter. Since
this application is not experimentally studied, it is
discussed in the case study of sub-Section 1.3.
Fig. 1. Cross-section of the radiator panel: Driven by the force
of gravity, the water trickles through the channels of the PPO
twin-wall sheet. The channels are filled with clay granulates in
order to enhance the heat transfer.
with a UV resistant coating. As shown in Fig. 2
the PPO material has no selective properties. The
thermal emittance of PPO for an incident angle of
88 is 0.94360.019 (FH-ISE, 2001). The twin-wall
sheet has an inner rectangular 131 cm channel
structure with a wall thickness of approximately 1
mm. The channels are filled with clay granulates,
LECA (light weight expanded clay aggregate),
of 2–5 mm diameter. The granulates cause a
turbulent flow for the heat carrier in the channels
and enhance the heat transfer between the liquid
and the low conductive PPO material. A maximum energy transfer to the heat carrier is obtained when the heat carrier’s flow rate is in the
range of 1.0 l (m 2 min)21 or more. The heat
carrier volume inside the radiator is approximately 3.5–4.0 l m 22 . Considering the fact that the
radiator loop contains heat carrier only when the
system is operative (night-time), the black colour
is of minor significance. In the present study the
2.2. Radiator
The flat plate radiator is an extruded, polymer
twin-wall sheet with dimensions 25536031 cm.
The cross-section is shown in Fig. 1. The material
is a modified black polyphenylenoxid (PPO) resin
which sustains the exposure to humidity and
temperatures over 1008C, which may occur during
daytime standstill. Due to the degradation of
polymers when exposed to UV radiation during
daytime, the PPO radiator needs to be protected
Fig. 2. Thermal and infrared emittance of a PPO surface
(black bold line refers to the left axis). Shown are further the
emittance of a black body at T5373 K and the solar radiation
spectrum received at the surface of earth (refer to the right
axis).
A study of a polymer-based radiative cooling system
Fig. 3. Experimental set-up for the radiative cooling measurements and recorded parameters.
radiator panels were insulated from underneath
with mineral wool of 10 cm thickness.
2.3. Experimental set-up
The experiments were carried out at the SolLab, a small free-standing outdoor test laboratory
at the Department of Physics, University of Oslo
(latitude 59.98, azimuth 18.48). Fig. 3 illustrates
the experimental set-up and the parameters, which
were recorded. Table 1 lists the design parameters
of the experimental set-up. A radiator field of four
modules with a total aperture area of 5.3 m 2 is
mounted on the roof of the test lab. In order to
obtain a good cooling performance and secure the
drain-back of the heat carrier, a tilt angle of
approximately 108 would be more optimal. The
present experiments have been carried out with
the tilt angle of 328 given by the existing roof.
Relative to horizontal placement, the cooling
power at 108 tilt angle is reduced by approximately 1% and by 7% with a tilt angle of 328.
The cooling reservoir which is placed inside the
test house, is a modified domestic hot water store,
405
type OSO Hotwater 16RAI 300, of stainless steel
with height 1.59 m, diameter 0.59 m, insulated
with 40 mm polyurethane hard foam. The circulation of the heat carrier was driven by a UBE
25-60B GRUNDFOS  pump. The flow rate in the
radiator loop is relatively high, approximately 1
l (m 2 min)21 . The instantaneous flow rate could be
read out at a flow meter, type 10A1287 from
Fisher & Porter with a range of 200 to 1600 l h 21
and a pressure loss of 78.8 mbar. The flow rate
was set to 3.060.2 l min 21 per module.
The temperatures were monitored by thermistors (Dale 9M1002-C3, 10 K) with an accuracy of
60.28C from 230 to 1908C. A battery powered
SolDat Tattle Tale Lite data logger (TT128)
recorded the store temperature at three different
levels, the ambient temperature and the temperature inside the lab at 2-min intervals from which
20 min average values were calculated and used
in the analysis.
The wind speed was monitored by a Porton
Anemometer A100E from Vector Instruments,
Clwyd, UK, with a precision of 1% or minimum
60.1 m s 21 for wind speeds between 0 and 10
m s 21 . The instrument was mounted on the test
roof in the same plane as the radiators. The
readings were recorded every minute from which
20 min average values were calculated.
Meteorological data such as relative humidity and
cloudiness were provided by the Norwegian
Meteorological Institute (DNMI) at Blindern,
located a few hundred meters from the experimental site. For the relative humidity RH,
hourly recordings were available, for the total
cloud amount N, cloud type and cloud height,
readings every third hour (Table 2). Interpolated
values were used in the calculations.
3. EXPERIMENTS
3.1. Experimental data
The data of the experiments from May–June
1999 are given in Fig. 4 and Table 2. The plots
Table 1. Design parameters of the experimental set-up; A /Vstore 50.019 m 2 l 21
System parameter
Short form
Value
Aperture area, radiator
Tilt angle
Mean elevation angle for surrounding
Effective tilt angle, a 9 5 a 1 b
Volume, reservoir / store
Heat capacity, cooling system
Heat loss capacity rate, system
Hemispheric emittance
Ground emittance
Ground reflectance
A
a
b
a9
Vstore
Csys
k sys
´r
´g
rg
5.3
32
7
39
280
1227.5
2.82
0.94
0.90
0.10
m2
+
+
+
l
kJ K 21
W K 21
406
M. G. Meir et al.
Fig. 4. Radiative cooling experiments carried out at the University of Oslo during May–June 1999. Shown are the temperature of
the reservoir T store , the ambient air temperature T a , the relative humidity RH, the wind speed and the temperature inside the test
lab T indoor . Meteorological data were not available for May 27–28 and for parts of June 2–3. The data of June 10–11 are not
shown. The total cloud amount N and height are given in Table 2. Sunset and sunrise are marked by the vertical lines.
show the mean reservoir temperature T store , the
ambient air temperature T a , the relative humidity
RH, the wind speed v and the indoor lab temperature T indoor . The time for sunset and sunrise are
given by the vertical lines.
The three sensors, monitoring the vertical temperature profile of the reservoir, show that its
thermal state is well presented by T store . This is
also expected due to the high flow rate in the
radiators. During operation, T store decreases less
A study of a polymer-based radiative cooling system
407
Fig. 4. (continued)
than 2 K per hour. Hence the local temperature
differences in the complete system are small at a
given time and T store is representative for the
complete reservoir volume. T store was in the range
of 15–308C when the experiments started. The
nocturnal ambient air temperature was between 9
and 198C, the relative humidity between 52 and
95% and the wind speed typically in the range
between 0.5 and 1.0 m s 21 . For the analysis, only
the periods between sunset and sunrise were
considered.
The cooling power Pc,exp of the radiators is
determined from the change of the system temperature T sys per time unit dt(dT / dt) sys and is
corrected for the heat losses / gains from the
reservoir, the pipes and the surrounding:
408
M. G. Meir et al.
Fig. 4. (continued)
S D
dT
Pc,exp 5 2 Csys ? ]
dt
2 k sys
sys
? (T sys 2 T indoor ) 1 Ppump ,
(1)
where Csys is the heat capacity of the cooling
system and Ppump is the heat which is transferred
by the circulation pump to the system water,
corresponding to approximately 75% of the elec-
tric power consumption in the pump (here:
Ppump 56063 W). The design parameters are
given in Table 1. In practice are T sys and hence
T rad , the mean temperature of the radiator, at a
given time equal to T store because of the high
mass flow and the negligible thermal stratification.
3.2. Interpretation
Fig. 5 shows the cooling power Pc,exp as a
A study of a polymer-based radiative cooling system
Table 2. Total cloud amount and height, measured by the
Norwegian Meteorological Institute, measuring station Blindern (close to the experimental site) in 1999
Date
Time
Total cloud
amount, N
Cloud base
height, z c
19.0–20.05.
21:00
00:00
03:00
21:00
00:00
03:00
21:00
00:00
03:00
21:00
00:00
03:00
21:00
00:00
03:00
21:00
00:00
03:00
0
0
0
0
0
1
3
7
6
3
8
8
8
5
8
7
8
7
–
–
–
–
–
.2500 m
2000–2500 m
2000–2500 m
2000–2500 m
1000–1500 m
1000–1500 m
100–200 m
1000–1500 m
1000–1500 m
300–600 m
300–600 m
300–600 m
200–300 m
20.0–21.05.
27.0–28.05.
02.0–03.06
09.0–10.06.
17.0–18.06.
clouds and where no cooling is measured for
DT # 0.
Notice the experimental data of June 2–3 (Fig.
4): The total cloud amount changes from partly
cloudy (N53) in the early evening to overcast
sky at midnight (N58). The cooling power
determined for the first part of the night (Fig. 5,
large DT ) lays close to the clear sky line Pc,exp 1
and approaches Pc,exp 2 with increasing cloud
cover.
4. THEORETICAL ANALYSIS
The heat loss of an uncovered night-sky
radiator is caused by radiation and convection.
The heat loss related to conductive heat transfer
between radiator and surrounding can be neglected, so that
Pc 5 Prad 1 Pconv ,
function of the temperature difference DT 5
T rad 2T a , calculated from the recordings of all
experiments. The uncertainty is estimated from
the precision of the temperature sensors and the
statistical scattering of the individual observations. The observed cooling rate Pc,exp can for
DT .0 be enclosed by two lines as shown in Fig.
5. The upper line Pc,exp 1 is interpreted as the
cooling power for clear night sky. The lower line
represents the cooling power Pc,exp 2 during
periods when the sky is completely covered by
409
(2)
where Pc is the total cooling power and Pconv the
convective cooling power of the radiator. The
long-wave radiative cooling power, Prad , of a
radiator with aperture area A and an emittance ´r
is given by
Prad 5 A ? ´r (s T 4rad 2 R),
(3)
R is the long-wave radiation incident on the
radiator’s surface. For a horizontal surface, the
down welling long-wave radiation originates
Fig. 5. The radiator’s cooling power as a function of the temperature difference T rad 2T a calculated from the experimental data.
Pc,exp 1 is interpreted as the net cooling power for ideal conditions with clear night sky; Pc,exp 2 reflects the cooling power during
periods when the sky is completely covered by clouds.
410
M. G. Meir et al.
mainly from a few hundred meters thick atmospheric layer near the ground (R 5 RA ). The air
temperature near the ground, T a , is fairly representative for this layer. In order to describe the
radiant heat transfer of the atmosphere RA , the
term ‘sky temperature’ T sky is introduced. It is
defined as the temperature of a black body
radiator emitting the same amount of radiative
power as the sky according to
4
RA 5 s ? T sky
5 s ? ´ ? T a4 ,
4.1. Cloudless sky
Several simple formulae for the estimation of
the long-wave atmospheric irradiance have been
compared to experimental and computed data by
Skartveit et al. (1996) and Olseth et al. (1994).
For normally stratified, cloud-free atmospheres, it
was found that the description by Berdahl and
Fromberg (1982) adequately reflects the radiation
physics over a wide range of T a and RH. We
apply an extended formula by Berdahl and Martin
(1984) which expresses the emittance of the night
sky as a function of the temperature and the
relative air humidity for cloudless atmospheres
(´ 5 ´0 ):
flnsRHd 1 C1g
T dp 5 C3 ]]]]]],
C2 2flnsRHd 1 C1g
(7)
where z c is the cloud base height (in km), and
z * 58.2 km. The hemispherical cloud emittance ´c
is assumed to be ¯1 for low and medium high
clouds. For cirrus clouds, ´c 50.7420.084(z c 24)
for 11.z c .4 km, and ´c 50.15 for z c .11 km.
The cloud height varied between 0.2 and 2.5 km
in the present experiments. n is the fractional
cloud amount of the sky covered by ‘non-transparent’ clouds, with n5N / 8.
4.3. Inclined surfaces
The long-wave radiation incident upon an
inclined surface is given by the sum of the
atmospheric RA and ground components R G . In
the model by Unsworth and Monteith (1975a,b),
the ground component has an isotropic angular
distribution while the atmospheric radiance has an
additional anisotropic term:
R(a ) 5 RA (a ) 1 R G (a ),
(8)
where
´0 5 0.711 1 0.0056 ? T dp 1 0.000073 ? T dp 2
S D
S D
zc
´ 5 ´0 1 (1 2 ´0 )´c n exp 2 ] , 0 # n # 1,
z*
(4)
where the sky emittance ´ is independent on
wavelength and s is the Stefan–Boltzmann constant. In the present experiments the effective sky
temperature has not directly been measured but
calculated indirectly as described below.
2pt m
1 0.013 ? cos ]] ,
24
tin and Berdahl (1984) describe ´ as an empirical
adjustment of the cloudless model given in Eqs.
(5) and (6). For overcast conditions, ´ is a
function of the fractional cloud cover, the cloud
emittance and the temperature difference between
surface and cloud base:
2
(5)
4
RA (a ) 5 RA cos sa / 2d 1 bI7 s T a ,
(9)
and
(6)
where t m is the number of hours from midnight in
solar time, T dp the dew point temperature in (8C),
RH the relative humidity, 0#RH#1, and C1 5
(C2 ? T dry ) /(C3 1 T dry ), C2 5 17.08085, C3 5
234.175, and the dry bulb temperature T dry 5 T a .
The experimental data by Berdahl and Martin
(1984) covered for T dp a range of 220 to 1308C
and for (T sky 2 T a ) a range of 5 K in a hot, humid
climate and 30 K in a cold, dry climate.
4.2. Overcast and partly overcast sky
The presence of clouds increases the atmospheric absorbance and hence the emittance. Mar-
R G (a ) 5 sin 2sa / 2d ? (´g s T g4 1 rg RA )
(10)
Here b ranges from 0.07 to 0.14 with a mean of
0.09. I7 is a function of the tilt angle a, I7 (a 5
398) ¯ 0.2. T g is the ground surface temperature,
´g the emittance and rg the reflectance of the
ground.
4.4. Influence of sheltering objects on outgoing
radiation
The influence of sheltering objects, as buildings
or landscape topography, on the effective outgoing long-wave radiation from the radiator is not
considered in Eqs. (8)–(10). As the experimental
set-up is surrounded by buildings of non-negli-
A study of a polymer-based radiative cooling system
Fig. 6. Influence of sheltering objects on outgoing radiation
from a radiator with tilt angle a. An effective tilt angle
a 9 5 a 1 b is introduced.
gible elevation, a mean elevation angle b is
introduced under which the buildings and sheltering objects occur to the tilted radiator surface
(Fig. 6). In order to model the experimental data
the tilt angle a in Eqs. (8)–(10), is replaced with
an effective tilt angle a 9:
a → a 9; a 9 5 a 1 b.
(11)
The simplification made in Eq. (11) may be
applied to cases where the thermal behaviour of
the ground is similar to that of the sheltering
objects. In the present experimental set-up the
surrounding ground and buildings are made of
brick stones and we assume in the first order a
similar thermal behaviour. A mean value of b
was determined from ‘fisheye’ photos of the
experimental site.
4.5. Convective heat transfer
The convective heat transfer can be described
by
Pconv 5 h conv A ? (T rad 2 T a )
(12)
411
In the present experiments, the operative temperature is most of the time larger than the ambient air
temperature, hence the convective heat loss represents primarily a positive contribution to the total
heat loss.
For surfaces without wind screen the coefficient
for convection h conv is in the first order a linear
function of the wind speed v which has the form
h conv 5a 1 b ? v. Previous studies show a large
variety in assigning values to a and b. Relations
applied by Clark and Berdahl (1980), by Mitchell
(1976), modified for forced convection over
buildings (Duffie and Beckmann, 1991), and
McAdams (1954), have been used to fit the
experimental data. The best fit was obtained by
using h conv as suggested by the Australian standards of 1989, reported and discussed by
Molineaux et al. (1994) with v in m s 21 :
h conv 5 3.1 1 4.1 ? v [W m 22 K 21 ]
(13)
The wind speeds in the present experiments were
in the range of 0.1–2.0 m s 21 (mean values over a
20-min interval) with an average of 0.8 m s 21 .
5. MODELLING
5.1. Cooling power, experiments May– June
1999
The cooling power was calculated with the
theory described above, using hourly mean values
of the experimental data T a , T rad , T g , N, RH, and
v of June–May 1999 (Fig. 4 and Table 2). Fig. 7
shows the modelled cooling power of the radiator
Fig. 7. Modelled cooling power Pc of the radiator from the experimental data in Fig. 4 and Table 2. The solid lines represent the
fits Pc,exp 1 and Pc,exp 2 in Fig. 5. There is good agreement between the experimental fits and the modelled results.
412
M. G. Meir et al.
as a function of DT, and the fits which were made
to the experimental results in Fig. 5 (solid lines).
The modelled results lay in-between the lines and
are in good agreement with the experimental
cooling power. Hence the parameterisation in Eqs.
(2)–(13) is appropriate to describe the thermal
performance of the radiators as a part of the
present cooling system. Fig. 8 shows the contributions of Prad and Pconv modelled for clear and
almost clear atmospheres, N50,1. The impact of
the wind speed v on the convective cooling power
is indicated for the range of 0–2 m s 21 .
For DT50 K, the cooling power is approximately 60 W m 22 . The mean sky temperature
depression evaluating the radiative cooling potential of a certain location is for the experiments
during June–May 1999, DT sky,mean 5(1 2
´ 1 / 4 )T a 58.3 K with a maximum of 19.6 K in the
early evening of May 19, 1999.
5.2. Radiator temperature, experiments May–
June 1999
A computer program has been written in order
to model the transient behaviour of a radiative
cooling system of the present design. The theory
described in Section 4 is used to calculate the
system’s instantaneous cooling rate from the
system design—and meteorological input data as
in the measurements during May–June 1999 (Fig.
4). Fig. 9 shows the experimental and calculated
T rad curve of May 19–20, June 2–3 and June
17–18, 1999. The measurements can be satisfyingly reproduced for nights with clear and cloudy
atmospheres.
The influence of various system parameters has
been investigated for the measurements of May
19–20, 1999: The cooling rate can be increased
by approximately 9% if a flat surrounding is
assumed ( b 508) and if the tilt angle a 5108 is
chosen (Fig. 10). The ratio between active
radiator area and reservoir volume A /V has been
varied and the impact on the T rad profile is
illustrated in Fig. 11. The ratio in the experiments
was A /Vstore,exp 50.019 m 2 l 21 . Due to the findings in Figs. 10 and 11, we choose for the case
study a tilt angle of 108 (in order to secure the
drain-back function) and an A /V ratio of 0.025
m 2 l 21 .
5.3. Case study
The program has been used to design a cooling
system of the present type for a typical residence
building. The case study is a one-family house of
150 m 2 living area with an effective U-value of
the insulation of 1.5 W m 22 K 21 . The radiator
roof cools a large reservoir during night. A
hydronic radiant floor cooling system is chosen as
emission system for the interior spaces. The
performance of such systems has been investigated, e.g. by Olesen (1997), Kast et al. (1994)
and Feustel and Stetiu (1995). The heat transfer
coefficient between a cooled floor and a room is
typically around Ufloor 57.0 W m 22 K 21 , where
5.5 W m 22 K 21 is related to radiative heat transfer. For comfort reasons, a floor surface temperature between 19 and 268C is recommended according to ISO 7730. This interval limits the
operative temperature of the reservoir and the
Fig. 8. Modelled radiative cooling power Prad (N50; 1) and convective cooling power Pconv . The convective cooling power is
calculated for the average wind speed in the experiments of vav g 50.8 m s 21 , for v50 and 2 m s 21 .
A study of a polymer-based radiative cooling system
413
Fig. 9. The radiator’s mean temperature is modelled (T rad s ) and compared to the measured values (T rad ). The experiments are
satisfyingly reproduced for the nights with cloudless atmospheres on May 19–20 and June 17–18 (a, b) and for overcast
conditions on June 2–3 (c). (a) Clear, humid night of May 19–20, 1999. (b) Clear, dry night of June 17–18, 1999. (c) Partly
overcast and overcast sky on June 2–3, 1999.
radiative cooling system, besides the external
parameters T a , T dp and v. Inside the building, the
lower limit for the cooled floor is given by the
indoor dew point temperature. The example simulated, is described in Table 3. The synoptic
weather data were chosen comparable to the
414
M. G. Meir et al.
Fig. 10. Impact of the effective tilt angle a 9 of the radiator’s surface on the mean reservoir temperature (T store,avg ¯T rad ),
modelled for the measurements of May 19–20, 1999 (system parameters in Table 1).
Fig. 11. Impact of the ratio between the radiator’s aperture area and the reservoir volume (A /V ) on the temperature decrease
T store,avg ¯T rad . The experiments of May 19–20, 1999 (A /V50.019 m 2 l 21 ) are compared to modelled results (system parameters
in Table 1).
experiments by Mostrel and Givoni (1982) carried
out at Sede Boquer, Israel, in August and October
1981. The ambient night temperature, the dew
point temperature and the wind speed are shown
in Figs. 12 and 13. For cloudless days, T a reaches
the maximum during daytime at approx. 3:00
p.m., which is assumed to be in the range of 358C
for a clear day in midsummer. For a day in
Table 3. System design parameters used in the case study
System parameter
Value
Cooled living area
Eff. U-value, insulation
Tilt angle, radiators
Radiator area
Volume, reservoir / store, Vstore
Heat capacity, cooling system, Csys
Estimated operation time, cooling system
150
1.5
10
50
2000
8352
8
m2
W m 22 K 21
+
m2
l
kJ K 21
h
A study of a polymer-based radiative cooling system
415
Fig. 12. Case study: Modelled cooling of the reservoir by the radiators for a clear, dry night comparable to October 13–14, 1981
(Mostrel and Givoni, 1982). The stored energy of 22.0 kW h (79.2 MJ) is sufficient to cool the building during the next day. T store
has been modelled for different start temperatures at 20:00. DT sky 514.4 K at 20:00 (system parameters in Table 3).
August, we estimate that a cooling energy of 12.5
kW h (45 MJ) is sufficient to provide a indoor
temperature in the range of 24–268C. For October
13–14, the demand is correspondingly less. We
set the forward temperature of the floor system
and consequently T store always #208C. For the
study, a radiator aperture area of 50 m 2 is chosen,
which is a realistic area, available on an average
roof of a house. A reservoir volume of 2 m 3 was
chosen. The parameter choice was partly due to
the availability of space in a single-family house
and partly due to the findings in Section 5.2.
The performance of the system has been modelled for a dry, clear night, comparable to October
13–14, 1981 in Mostrel and Givoni (1982). Fig.
12 shows that T store cools down from 208C at
20:00 to approximately 10.58C at 5:00, corresponding to a stored energy of 22.0 kW h (79.2
MJ). The radiative cooling system provides sufficient energy to cool the building. The cooling
performance was modelled for different start
temperatures of T store (15 and 188C); for October
13–14 this has no impact on the temperature to
which the reservoir cools down during the night.
Fig. 13. Case study: Modelled cooling of the reservoir by the radiators for a clear, humid night comparable to August 1–2, 1981
(Mostrel and Givoni, 1982). The stored energy of 7.0 kW h (25.1 MJ) covers approximately 56% of the forthcoming day’s
cooling demand. T store has been modelled for different start temperatures at 20:00. DT sky 511.2 K at 20:00 (system parameters in
Table 3).
416
M. G. Meir et al.
The cooling performance has also been modelled for a humid, clear night, comparable to
August 1–2, 1981 in Mostrel and Givoni (1982)
with a start temperature of T store 5208C at 20:00
(Fig. 13). An energy of 6.96 kW h (25.1 MJ) is
stored in the reservoir at 5:00 o’clock which
covers approximately 56% of the cooling demand
of the following day. The wind speed has been
equal for August 1–2 and October 13–14 and are
close to the measured values of August 1–2,
1981.
The present case study investigated the performance for conditions in midsummer and in
autumn. The cooling system may cover the cooling demand for clear nights with low air humidity.
For high humidity and cloudy atmospheres, auxiliary cooling sources seem to be necessary. It
should be noticed that for cloudy conditions, the
daytime temperatures are lower, and hence the
cooling demand is smaller than for clear sky
conditions. It should be considered that the study
provides limited information on the performance
of such a cooling system over a period of time,
when exposed to stronger fluctuations of the
external parameters.
The typical investment costs for a PPO-radiator
roof, replacing conventional roof cover materials,
is in the range of 60–100 EURO m 22 . Hence, the
present cooling concept offers an economical
alternative to conventional active cooling concepts.
6. SUMMARY AND CONCLUSION
This paper has evaluated the performance of a
polymer-based radiative cooling system from
experiments and computer simulations. The results and the parameterisation obtained from a
small-scale system were used to design a radiative
cooling system for a single-family house. It has
been shown that even under unfavourable conditions, the system has the capacity to cover a
significant fraction of the cooling demand. Generally, the simulations indicate that sufficient radiative cooling is obtained in periods with modest air
humidity and ambient night temperatures, cooling
down below 208C.
Important advantages of the radiative cooling
system are the relatively low investment costs of
the PPO-radiators, the complete building integration and a simple over-all system design where
parts can be used in common for heating and
cooling of buildings.
In order to carry out a full evaluation, a longer
period of time (season) should be simulated;
unfortunately the appropriate data for such a study
have not been available to us. An interesting
future task will be to realize a cooling system of
the present design under climates with significant
cooling demand and verify the modelled results of
sub-section 5.3.
NOMENCLATURE
A
C1
C2
C3
Csys
h conv
k sys
n
N
Pc
Pconv
Ppump
Prad
R(a )
RA (a )
R G (a )
RS
RH
Ta
T dp
T dry
Tg
T indoor
tm
T rad
T sky
T store
T store,avg
T sys
DT
DT sky
Vstore
zc
radiator’s aperture area (m 2 )
5(C2 ?T dry ) /(C3 1T dry )
17.08085
234.175
total heat capacity of the cooling system, incl.
radiator (kJ K 21 )
convection coefficient (W m 22 K 21 )
heat loss capacity rate of the complete cooling
system, excl. radiator (W K 21 )
fractional cloud amount covered by ‘non-transparent’ clouds, n 5 N / 8, 0 # n # 1
total cloud amount in integers, 0 # N # 8
total cooling power of the radiator (W m 22 )
convective cooling power of a surface (W m 22 )
thermal gain of the cooling system by the pump (W)
long-wave radiative cooling power of a surface
(W m 22 )
long-wave radiation incident on a surface inclined at
an angle a to horizontal (W m 22 )
atmospheric radiation incident on a surface inclined
at an angle a to horizontal (W m 22 )
ground radiation incident on a surface inclined at an
angle a to horizontal (W m 22 )
radiation emitted by the surrounding (W m 22 )
relative air humidity, 0#RH#1
ambient air temperature (K)
dew point temperature (8C)
dry bulb temperature (8C)
temperature of the ground surface (K)
indoor temperature of the lab (8C)
number of hours from midnight in solar time
mean radiator temperature (K)
sky temperature (K)
mean temperature of the store / reservoir (8C)
mean store / reservoir temperature (8C)
mean system temperature (8C)
5T rad 2 T a (K)
5T sky | T a , sky temperature depression (K)
volume of the cooling reservoir (l)
cloud base height (km)
Greek letters
a
tilt angle (8)
a9
effective tilt angle, a 9 5 a 1 b (8)
b
mean elevation angle of the surrounding (8)
´0
emittance of clear sky
´g
emittance of the ground surface
´r
emittance of the radiator’s surface
´c
hemispheric cloud emittance
´
emittance of arbitrary sky
n
wind speed (m s 21 )
rg
reflectance of the ground
s
Stephan Boltzmann constant (55.67051?10 28
W m 22 K 24 )
A study of a polymer-based radiative cooling system
Acknowledgements—The authors wish to thank the Norwegian
Meteorological Institute for providing the relevant synoptic
data. Financial support of the Norwegian Research Council
under the Program Fundamental Energy Research with reference no. 119176-431 is acknowledged.
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