Comparative analysis of different surfaces for integrated solar heating and radiative cooling: A numerical study

Accepted Manuscript Comparative analysis of different surfaces for integrated solar heating and radiative cooling: A numerical study

Mingke Hu, Bin Zhao, Xianze Ao, Yuehong Su, Yunyun Wang, Gang Pei PII:

S0360-5442(18)30768-0

DOI:

10.1016/j.energy.2018.04.152

Reference:

EGY 12791

To appear in:

Energy

Received Date:

17 October 2017

Revised Date:

23 March 2018

Accepted Date:

25 April 2018

Please cite this article as: Mingke Hu, Bin Zhao, Xianze Ao, Yuehong Su, Yunyun Wang, Gang Pei, Comparative analysis of different surfaces for integrated solar heating and radiative cooling: A numerical study, Energy (2018), doi: 10.1016/j.energy.2018.04.152

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

1

Comparative analysis of different surfaces for integrated solar

2

heating and radiative cooling: A numerical study

3

Mingke Hu a, Bin Zhao a, Xianze Ao a, Yuehong Su b, Yunyun Wang a, c, Gang Pei a, *

4

a

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China

5

b

Institute of Sustainable Energy Technology, University of Nottingham, University Park, Nottingham NG7 2RD, UK

6

c

7

Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

8 9

_____________________________

10

* Corresponding author. 0551-63601652. [email protected]

11

Abstract

12

The spectral selectivity of solar selective absorbing coatings enhances coating performance in

13

diurnal heating collection but also limits the potential application of these materials in nocturnal

14

radiative cooling. A radiative cooling surface shows poor solar heating performance due to the same

15

reason. The present study proposed a novel surface that combines solar heating and radiative cooling

16

(SH-RC) considering the spectral selectivity of photo-thermic conversion and radiative cooling. A

17

hypothetical SH-RC surface was also proposed. This hypothetical surface had an absorptivity of 0.92

18

in the solar radiation band, emissivity of 0.70 in the “atmospheric window” band, and absorptivity

19

(emissivity) of 0.05 in other bands. The thermal performance of this spectrally selective SH-RC

20

surface (SH-RCs surface) was numerically investigated by comparing it with three surfaces, namely,

21

solar selective absorbing coating surface (SH surface), spectrally selective radiative cooling surface

22

(RC surface), and spectrally non-selective black surface (SH-RCblack surface). Results indicated that

ACCEPTED MANUSCRIPT 23

the SH-RCs surface is most suitable for achieving integrated SH and RC. In a typical summer day,

24

the heat gains of the SH, RC, SH-RCblack, and SH-RCs surfaces are 17.14, 0, 15.57, and 13.22 MJ/m2,

25

respectively. The cooling energy gains of the four surfaces are 0, 1.02, 0.95, and 1.01 MJ/m2,

26

respectively.

27

Keywords: Solar heating; Radiative cooling; Spectral selectivity; Thermal performance.

28

1. Introduction

29

Given the increasing concern on fossil energy and environmental crises, sustainable energy,

30

such as solar energy and radiative cooling (RC) energy, are regarded as promising alternatives with

31

an increasingly important role in recent decades [1-4].

32

Photo-thermal technology is one of the most developed and utilized forms of solar energy. Due

33

to the increasing energy consumption in buildings, the solar collector is becoming widely used in

34

building energy conservation [5]. It is well known that the thermal efficiency of a solar thermal

35

collector highly depends on its photo-thermal conversion efficiency and heat loss [6]. Approximately

36

99% of solar irradiance is concentrated in the 0.2–3 μm range (hereafter referred to as the “SH

37

band”). By contrast, terrestrial infrared radiation is mainly concentrated in the middle and far

38

infrared wavelengths (>4 μm) [7]. Therefore, the thermal performance of a conventional solar

39

thermal collector immensely relies on its spectral absorptivity in the SH band and the radiative heat

40

loss in the infrared band. The introduction and development of solar selective absorbing coatings

41

(SSAC) have significantly enhanced the thermal efficiency of solar collectors [8]. The performance

42

of a SSAC could be evaluated by the ratio of its absorptivity in the SH band to its emissivity in the

43

rest of wavelengths (i.e., α/ε). State-of-the-art SSAC could achieve an absorptivity of approximately

44

0.95 and an emissivity of as low as 0.05 [8, 9]. A lot of researches focus on the thermal stability and

ACCEPTED MANUSCRIPT Nomenclature a0, a1, a2, a3

fitting coefficients, -

α

absorptivity, -

d

distance/thickness, m

ε

emissivity, -

E

radiation power, W/m2

ρ

reflectance, -

G

solar irradiance, W/m2

σ

Stefan–Boltzmann constant, -

h

heat transfer coefficient, W/(m2·K)

λ

wavelength, µm

k

thermal conductivity, W/(m·K)

β

inclination angle, rad

L

length, m

θ

zenith angle, rad

Nu

Nusselt number , -

τ

transmittance, -

Pr

Prandtl number, -

ηth

Thermal efficiency, -

Q

thermal power, W/m2

Abbreviation and subscripts

Ra

Rayleigh number, -

a

ambient air

T

Temperature, K

avg

average

ΔT

temperature difference

b

back insulator / blackbody

td

Dew point temperature, °C

c

transparent cover

U

Overall heat-transfer coefficient, W/(m2·K) conv

Convection

u

wind velocity, m/s

p

collecting plate

w

precipitable water vapor amount, cm

rad

Radiation

Greek Symbols

rad_net

net radiation

(τα)

s

sky

Transmittance-absorptance product, -

45

corrosion resistance of the SSAC in recent years. J. Jyothi et al. proposed and manufactured a

46

nanostructured TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem SSAC. This coating achieved

47

a high absorptivity of 0.961 and an emissivity of 0.07 at 82°C. Besides, the coating still showed good

48

spectral selectivity and thermal stability under 650°C for 100 hours [10]. C. Wang et al. prepared an

49

Al–N cermet SSAC. The coating showed an absorptivity of 0.942 and a normal emissivity of 0.066

50

at 80 °C. Thermal accelerated aging tests results showed that the absorber is durable for at least 25

51

years. Neutral salt spray test proved that the absorber exhibit good corrosion resistance because the

ACCEPTED MANUSCRIPT 52

spectral selectivity of the coating kept almost the same after a 200 hours test [11]. The spectral

53

properties of a typical Ti-based SSAC provided by our cooperative enterprise, namely, Guangdong

54

Five Star Solar Energy Co., Ltd. and the ideal SSAC are shown in Fig. 1 [3]. This figure illustrates

55

that the spectral absorptivity and emissivity of the two coatings are rather close.

56 57

Fig. 1. Spectral properties of real and ideal solar selective absorbing coatings [3].

58

RC is another renewable energy technology that maximizes the high spectral transmittance of

59

the atmosphere in the so-called “atmospheric window” band (8–13 μm; hereafter referred to as the

60

“RC band”) to extract heat from objects on Earth to the extremely cold outer space [12-17]. RC is a

61

completely passive cooling approach without any external driving energy input, thereby playing a

62

positive role in energy saving and emission reduction [18, 19]. The cooling performance of a

63

radiative cooler is highly affected by environmental conditions and the spectral properties of the

64

cooling surface. Basically, The atmospheric transmittance is relatively higher in arid climate than in

65

humid climate [20, 21]. Hence, RC power is higher under the former than the latter environment. For

66

example, a photonic RC collector could provide cooling effect during daytime under California’s

67

cold and arid climate but fail to achieve daytime cooling effect under Hong Kong’s hot and humid

68

climates [20]. With regard to the radiative cooler, the cooling surface should show high spectral

69

emissivity in the RC band to obtain considerable cooling power by radiating heat to the cold universe

ACCEPTED MANUSCRIPT 70

[22]. To maintain the surface temperature as low as possible, the cooling surface should have the

71

lowest possible spectral absorptivity in the bands excluding the RC band, thereby indicating that the

72

surface could reject the vast majority of radiated heat from the surroundings [23]. The spectral

73

property of a RC coating is of great concern since it has a great extent to determine the performance

74

of a RC cooler. Recently, with the booming development of materials science in micro-nano scale,

75

the spectral selectivity of RC coatings has been further strengthened and thus the daytime RC has

76

also been successfully achieved [12-14, 24, 25]. A. P. Raman et al. introduced an integrated photonic

77

solar reflector and thermal emitter consisting of seven layers of HfO2 and SiO2 that shows a 0.03

78

absorptivity in the SH band while emitting strongly and selectively in the RC band. The photonic

79

coating could reach about 5°C lower than the ambient temperature when exposed to direct sunlight

80

exceeding 850 W/m2 [12]. From economic considerations, Y. Zhai et al. embedded resonant polar

81

dielectric microspheres randomly in a polymeric matrix, resulting in a metamaterial that is fully

82

transparent to the solar spectrum while having an infrared emissivity greater than 0.93 across the RC

83

band. When backed with silver coating, the metamaterial shows a noon-time radiative cooling power

84

of 93 W/m2 under direct sunshine [13]. Fig. 2 illustrates the spectral properties of the RC coating

85

reported by A. P. Raman et al. and the ideal one in 0.2–25 μm [12].

86 87

Fig. 2. Spectral properties of the real and ideal radiative cooling surfaces [12].

ACCEPTED MANUSCRIPT 88

Figs. 1 and 2 show that the spectral selectivity of the solar heating (SH) coating and RC coating

89

are incompatible. That is, a conventional solar collector is barely able to achieve RC due to its

90

extremely low spectral emissivity in the middle and far infrared bands, particularly in the RC band.

91

By contrast, a traditional radiative cooler cannot achieve considerable SH performance owing to its

92

low spectral absorptivity in the SH band. Therefore, solar collectors cannot run at nighttime and most

93

of radiative coolers normally remain idle at daytime. Besides, the solar heat collector is almost

94

useless in summer and the RC collector is of little value in spring, autumn and winter. Additionally,

95

the power density of the RC collector is still low compared with the vapor compression refrigeration

96

system. These characteristics lower the time utilization ratio and prolong the payback period of both

97

SH and RC apparatuses. If we could integrate diurnal SH and nocturnal RC functions into one single

98

collector, then the new collector should possess multi-function, all-day operating superiority and

99

better seasonal adaptability compared with conventional solar collectors and RC units. In the

100

previous study, we proposed an ideal surface for both SH and RC with consideration of spectral

101

selectivity. In addition, the spectral property of this ideal SH-RC surface was presented as well. We

102

also installed a SH-RC system and experimentally investigated its diurnal thermal efficiency under

103

different ambient temperatures, inlet temperatures and solar irradiances, as well as tested it nocturnal

104

cooling power under different inlet temperatures and sky conditions [3]. In the present work, to

105

evaluate if it is worthwhile to pursue the spectral selectivity of surfaces for the comprehensive

106

utilization of SH and RC, we proposed a hypothetical, spectrally selective SH-RC surface whose

107

spectral property in the SH band, the RC band and the spectra that exclude the aforementioned two

108

bands are respectively close to that of the state-of-the-art SSAC, RC coatings and SSAC. Then we

109

developed a mathematic model that considers the spectral radiant distribution of the coating and

ACCEPTED MANUSCRIPT 110

atmosphere. Numerical calculation was performed to investigate the heating and cooling

111

performance of the hypothetical, spectrally selective SH-RC surface by comparing it with three other

112

typical surfaces.

113

2.

Spectral characteristics of different surfaces

114

Solar collectors should have high spectral absorptivity in the SH band and radiative coolers

115

should have high spectral emissivity in the RC band. Therefore, the necessary conditions for an

116

integrated SH and RC collector (SH-RC collector) are high spectral absorptivity (i.e., spectral

117

emissivity) in the SH and RC bands. Accordingly, we considered that two ideal surfaces could meet

118

the aforementioned requirements. One ideal surface is a blackbody surface, the spectral absorptivity

119

and emissivity of which are equal to 100% throughout all spectra. The other ideal surface is that

120

which shows spectral absorptivity (emissivity) of 100% in the SH and RC bands and zero

121

absorptivity in the spectra that exclude the aforementioned two bands (hereafter referred to as “other

122

bands”). We named the latter as the ideal SH-RC surface. The spectral properties of the two ideal

123

surfaces are shown in Fig. 3 [3, 26].

124 125

Fig. 3. Spectral properties of the blackbody and ideal SH-RC surface [3, 26].

126

The ideal SH surface, ideal RC surface, blackbody, and ideal SH-RC surface are nonexistent in

127

practical applications. However, the real SH surface (see Fig. 1), real RC surface (see Fig. 2), and

ACCEPTED MANUSCRIPT 128

real black surface [21] are spectrally near to the ideal ones and are easy to obtain. It seems unfair if

129

we select the ideal SH-RC surface to compare its solar heating and radiative cooling ability with the

130

other three real surfaces. Therefore, we proposed a hypothetical SH-RC surface with an average

131

absorptivity of 0.92 (i.e., nearly the same as that of the real SH surface) in the SH band, average

132

emissivity of 0.70 (i.e., nearly the same as that of the real RC surface) in the RC band, and average

133

absorptivity (emissivity) of 0.05 (i.e., nearly the same as that of the real SH surface) in other bands.

134

The real black surface is a spectrally non-selective SH-RC coating and the hypothetical SH-RC

135

surface is a spectrally selective SH-RC material. Accordingly, we named the real black surface as the

136

“SH-RCblack surface” and the hypothetical SH-RC surface as the “SH-RCs surface”. Fig. 4

137

summarizes the spectral properties of the four typical surfaces.

138 139

Fig. 4. Spectral properties of the SH, RC, SH-RCblack, and SH-RCs surfaces.

140

To evaluate the heating and cooling performances of the four surfaces, we introduced a typical

141

collector that mainly includes a transparent cover, collecting surface, and insulation layer. The

142

schematic diagram of the collector is shown in Fig. 5. The collector was set horizontally with an

143

unobstructed view of the sky. The transparent cover was a 6 µm-thick low-density polyethylene film

144

with high transmittance in most of the 0.2–25 µm region (see Fig. 6). Thus, most radiation in the SH

ACCEPTED MANUSCRIPT 145

and RC bands could go through this cover. The collecting surface was positioned parallel to the

146

transparent cover and measured 200 mm × 200 mm × 0.4 mm. The vertical distance between the

147

collecting surface and transparent cover was 35 mm. The collecting surface was surrounded by the

148

insulation layer, which was a 56 mm-thick phenolic foam.

149 150

Fig. 5. Schematic diagram of the collector.

151 152

153

Fig. 6. Spectral transmittance of the 6 μm-thick low-density polyethylene film [27].

3. Theoretical analysis of the collector The schematic diagram of the heat transfer of the components of the collector is shown in Fig.

154 155

7. The following assumptions were made to simplify the analysis [12, 21, 28]:

156



157

The weather condition (solar irradiation, ambient temperature, wind velocity, relative humidity, etc) are unchanged in each calculation time-step, and thus the collector operates under steady-

ACCEPTED MANUSCRIPT state conditions in each time-step.

158 159



The temperatures of the collecting surface in the length and width directions are equal.

160



The collecting plate and transparent cover are treated as diffuse emitters, and thus their spectral

161

absorptivity and emissivity are not angle-related parameters.

162

A quasi-steady-state mathematical model based on the preceding assumptions was developed to

163

describe the thermal performance of the collector. The mathematical model comprised two main

164

equation sets, namely, (i) heat balance equation of the transparent cover and (ii) heat-balance

165

equation of the collecting surface.

166 167

168 169 170

Fig. 7. Heat transfer of the components of the collector.

3.1 Heat balance equation of the transparent cover The heat balance equation of the transparent cover is expressed as follows:

hac Ta  Tc   hsc Ts  Tc   hpc Tp  Tc    c G  0 ,

(1)

171

where hac and hsc are the convective and radiation heat transfer coefficients between the transparent

172

cover and surroundings, respectively, W/(m2·K); hpc is the heat transfer coefficient between the

173

transparent cover and the collecting surface, W/(m2·K); Ta, Tc, Ts, and Tp are the temperatures of the

174

environment, cover, sky, and collecting surface, respectively, K; αc is the absorptivity of the cover in

175

the SH band; and G is the incident solar irradiation per square meter, W/m2.

ACCEPTED MANUSCRIPT The sky temperature is calculated as follows [29]:

176

Ts  0.0552Ta1.5 .

177

The convective and radiation heat transfer coefficients between the transparent cover and the

178 179

(2)

surroundings are expressed as Eqs. (3) and (4), respectively [28]:

hac  2.8  3.0ua

(3)

182

hsc   c Ts2  Tc2  Ts  Tc  ,

(4)

183

where ua is the wind velocity, m/s; εc is the emissivity of the cover; and σ is the Stefan–Boltzmann

184

constant.

180 181

185 186 187

and

Heat transfer between the transparent cover and collecting surface comprised two parts, namely, radiation and convection. The heat transfer coefficient can be written as follows:

hpc  hpc _ rad  hpc _ conv .

(5)

188 189 190 191

Fig. 8. Schematic diagram of the radiative heat change between the cover and surface.

As is shown in Fig. 8, take the cover as the control volumn, the net radiative power between the cover and surface can be derived as follows [7]:

ACCEPTED MANUSCRIPT

Q pc _ rad _ net  E (Tp )  lim

 c 1  ( c  p ) n  1  c  p

n 

  p Tp4 

192

 E (Tc )  lim

 p 1  ( c  p ) n 

n 

1  c  p

p c   c Tc4  1  c  p 1  c  p

,

(6)

 c p Tp4   p c Tc4  1  c  p 193

Therefore, the radiative heat transfer coefficient is derived as follows:

hpc _ rad 

194

Q pc _ rad _ net Tp  Tc

 c p Tp4   p c Tc4 .  (1  c  p )  (Tp  Tc )

(7)

195

where εp is the emissivity of the collecting surface; αc and αp are the emissivity of the cover and

196

collecting surface, respectively; ρc and ρp are the reflectance of the cover and collecting surface,

197

respectively;

198

The convective heat transfer coefficient is expressed as follows [7]: hpc _ conv 

199

Nu  ka , d pc

(8)

200

where Nu is the Nusselt number; ka is the thermal conductivity of air, W/(m·K); and dpc is the

201

vertical distance between the cover and the collecting surface, m.

202 203

For collectors with inclination angles ranging from 0° to 75°, if Tp > Tc, then the Nusselt number can be expressed as follows [7]: 

204

 13   1708  (sin1.8 )1.6   1708   Ra  cos   Nu  1  1.14 1  1       1 ,  Ra  cos      Ra  cos    5830 

(9)

205

where the + exponent indicates that only positive values are used for terms within the square

206

brackets; in case of negative values, zero is used; β is the inclination angle of the collector, rad; and

207

Ra is the Rayleigh number.

208

If Tp < Tc, then the Nusselt number is derived as follows [30]:

ACCEPTED MANUSCRIPT   L Nu  1  0.364 p Ra1 4  1 sin  , d pc  

209

210 211

(10)

where Lp is the length of the collecting surface, m. If Tp = Tc, then no heat convection is observed between the transparent cover and the collecting

212

surface. Therefore, the Nusselt number is equal to zero.

213

3.2 Heat balance equation of the collecting surface

214

The heat balance equation of the collecting surface is expressed as follows:

215

uap (Ta  Tp )  hpc _ conv (Tc  Tp )  ( ) p G  Qrad_net  Q_ output  0 ,

(11)

216

where uap is the heat transfer coefficient between the collecting surface and the surroundings,

217

W/(m2·K); (τα)p is the effective transmittance–absorptance product of the apparatus; Qrad_net is the

218

net radiative power of the collecting surface, W/m2; Q_output is the heat (“-” sign) or cooling energy

219

(“+” sign) extracted from the collecting surface by the hypothetical working medium, W/m2. In the

220

absence of a working medium, the collecting surface reaches its stagnation temperature and the

221

Q_output is then equal to zero.

222

The diurnal thermal efficiency of the collector is expressed as follows:

 th 

223 224 225

Qoutput G

.

(11)

The heat transfer coefficient between the collecting surface and the surroundings can be written as follows:

226

 1 db  uap  1   , h  ac kb 

227

where db is the thickness of the insulation layer, m; and kb is the thermal conductivity of the

228

insulation layer, W/(m·K).

(12)

ACCEPTED MANUSCRIPT 229

The effective transmittance–absorptance product of the apparatus is expressed as follows [29]:

( ) p 

230

 c p , 1  (1   p ) c

(13)

231

where αp is the absorptivity of the collecting surface; and τc and ρc are the transmittance and

232

reflectance of the cover, respectively.

233

The net radiative power of the collecting surface is expressed as follows:

Qrad _ net  Qrad _ p  Qrad _ sp .

234 235

(14)

The outward radiation of the collecting surface (Qrad_p) is computed as follows [21]: E (T )  (1  c , )   c  Eb , (Tc )  Qrad _ p    b , p d  , 0  1  p ,  ((1   p , )  p , )  c , 

236

(15)

237

where Eb,λ is the spectral radiation power of the blackbody, W/(m2∙μm); ρc,λ and εc,λ are the spectral

238

reflectance and emissivity of the cover, respectively; and εp,λ is the spectral emissivity of the

239

collecting surface.

240 241

The radiation from the sky to the collecting surface (Qrad_sp) is expressed as follows [21]: Qrad _ sp  2 



0



 2

0

 s , ( , )  Eb , ( , Ta )   p , ( , )  c , ( , ) sin  cos  d d  ,

(16)

242

where εs,λ and τc,λ are the spectral emissivity of the sky and transmittance of the cover, respectively;

243

and θ is the zenith angle, rad. The definition of θ is the angle between the local zenith (i.e. directly

244

above the point on the ground) and the incident radiation (as is shown in Fig. 9). Therefore the θ

245

changes from 0° to 90°, i.e., 0   

 2

. Zenith Incident radiation

θ

246 247

Horizon

Fig. 9. Schematic diagram of the zenith angle.

ACCEPTED MANUSCRIPT 248

The rigorous method for computing the spectral emissivity of the sky (εs, λ) requires a large

249

amount of data and is complex to use. In our model, we adopted a new and accurate method to

250

calculate εs, λ by using the amount of precipitable water vapor as the only input parameter for any

251

geographic area and season. The fitted formula is expressed as follows [31]:

 s ,  1  exp(a 0   a1 w  a 2  w2  a 3 w3 )

252

(15)

253

where w is the precipitable water vapor amount, cm; a0λ, a1λ, a2λ and a3λ are the fitting coefficients;

254

5.25 ≤ λ ≤ 42.83 μm.

255

Generally, the w shows a positive and non-significant effect on SH performance but a negative

256

and significant influence on the RC performance [21]. The w is related to the dew point temperature,

257

which can be measured easily. Therefore, we can obtain εs, λ by using a simple and precise method.

258

The dew point temperature substantially depends on geographic area and season. For Hefei, the w

259

can be expressed using the following semi-empirical equations [32]:

260

261

exp(0.397  0.081td ), spring exp(0.508  0.089t ), summer  d w , exp(0.575  0.092td ), autumn exp(0.485  0.125td ), winter

(16)

where td is the dew point temperature, °C.

262

In our solution procedure, the weather data (i.e., solar radiation, ambient temperature, dew point

263

temperature, wind velocity, etc.) were directly derived from an automatic meteorological station

264

located at the roof platform of a building in the University of Science and Technology of China,

265

Hefei, China. On the basis of these data, Eqs. (1) and (11) could be calculated by iterative

266

computations. In addition, the quasi-steady-state equilibrium temperature of the collecting surface

267

and transparent cover and the heat or cooling energy extracted from the collecting surface by the

268

hypothetical working medium could be obtained.

ACCEPTED MANUSCRIPT 269

4. Results and discussion

270

4.1 Stagnation temperatures of the different surfaces

271

To investigate the SH and RC performances of the four collecting surfaces, we first calculated

272

their stagnation temperatures in a 24 h period. The consecutive weather data of a typical summer day

273

(from 7:00 am July 19, 2017 to 7:00 am July 20, 2017) in Hefei provided by the automatic

274

meteorological station were employed (see Fig. 10).

275 276

Fig. 10. Weather data from 7:00 am July 19, 2017 to 7:00 am July 20, 2017.

277

The stagnation temperatures of the four typical collecting surfaces, namely, SH, RC, SH-

278

RCblack, and SH-RCs surfaces, were calculated and compared. We defined ΔTsa_avg as the average

279

temperature difference between the stagnation temperatures of the surfaces and ambient temperature.

280

Different stagnation temperatures are observed among the different collecting surfaces (see Fig. 11).

281

During the SH period (8:00–16:00), the SH surface exhibits the highest stagnation temperature, with

282

ΔTsa_avg being 145.50 °C. This result indicates that this surface achieves the optimum SH

283

performance among the four collecting surfaces. Although the SH-RCs surface shows nearly the

284

same spectral properties in the SH band and other bands, its spectral emissivity in the RC band is

ACCEPTED MANUSCRIPT 285

substantially higher than that of the SH surface. Therefore, the SH-RCs surface inevitably radiates

286

heat to the surroundings. This condition can be illustrated by the stagnation temperatures of the two

287

surfaces. ΔTsa_avg of the SH-RCs surface is 110.41 °C, which is 35.09 °C lower than that of the SH

288

surface. However, the SH-RCs surface shows considerably better SH performance than the SH-

289

RCblack surface, with its ΔTsa_avg being 47.15 °C higher than that of the latter. This result could also

290

be explained by the differences in the spectral properties of the two surfaces. Although the spectral

291

absorptivity of the SH-RCblack surface is slightly higher than that of the SH-RCs surface in the SH

292

band, its spectral emissivity in the middle and far infrared wavelengths, particularly in the other

293

bands, is substantially higher than that of the SH-RCs surface (see Fig. 4). Therefore, the radiative

294

heat loss of the SH-RCblack surface considerably exceeds that of the SH-RCs surface. The RC surface

295

shows the poorest SH performance because it rejects most of the solar irradiance while radiating a

296

considerable amount of heat to the sky through its high spectral emissivity in the RC band. The RC

297

surface fails to achieve RC below ambient air under direct sunlight exceeding 850 W/m2; this result

298

is different from that reported by A. P. Raman et al [12]. The relative humidity in the summer of

299

Hefei is considerably higher than that in the winter of Stanford, California. Therefore, the RC effect

300

in Hefei is considerably worse than that in California. This result proves that a radiative cooler

301

exhibits satisfactory cooling performance in arid areas and arid climate.

302

During the RC period (19:00–5:00), the SH-RCs surface exhibits the lowest stagnation

303

temperature, with its ΔTsa_avg being −15.93 °C. The RC and SH-RCblack surfaces occupy the second

304

and third lowest stagnation temperatures, respectively, among the four surfaces (ΔTsa_avg being

305

−14.05 °C and −9.62 °C, respectively). Note that the stagnation temperature of the SH surface is only

306

a few degrees lower than the ambient temperature due to its extremely low spectral emissivity in the

ACCEPTED MANUSCRIPT 307

RC band. Although the SH-RCblack surface shows higher spectral emissivity than the SH-RCs surface

308

in the RC band, its spectral absorptivity in the other bands is considerably higher than that of the

309

latter. That is, the SH-RCblack surface absorbs immense heat from the surroundings. Therefore, the

310

stagnation temperature of the SH-RCblack surface is significantly higher than that of the SH-RCs

311

surface. Table 1 lists the average temperature differences between the stagnation temperatures of the

312

surfaces and the ambient temperature.

313 314

Fig. 11. Stagnation temperatures of the different surfaces in a typical summer day.

315

Table 1. Average temperature differences between the stagnation temperatures

316

of the surfaces and the ambient temperature. Surface type

ΔTsa_avg in SH period (°C)

Order

ΔTsa_avg in RC period (°C)

Order

SH surface

145.50

1

−3.81

4

RC surface

2.54

4

−14.05

2

SH-RCblack surface

63.26

3

−9.62

3

SH-RCs surface

110.41

2

−15.93

1

317

We can conclude from Fig. 11 and Table 1 that although the SH-RCs and SH-RCblack surfaces

318

could achieve the SH and RC functions, the SH-RCs surface exhibits better performance than the

ACCEPTED MANUSCRIPT 319

SH-RCblack surface in terms of both functions. This difference is due to their distinct and different

320

spectral properties in the other bands. The SH-RCblack surface radiates certain net heat to the

321

environment in the SH period and absorbs non-negligible net heat from the surroundings in the RC

322

period owing to its high spectral absorptivity and emissivity in the other bands. By contrast, the heat

323

exchange between the SH-RCs surface and the environment in the other bands could be substantially

324

suppressed thanks to the extremely low spectral absorptivity and emissivity of the surface in these

325

bands. Hence, the SH-RCs surface can reduce the radiant heating loss during the SH period and the

326

radiant cooling loss during the RC period.

327

4.2 Heat and cooling power of the different surfaces

328

To further describe the SH and RC performances of the different collecting surfaces, we studied

329

their heat and cooling powers under different ΔTsa. The weather data for both modes (i.e., average

330

value) from 7:00 am July 19, 2017 to 7:00 am July 20, 2017 in Hefei were employed (see Table 2).

331

Table 2. Weather data for solar heating and radiative cooling modes in a typical summer day (from 7:00 am July

332

19, 2017 to 7:00 am July 20, 2017 in Hefei). Parameter

SH period

RC period

Ambient temperature (°C)

33.55

30.48

Dew point temperature (°C)

24.74

23.19

Wind velocity (m/s)

2.54

1.63

Solar irradiance (W/m2)

777.00

0

333

In solar heating mode, only the three surfaces with the SH function, namely, SH, SH-RCblack,

334

and SH-RCs surfaces, were selected to calculate their diurnal thermal efficiencies. The results are

335

shown in Fig. 12. All the three surfaces show decreased thermal efficiency at elevated ΔTsa.

ACCEPTED MANUSCRIPT 336

However, the decreased velocities are varied. The SH surface radiates the least heat loss. Hence, this

337

surface constantly possesses the optimum thermal efficiency and shows the slowest decline trend of

338

thermal efficiency as ΔTsa increases. The thermal efficiency of the SH-RCs surface is relatively lower

339

than that of the real SH surface because it radiates a large amount of heat in the RC band. The SH-

340

RCblack surface shows the lowest thermal efficiency and the fastest decline trend of thermal efficiency

341

as ΔTsa increases. When ΔTsa is zero, the thermal efficiency of the SH-RCblack surface is only slightly

342

lower than that of the SH-RCs surface. However, the gaps between the two efficiencies become

343

increasingly large as the surface temperature increases. For example, when ΔTsa increases to 50 °C,

344

the SH-RCs surface still shows an acceptable thermal efficiency of 49.60%, whereas the SH-RCblack

345

surface exhibits a poor thermal efficiency of 22.02%. This result is due to the fact that the overall

346

emissivity in the middle and far infrared bands of the SH-RCblack surface is approximately 0.95,

347

whereas that of the SH-RCs surface is merely 0.30. Therefore, the radiating heat loss of the former at

348

an elevated surface temperature is higher than that of the latter.

349 350

Fig. 12. Diurnal thermal efficiencies of the different typical surfaces at different surface-ambient temperatures.

351

In the RC mode, three surfaces with RC functions, namely, RC, SH-RCblack, and SH-RCs

352

surfaces, were selected to calculate their nocturnal cooling powers. The results are shown in Fig. 13.

ACCEPTED MANUSCRIPT 353

As ΔTsa decreases, the cooling powers of the three surfaces diminish almost linearly with different

354

decreasing velocities. The SH-RCblack surface shows the fastest decline of cooling power and the SH-

355

RCs surface shows the lowest one. The coordinates of the cross-point for the non-selective and SH-

356

RCs surfaces in the changing curves of cooling power are (−4.45, 29.44) and that for the RC surface

357

and SH-RCs surface are (−5.53, 26.69). Take the first coordinate as an example. When ΔTsa is above

358

−4.45 °C, the cooling power of the SH-RCblack surface exceeds that of the SH-RCs surface. In

359

practical scenarios, however, ΔTsa is often below −5 °C to effectively cool ambient air to sub-

360

ambient temperature. Therefore, the SH-RCs surface will exhibit better cooling performance than the

361

SH-RCblack surface in actual situations.

362 363 364

Fig.13. Nocturnal cooling powers of the different surfaces at different surface-ambient temperatures.

4.4.3 All-day overall energy gains of the different surfaces

365

To evaluate the overall performance of the different typical surfaces for an entire day, we

366

further investigated their overall energy gains from 7:00 am July 19, 2017 to 7:00 am July 20, 2017

367

in Hefei. The calculated SH period covered 8:00–16:00 and the calculated RC period was 19:00–

368

5:00. The surface temperature was set 20 °C higher than the ambient temperature in the SH mode

369

and 5 °C lower than the ambient temperature in the RC mode. Fig. 14 shows the energy gains of the

ACCEPTED MANUSCRIPT 370

different surfaces during the day. The SH surface shows the highest heat gain of 17.14 MJ/m2,

371

followed by the SH-RCs surface (15.57 MJ/m2) and SH-RCblack surface (13.22 MJ/m2), the heat gains

372

of which are 90.84% and 77.13%, respectively, of that of the SH surface. The heat gain of the RC

373

surface is negligible due to its extremely low absorptivity in the SH band. The RC surface also

374

exhibits an optimum cooling gain with a value of 1.02 MJ/m2, followed by the SH-RCs surface (1.01

375

MJ/m2) and SH-RCblack surface (0.95 MJ/m2). The SH surface possesses negligible cooling gain

376

owing to its extremely low emissivity in the middle and far infrared bands, although cooling energy

377

is more necessary than heat in the summer.

378

As is shown in Fig. 4, the SH-RCs surface shows relatively low absorptivity and/or emissivity in

379

the SH and RC bands than the SH-RCblack surface, not to mention the ideal SH-RCs surface. But even

380

in such an adverse case, the SH-RCs surface still possessed better SH and RC performance than the

381

SH-RCblack surface. If we set the absorptivity and/or emissivity of the SH-RCs surface equal to that of

382

the SH-RCblack surface in the SH and RC bands, its all-day heat and cooling energy gains will be

383

15.59 MJ/m2 and 1.26 MJ/m2 respectively, which are much greater than those of the SH-RCblack

384

surface. Moreover, the all-day heat and cooling energy gains of the ideal SH-RCs surface are 16.70

385

MJ/m2 and 1.30 MJ/m2, respectively, which indicates the greatest possible energy gains of a SH-RCs

386

surface in this specific weather condition.

387

Besides, although the SH-RCs surface shows worse SH performance than the SH surface, the

388

former shows radiative cooling ability that the latter lacks. We believe that certain cooling energy

389

can be reasonably obtained by losing a small amount of heat gain, particularly in hot seasons and

390

regions. In addition, the SH-RCs surface exhibits a RC power that is comparable to that of the RC

ACCEPTED MANUSCRIPT 391

surface. Moreover, the SH-RCs surface possesses a considerable SH efficiency that the RC surface

392

cannot match.

393 394 395

Fig. 14. Overall energy gains of different surfaces from 7:00 am July 19, 2017 to 7:00 am July 20, 2017 in Hefei.

4.4.4 Seasonal energy gains of the different surfaces

396

In practical scenarios, heat energy is needed mainly in spring, autumn and winter, while cooling

397

energy is required in summer. Therefore, we additionally investigated the heating and/or cooling

398

performance of different surfaces in different seasons in Hefei. The Chinese Typical Year Weather

399

data of Hefei was employed in the calculations

400

Firstly, we calculated the heat gains of the SH, SH-RCblack and SH-RCs surfaces in spring,

401

autumn and winter. As shown in Fig. 15 and Table 3, although the SH-RCs surface exhibits worse

402

heating performance than the SH surface, it possesses greater heat gain than the black surface. The

403

overall heat gains of the SH, SH-RCblack and SH-RCs surfaces are 1876.57, 1161.42 and 1531.97

404

MJ/m2, respectively.

ACCEPTED MANUSCRIPT

405 406

Fig. 15. The heat gains of the SH, SH-RCblack and SH-RCs surfaces in spring, autumn and winter.

407

Table 3. The heat gains of the SH, SH-RCblack and SH-RCs surfaces in spring, autumn and winter (MJ/m2). Sep

Oct

Nov

Dec

Jan

Feb

Mar

Apr

May

Total

SH surface

223.84

254.52

205.24

171.73

143.47

158.09

198.27

240.51

280.90

1876.57

Black surface

127.33

166.75

131.12

99.05

74.84

94.69

131.30

151.80

184.54

1161.42

SH-RCs surface

179.85

211.68

169.14

134.70

109.12

127.66

166.55

197.79

235.48

1531.97

408

Then we investigated the cooling energy gains of the RC, SH-RCblack and SH-RCs surfaces in

409

summer, and the results are shown in Fig. 16 and Table 4. In June, the cooling energy gains of the

410

three surfaces are almost the same. In July and August, however, the SH-RCs surface exhibits greater

411

heat gain than the SH-RCblack surface and slightly less heat gain than the RC surface. Specifically, the

412

overall cooling energy gains of the RC, SH-RCblack and SH-RCs surfaces in summer are 78.87, 73.85

413

and 77.71 MJ/m2, respectively.

ACCEPTED MANUSCRIPT

414 415

Fig. 16. The cooling energy gains of the RC, SH-RCblack and SH-RCs surfaces in summer.

416

Table 4. The cooling energy gains of the RC, SH-RCblack and SH-RCs surfaces in summer (MJ/m2). Jun

Jul

Aug

Total

RC surface

26.88

24.58

27.41

78.87

Black surface

26.97

21.94

24.94

73.85

SH-RCs surface

26.66

24.18

26.87

77.71

417

Comparing to the SH-RCblack surface, the SH-RCs surface possesses greater heat gain in spring,

418

autumn and winter, as well as greater cooling energy gain in summer, even though the SH-RCblack

419

surface shows greater absorptivity/emissivity in both SH and RC bands (see Fig. 4). Therefore, we

420

can conclude that the SH-RCs surface shows better seasonal adaptability than the SH-RCblack surface.

421

It is of significance to realize the spectral selectivity of surfaces for the combined SH-RC collector.

422

5. Conclusions

423

The present study proposed the ideal spectral properties of surfaces to achieve combined diurnal

424

SH and nocturnal RC. A hypothetical, spectrally selective SH-RC surface, with spectral

ACCEPTED MANUSCRIPT 425

characteristics that approximate those of the ideal SH-RC surface, was introduced and its heating and

426

cooling performances were investigated and compared with those of other typical surfaces. The

427

results facilitated the formulation of the following conclusions.

428

(1) From the stagnation temperature perspective, the SH surface barely have RC ability; the RC

429

surface nearly shows no solar heating function. By contrast, the SH-RCblack and SH-RCs surfaces

430

exhibit both SH and RC potential.

431

(2) The SH-RCs surface shows better performance than the SH-RCblack surface in terms of SH

432

and RC in practical scenarios. When the absolute value of the difference in the surface and ambient

433

temperatures gets higher, the SH-RCs surface shows its increasing superiority to the SH-RCblack

434

surface. Therefore, pursuing for the spectral selectivity of surfaces for the integrated SH and RC

435

collectors is worthwhile.

436

(3) In a typical summer day of Hefei, the heat gains of the SH, RC, SH-RCblack, and SH-RCs

437

surfaces are 17.14, 0, 15.57, and 13.22 MJ/m2, respectively. Meanwhile, the cooling energy gains of

438

the four surfaces are 0, 1.02, 0.95, and 1.01 MJ/m2, respectively.

439

(4) Based on the Chinese Typical Year Weather data of Hefei, The overall heat gains of the SH,

440

SH-RCblack and SH-RCs surfaces in seasons excluding summer are 1876.57, 1161.42 and 1531.97

441

MJ/m2, respectively. The overall cooling energy gains of the RC, SH-RCblack and SH-RCs surfaces in

442

summer are 78.87, 73.85 and 77.71 MJ/m2, respectively.

443

Overall, the spectral selectivity of the SH-RCs surface enables it to perform better than the SH,

444

RC, and SH-RCblack surfaces regardless of the multi-functionality, seasonal adaptability, and overall

445

energy gain. In the future, we will manufacture a real SH-RC surface that closely resembles the ideal

446

SH-RC surface in terms of spectral properties.

ACCEPTED MANUSCRIPT 447

Acknowledgment

448

This study was sponsored by the National Science Foundation of China (NSFC 51476159,

449

5171101721 and 51776193), National Postdoctoral Program for Innovative Talents (BX201700223),

450

China Postdoctoral Science Foundation (2017M622018), Fundamental Research Funds for the

451

Central Universities, and International Technology Cooperation Program of the Anhui Province of

452

China (BJ2090130038).

453

References

454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483

[1] Sakr I, Abdelsalam AM, El-Askary W. Effect of electrodes separator-type on hydrogen production using solar energy. Energy. 2017;140:625-32. [2] Prinsloo G, Mammoli A, Dobson R. Discrete cogeneration optimization with storage capacity decision support for dynamic hybrid solar combined heat and power systems in isolated rural villages. Energy. 2016;116:1051-64. [3] Hu M, Pei G, Wang Q, Li J, Wang Y, Ji J. Field test and preliminary analysis of a combined diurnal solar heating and nocturnal radiative cooling system. Applied energy. 2016;179:899-908. [4] Zhu L, Raman AP, Fan S. Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody. Proceedings of the National Academy of Sciences. 2015;112(40):12282-7. [5] Huide F, Xuxin Z, Lei M, Tao Z, Qixing W, Hongyuan S. A comparative study on three types of solar utilization technologies for buildings: Photovoltaic, solar thermal and hybrid photovoltaic/thermal systems. Energy Conversion and Management. 2017;140:1-13. [6] Yang H, Wang Q, Huang X, Li J, Pei G. Performance study and comparative analysis of traditional and doubleselective-coated parabolic trough receivers. Energy. 2017. [7] Bergman TL, Incropera FP, DeWitt DP, Lavine AS. Fundamentals of heat and mass transfer: John Wiley & Sons, 2011. [8] Dan A, Barshilia HC, Chattopadhyay K, Basu B. Solar energy absorption mediated by surface plasma polaritons in spectrally selective dielectric-metal-dielectric coatings: A critical review. Renewable and Sustainable Energy Reviews. 2017;79:1050-77. [9] Ning Y, Wang W, Wang L, Sun Y, Song P, Man H, et al. Optical simulation and preparation of novel Mo/ZrSiN/ZrSiON/SiO2 solar selective absorbing coating. Solar Energy Materials and Solar Cells. 2017;167:178-83. [10] Jyothi J, Chaliyawala H, Srinivas G, Nagaraja H, Barshilia HC. Design and fabrication of spectrally selective TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber for high-temperature solar thermal power applications. Solar Energy Materials and Solar Cells. 2015;140:209-16. [11] Wang C, Shi J, Geng Z, Ling X. Polychromic Al–AlN cermet solar absorber coating with high absorption efficiency and excellent durability. Solar Energy Materials and Solar Cells. 2016;144:14-22. [12] Raman AP, Anoma MA, Zhu L, Rephaeli E, Fan S. Passive radiative cooling below ambient air temperature under direct sunlight. Nature. 2014;515(7528):540-4. [13] Zhai Y, Ma Y, David SN, Zhao D, Lou R, Tan G, et al. Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling. Science. 2017;355(6329):1062-6. [14] Chen Z, Zhu L, Raman A, Fan S. Radiative cooling to deep sub-freezing temperatures through a 24-h day-night cycle. Nat Commun. 2016;7:13729.

ACCEPTED MANUSCRIPT 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500

[15] Vall S, Castell A. Radiative cooling as low-grade energy source: A literature review. Renewable and Sustainable

501 502 503 504 505 506 507 508 509 510 511 512 513 514

[24] Gentle AR, Smith GB. A subambient open roof surface under the Mid‐Summer sun. Advanced Science. 2015;2(9).

515

Energy Reviews. 2017;77:803-20. [16] Gentle AR, Dybdal KL, Smith GB. Polymeric mesh for durable infra-red transparent convection shields: Applications in cool roofs and sky cooling. Solar Energy Materials and Solar Cells. 2013;115:79-85. [17] Ali AHH. Passive cooling of water at night in uninsulated open tank in hot arid areas. Energy Conversion and Management. 2007;48(1):93-100. [18] Dyreson A, Miller F. Night sky cooling for concentrating solar power plants. Applied Energy. 2016;180:276-86. [19] Hanif M, Mahlia T, Zare A, Saksahdan T, Metselaar H. Potential energy savings by radiative cooling system for a building in tropical climate. Renewable and sustainable energy reviews. 2014;32:642-50. [20] Tso CY, Chan KC, Chao CYH. A field investigation of passive radiative cooling under Hong Kong’s climate. Renewable Energy. 2017;106:52-61. [21] Hu M, Zhao B, Li J, Wang Y, Pei G. Preliminary thermal analysis of a combined photovoltaic–photothermic– nocturnal radiative cooling system. Energy. 2017;137:419-30. [22] Zou C, Ren G, Hossain MM, Nirantar S, Withayachumnankul W, Ahmed T, et al. Metal-Loaded Dielectric Resonator Metasurfaces for Radiative Cooling. Advanced Optical Materials. 2017;5(20). [23] Gentle AR, Smith GB. Radiative heat pumping from the Earth using surface phonon resonant nanoparticles. Nano Lett. 2010;10(2):373-9. [25] Kou J-l, Jurado Z, Chen Z, Fan S, Minnich AJ. Daytime Radiative Cooling Using Near-Black Infrared Emitters. ACS Photonics. 2017;4(3):626-30. [26] Zhao B, Hu M, Ao X, Pei G. Conceptual development of a building-integrated photovoltaic–radiative cooling system and preliminary performance analysis in Eastern China. Applied Energy. 2017;205:626-34. [27] Hu M, Pei G, Li L, Zheng R, Li J, Ji J. Theoretical and experimental study of spectral selectivity surface for both solar heating and radiative cooling. International Journal of Photoenergy. 2015;2015. [28] Guo C, Ji J, Sun W, Ma J, He W, Wang Y. Numerical simulation and experimental validation of tri-functional photovoltaic/thermal solar collector. Energy. 2015;87:470-80. [29] Duffie JA, Beckman WA. Solar engineering of thermal processes: John Wiley & Sons, 2013. [30] Bejan A. Convection heat transfer: John wiley & sons, 2013. [31] Das A, Iqbal M. A simplified technique to compute spectral atmospheric radiation. Solar Energy. 1987;39(2):143-55. [32] Chao L, He-li W, Hou-tong L, Xiu-hong C, Dong L, Jian-bo Z, et al. Correlation analyses on total precipitable water and surface dew point temperature over Hefei. Plateau Meteorology. 2009;2:025.

ACCEPTED MANUSCRIPT Highlights 1. A surface to realize combined solar heating and radiative cooling (SH-RC) functions. 2. The ideal spectral selectivity of the SH-RC surface was introduced. 3. A thermal model considering spectral radiant distribution was established. 4. The performance of a SH-RC surface was studied and compared with other surfaces.