Active daytime radiative cooling using spectrally selective surfaces for air conditioning and refrigeration systems

Solar Energy 174 (2018) 16–23

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Active daytime radiative cooling using spectrally selective surfaces for air conditioning and refrigeration systems Theodore L. Bergman

T

⁎

Department of Mechanical Engineering, University of Kansas, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Air conditioning Radiation cooling Atmospheric window

Surfaces that exhibit high reflectivity at short (solar) wavelengths and high emissivity at long (terrestrial) wavelengths can experience net radiation cooling, even when subjected to high levels of solar irradiation. A model is developed to quantify passive cooling rates provided by such a surface for an air conditioning application. The model is then extended to predict the performance of a new, photovoltaic-powered air conditioning or refrigeration system where the selective surface actively rejects heat from the air conditioning unit by radiation and convection. It is shown that use of spectrally selective surfaces that have been recently suggested for passive cooling might be better used actively to more effectively: match cooling loads, reduce the required heat rejection surface area, and increase the heat transferred from Earth through the atmospheric window. The proposed active daytime radiative cooling concept also has advantages over more traditional air conditioning approaches.

1. Introduction

(2016) achieved temperature reductions in excess of 40 °C relative to the ambient while the surface was exposed to peak solar irradiation. This large temperature reduction was accomplished by meticulously insulating the surface to minimize conduction and convection gains from the environment. Recently, Zhai et al. (2017) measured the temperature decrease of a small volume of liquid water, to 8 °C below that of the ambient, by placing a spectrally selective film in contact with the underlying water layer and exposing the filled container to direct solar irradiation. The film was a polymer-glass bead composite backed with a reflective metal layer that was reported to be amenable to low-cost, high-volume production. Additional materials designed to provide passive temperature reduction of surfaces exposed to solar irradiation have been recently proposed (Bao et al., 2017; Huang and Ruan, 2017; Kecebas et al., 2017).

There has been considerable recent interest in developing radiation surfaces that exhibit sharp spectral variations of emissivity, absorptivity and reflectivity so as to simultaneously (i) inhibit absorption of short wavelength solar irradiation and (ii) promote long wavelength surface emission. Achieving the desired spectral properties allows for passive daytime radiative cooling (PDRC) of the surfaces, even when the surfaces are exposed to direct solar irradiation (Chang et al., 1995; Chen et al., 2016; Raman et al., 2014). In addition to contributing to daytime radiation heat losses, high surface emission within the atmospheric window (8 μm < λ < 13 μm) is desirable because terrestrial (low source ∼ ∼ temperature) radiation in this wavelength range is relatively unaffected by absorption and scattering as it propagates upward through the atmosphere to deep space (Granqvist and Hjortsberg, 1981; Nilsson and Niklasson, 1995). It has been suggested that widespread use of spectrally selective surfaces that are characterized by low solar absorptivity and high emissivity can provide a pathway to energy sustainability, and could reduce global temperatures (Chu et al., 2017; Wong, 2017). It has been reported that the first measured reduction of the temperature of a surface that is exposed to direct sunlight to values below that of the ambient air was by Raman et al. (2014). Temperature drops of approximately 5 °C were achieved by using a photonic surface that exhibited desired radiative properties as described by Granqvist and Hjortsberg (1981) and the references therein. Subsequently, Chen et al.

⁎

1.1. Temperature reduction versus cooling rate Because of (i) their ability to achieve sub-ambient temperatures when exposed to direct solar irradiation and (ii) their potentially inexpensive manufacture, the recently developed spectrally selective surfaces and films have been proposed for passive daytime refrigeration as well as passive daytime cooling of automobiles, buildings and other infrastructure by reducing interior temperatures to sub-ambient values that are approximately equal to those of the adjoining cold spectrally selective surfaces (Chang et al., 1995; Fernandez et al., 2015; Lu et al.,

Address: University of Kansas, Department of Mechanical Engineering, 1530 West 15th Street, Lawrence, KS 66045, USA. E-mail address: [email protected].

https://doi.org/10.1016/j.solener.2018.08.070 Received 27 January 2018; Received in revised form 22 June 2018; Accepted 24 August 2018 0038-092X/ © 2018 Elsevier Ltd. All rights reserved.

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T.L. Bergman

β ε η λ ν σ

Nomenclature A C1, C2 COP E Eλ g G h k L NuL P Pr q q′ ′ RaL ReL T u∞ Ẇ

area (m2) radiation constants for Planck distribution coefficient of performance emissive power (W/m2) spectral emissive power (W/m2 μm) gravitational acceleration (m/s2) irradiation (W/m2) convection heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) characteristic length (m) Nusselt number (= hL/k) perimeter (m) Prandtl number (ν/α) heat rate (W) heat flux (W/m2) Rayleigh number (= gβ(Ts - T∞)L3/να) Reynolds number (= u∞L/ν) temperature (K) ambient velocity (m/s) rate of work (W)

Subscripts atm AW b c F h N net pv rad s S sky t λ ∞

Greek α

thermal expansion coefficient (K−1) emissivity efficiency wavelength (μm) kinematic viscosity (m2/s) Stefan Boltzmann constant

absorptivity, thermal diffusivity (m2/s)

atmosphere atmospheric window blackbody cooling, cold forced convection hot natural or free convection net photovoltaic radiation surface solar sky total spectral ambient

practical applications is in need of closer attention, and more effective usage of the recently developed spectrally selective surfaces might be made. Based on the preceding discussion, spectrally selective surfaces that have been recently proposed for PDRC might be more effectively deployed as hot (relative to the ambient temperature) heat rejection surfaces used in conjunction with established refrigeration and air conditioning hardware in order to both (i) provide high refrigeration or air conditioning cooling rates when the temperatures of the refrigerated or air conditioned spaces are low and (ii) increase heat rejection from Earth through the atmospheric window. More specifically, the identical spectrally selective surface that exhibits high reflectivity at short (solar) wavelengths, and high emissivity at long (terrestrial temperature)

2016; Raman et al., 2017; Vall and Castell, 2017). Importantly, however, all radiation surfaces designed for PDRC provide their highest cooling rates (qc) when their temperatures are relatively high. Low surface temperatures (corresponding to low temperatures in the refrigerated or air conditioned space) can be achieved only when the surface is insulated from, for example, the volume (that is, the refrigerated or air conditioned space) or material to be cooled (qc → 0). Hence, the thermal behavior of PDRC surfaces (smaller cooling rates at lower temperatures of the refrigerated or air conditioned space) runs counter to the demands of nearly all air conditioning and refrigeration applications for which the highest cooling loads correspond to the lowest room or refrigeration temperatures. Therefore, the notion that PDRC refrigeration or air conditioning might be widely used in

Fig. 1. Schematic of the cooling scenarios showing the relevant heat transfer and thermodynamic processes. (a) Passive (Tc = Ts,PDRC < T∞) operation. (b) Active (Ts,ADRC > T∞ > Tc) operation. 17

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wavelengths might be considered for both of the cooling scenarios shown in Fig. 1. In lieu of daytime operation with a cooled space temperature of Tc ≈ Ts,PDRC < T∞ as in Fig. 1a (the PDRC concept), the same spectrally selective surface will be used to reject heat from a novel refrigeration cycle or unit as in Fig. 1b (the active daytime radiative cooling concept that is being proposed in this study, or ADRC). In addition, since Ts,ADRC > T∞ > Tc in the ADRC scenario of Fig. 1b, heat would be lost from the surface by both radiation and convection, with convection improving the radiation-only system performance. The beneficial role of convection in ADRC is in contrast to its debilitating role in PDRC (Fig. 1a) since convective heating of the surface from the ambient will limit the temperature reduction of the PDRC surface and, in turn, limit the temperature reduction of the cooled space.

αS (TS ) =

∞ ∫0 ελ (λ, TS ) Eλ, b (λ, TS ) dλ

Eb (TS ) +

∞ ε E (λ, 2.5μm λ,2 λ, b

∫

=

∫0

2.5μm

ελ,1 Eλ, b (λ, TS ) dλ Eb (TS )

TS ) dλ

Eb (TS )

(2)

The right-hand sides of Eqs. (1) and (2) are evaluated using a band fraction calculation based upon the Planck blackbody distribution (Bergman and Lavine, 2017). Irradiation of the spectrally selective surface due to atmospheric emission is described through use of an effective sky temperature model (Eicker and Dalibard, 2011. Since Tsky ≈ Ts, the absorptivity of the surface to atmospheric irradiation is assumed to be equal to its emissivity, allowing the net radiation flux between the surface and the atmosphere to be written as

1.2. Objectives

4 ′ ′ , atm = εσ (Ts4−Tsky qrad )

A new concept, active daytime radiative cooling, is proposed here. To gauge the benefits of the proposed concept, a system-level model is developed to quantify and compare the performance of hot (ADRC) and cold (PDRC) selective surfaces used to reject heat from a conditioned space such as shown in Fig. 1 and discussed in the previous sub-section. In addition, radiation heat transfer rates from Earth through the atmospheric window are predicted for both PDRC and ADRC.

In the effective sky temperature modeling approach, the ambient temperature as well as the complex spectral variation of atmospheric radiation properties are accommodated by specifying a sky temperature ′ ′ , atm that are similar to those predicted with that yields values of qrad advanced radiation models. In this regard, prediction of net surface radiation fluxes using Eq. (3) are compared to benchmark predictions (Huang and Ruan, 2017) in the Appendix. The detailed model of Huang and Ruan accounts for (i) the directional nature of the atmospheric irradiation and (ii) the highly variable spectral distribution of the solar irradiation after it has propagated through (iii) a humid atmosphere. Good quantitative agreement between the predictions of the detailed model and those using Eq. (3) is observed over a broad range of surface temperatures, as quantified in the Appendix, validating the effective sky temperature modeling approach taken here.

2. Theory To facilitate a comparison with the PDRC operation shown schematically in Fig. 1a, the ADRC air conditioning (or refrigeration) cycle or unit of Fig. 1b is powered by way of the photovoltaic conversion of solar irradiation. (Alternatively, the ADRC system of Fig. 1b could be powered electrically by sources other than photovoltaic panels.) Regardless of the source of electric power, the air conditioning unit is characterized by its coefficient of performance with, for example, lower COP values associated with thermoelectric coolers (Zhao and Tan, 2014), and higher COPs affiliated with vapor compression cycles (Moran et al., 2014).

2.2. Energy balances and rate equations To complete the system-level model, steady-state energy balances and heat transfer rate equations are applied to (i) the solar-irradiated, spectrally selective cooling surface, (ii) the air conditioning (or refrigeration) cycle or unit, and (iii) the solar-irradiated photovoltaic panel of Fig. 1b. Both the selective and photovoltaic surfaces are assumed be oriented horizontally. Neglecting conduction to or from the spectrally selective surface of area As, the rate of heat rejected by the air conditioning unit of Fig. 1b, qh, is expressed as

2.1. Radiation sub-model An idealized, spectrally selective surface is assumed for the analysis of the concepts of both Fig. 1a and 1b. The radiative properties of the surface exhibit sharp spectral variation, and are taken to be directionally independent. Specifically, the surface is characterized by ελ,1 = 0 at short wavelengths (λ ≤ 2.5 μm, which includes the solar spectral range of 0.3 μm < λ < 2.5 μm), and ελ,2 = 1 at long wavelengths (λ > 2.5 μm, ∼ ∼ which includes the atmospheric window, 8 μm < λ < 13 μm; Huang and ∼ ∼ Ruan, 2017). Hence, the total emissivity of the surface, at temperature Ts (it will be obvious in the following discussion when active or passive operation is being considered, so subscripts ADRC and PDRC will no longer be applied to Ts) is (Bergman and Lavine, 2017)

ε (Ts ) =

∞ ∫0 ελ (λ, Ts ) Eλ, b (λ, Ts ) dλ

Eb (Ts )

=

∫0

2.5μm

4 qh = As [εσ (Ts4−Tsky ) + h (Ts−T∞)−αS GS ]

qh = qc + Ẇ

(5)

where qc is the rate at which thermal energy is extracted from the airconditioned space (the cooling rate) and Ẇ is the rate of work required by the air conditioning cycle or unit described by its coefficient of performance

ελ ,1 Eλ, b (λ, Ts ) dλ Eb (Ts )

COP = qc Ẇ

∫2.5μm ελ ,2 Eλ, b (λ, Ts ) dλ Eb (Ts )

(4)

where the convection heat transfer coefficient is calculated using standard correlations to be described shortly. An energy balance on the air conditioning unit of Fig. 1b yields

∞

+

(3)

(6)

Finally, the energy balance on the photovoltaic panel of surface area Apv is written as

(1)

For sake of generality, the time- and location-dependence of the solar irradiation is not considered, and its spectral distribution is assumed to be proportional to that of a blackbody at TS = 5800 K (Bergman and Lavine, 2017). Since directional effects are neglected, Kirchhoff’s law may be applied and the solar absorptivity is approximated as

Ẇ = Apv ηpv GS

(7)

where ηpv is the efficiency of the photovoltaic conversion process. Equations (1) through (7), along with expressions used to quantify the convection heat transfer coefficient, may be solved to determine the relationships between GS, Tsky, T∞, h, COP,ηpv, As, Ts, qh, qc, Ẇ and Apv. 18

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3. Results

rates associated with the conditioned space, qc, ADRC, for various selective surface temperatures and COPs. During ADRC, the temperature of the selective surface is higher than the temperature of the space that is being conditioned, with temperature differences across air conditioning or refrigeration units (Th – Tc) of 10 to 25 °C (where Ts = Th) being common. For a desirable conditioned space temperature of Tc = 300 K and Th = Ts = 325 K, room cooling rates are qc,ADRC = 1421, 2132, 2842, and 3197 W for COP = 0.5, 1, 2, and 3, respectively. Hence, the cooling rate experienced by the Tc = 300 K cooled space is increased from 1897 W to 3197 W (an increase of ≈ 70%) by using ADRC with COP = 3, relative to PDRC operation. Actual improvements in the cooling rate are expected to significantly exceed 70% because of the purposeful over- and under-prediction of PDRC and ADRC performance, respectively, as discussed in Section 3.1. The power that must be provided to the air conditioning unit during ADRC is reported in Fig. 3a. As expected, the required power decreases with increasing COP, and increases as the rate of heat rejection from the selective surface is increased at higher surface temperatures. At Ts = 325 K, the required electrical power is Ẇ = 2842, 2132, 1421, and 1066 W for COP = 0.5, 1, 2, and 3, respectively. As shown schematically in Fig. 1b, the electric power is assumed to be delivered to the air conditioner unit from a photovoltaic panel. With GS = 900 W/m2 as for the selective surface, and assuming a photovoltaic conversion efficiency of ηpv = 0.20 (Woodhouse et al., 2016), the required photovoltaic surface areas may be calculated and the results are shown in Fig. 3b. At Ts = 325 K, the required areas are Apv = 15.8, 11.8, 7.90 and 5.92 m2 for COP = 0.5, 1, 2, and 3, respectively. Photovoltaic surface areas will be discussed further in Section 3.4.

Base case results are reported below, followed by the results of parametric simulations. Also note that for qh = qc = 0 W, the equilibrium temperature of the spectrally selective surface under direct solar irradiation is Ts = 262.7 K, while that of any non-spectrally selective (gray) surface is Ts = 376.4 K. Hence, non-spectrally selective surfaces cannot be utilized for either PDRC or ADRC because of solar heating of the heat rejection surface, and are not considered here. 3.1. The base case To compare the passive (Ts < T∞) and active (Ts > T∞) daytime radiative cooling concepts of Fig. 1, base case conditions of GS = 900 W/m2 (normal to the surface), Tsky = 255 K (see the Appendix) and T∞ = 310 K are specified. The horizontal selective surface is assumed to be square in shape with an area of As = 10 m2. As noted in Section 1.1, convection heat transfer between the selective surface and the ambient air adversely affects cooling performance during PDRC, but enhances performance when the selective surface is hot relative to the ambient (ADRC). In the base case, PDRC performance is purposely overpredicted and ADRC performance is purposely under-predicted by assuming that (i) convection heat transfer can be somehow eliminated during PDRC, and (ii) the ambient air is quiescent during ADRC so that only free convection occurs on the top side of the selective surface of Fig. 1b. The free convection values of h during ADRC are determined with the expression (Bergman and Lavine, 2017)

NuL, N = 0.15RaL1/3

(8) 3.3. Radiative cooling of earth

where L = As/P. Air properties are evaluated atT = (Ts + T∞)/2 .

Fig. 4 shows the rate of radiation heat transfer from the spectrally selective surface that leaves Earth through the atmospheric window, as determined by integrating the Planck spectral emissive power distribution over the wavelength range of the atmospheric window

3.2. Base case performance Heat losses from the selective surface during PDRC operation with h = 0 W/m2 K are shown in Fig. 2a. The rate of heat loss from the spectrally selective surface (and, in turn, the cooling rate of the conditioned space adjacent to the surface since qh = qc for PDRC as shown in Fig. 1a) becomes small as its temperature (and the temperature of the conditioned space) decreases. For example, at a desirable room set temperature of Tc = Ts = 300 K, the PDRC cooling rate is only qc,PDRC = qh = 1897 W. Fig. 2b shows the selective surface heat loss, qh, and ADRC cooling

qAW = As

∫8

13μm

C1 dλ λ5 [exp(C2/ λTs )−1]

(9)

where C1 = 3.742 × 10 W μm /m and C2 = 1.439 × 10 μm K are the first and second radiation constants, respectively (Bergman and Lavine, 2017). In writing Eq. (9), it is noted that (i) the spectral emissivity of the surface over the range of the integration is unity, (ii) irradiation from cold, deep space is assumed to be negligible, and (iii) absorption and 8

4

2

4

5000

3000

q

c

2500

4000

2000

COP = 3 COP = 2 COP = 1 COP = 0.5

q

h

q (W)

1500

h

q (W)

3000

2000

1000 1000

500 0 280

(a) 290

300

0 310

310

T (K)

(b) 315

320

325

330

T (K)

s

s

2

2

Fig. 2. Base case performance for As = 10 m , Tsky = 255 K, T∞ = 310 K, and GS = 900 W/m . (a) Rate of heat loss during PDRC versus cooling surface temperature. (b) Rate of heat loss (qh) during ADRC as well cooling rates (qc) for various coefficients of performance and Tc = 300 K. 19

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T.L. Bergman

4000

20

3000

15

2000

1

2

A (m )

1

10

pv

.

W (W)

COP = 0.5

COP = 0.5

2

2 1000

3 (a)

0 310

315

320

3

5

325

(b)

0 310

330

315

320

T (K)

325

330

T (K)

s

s

Fig. 3. Base case ADRC behavior for As = 10 m2, Tsky = 255 K, T∞ = 310 K, GS = 900 W/m2 and Tc = 300 K. (a) Electric power required by the air conditioning unit for various COP values. (b) Photovoltaic surface area required to supply electric power to the air conditioning unit for various COP and ηpv = 0.20.

2500

scattering of the upward-propagating radiation within the spectral range of the atmospheric window is neglected. As evident, use of ADRC (Ts > 310 K) releases more thermal energy to deep space than PDRC ∼ (Ts < 310 K), demonstrating that ADRC is more effective than PDRC in ∼ potentially reducing the temperature of Earth.

Active Operation

1500

3.4. Parametric simulations The preceding base case results are predicated on the assumption that convection heat transfer from the spectrally selective surface occurs exclusively by free convection during ADRC. Assuming an air flow (wind) parallel to the surface at a speed of u∞ with turbulent conditions covering the entire surface, the forced convection coefficient may be estimated using (Bergman and Lavine, 2017)

q

AW

(W)

2000

1000

Passive Operation

NuL, F = 0.037ReL4/5 Pr 1/3

500 280

290

300

310

320

330

and the combined free and forced (mixed) convection heat transfer coefficient may be estimated with an expression of the form (Bergman and Lavine, 2017)

T (K) s

Fig. 4. Rate of radiation heat transfer from the hot spectrally selective surface that escapes through the atmospheric window to deep space for As = 10 m2, Tsky = 255 K, T∞ = 310 K, and GS = 900 W/m2.

10000

(10)

3.5 NuL3.5 = NuL3.5 , F + NuL, N

(11)

with air properties again evaluated at T¯ . Fig. 5a shows the rate of heat loss from the selective surface, qh, as

8000

q

40

c

COP = 3 COP = 2 COP = 1 COP = 0.5

q

h

6000

1

2

1

pv

4000

20

A

. 4000

W (W)

q (W)

6000

2

2 3

2000

2000

0

COP = 0.5

30

COP = 0.5

(m )

8000

(a) 0

1

2

3

0

(b) 0

1

2

u

0

3

(m/s)

(c) 0

1

2

3

u (m/s) 8

8

8

u (m/s)

3

10

2

2

Fig. 5. ADRC performance for As = 10 m , Tsky = 255 K, T∞ = 310 K, Ts = 325 K, Tc = 300 K, and GS = 900 W/m and various air velocities. (a) Heat rates. (b) Air conditioning power requirements. (c) Photovoltaic surface areas. 20

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well as cooling rates, qc, for As = 10 m2, Tsky = 255 K, T∞ = 310 K, Ts = 325 K, Tc = 300 K, and GS = 900 W/m2 at various COPs and air velocities. As expected, the heat transfer rates become large as the convection coefficient increases due to forced convection effects (for example, h = 4.2 W/m2 K and 44 W/m2 K at u∞ = 0 and 3 m/s, respectively). Because of the desirable increase in cooling rates at higher air velocities, both the power required by the air conditioning unit (Fig. 5b) and the required photovoltaic surface areas (Fig. 5c) increase with increasing u∞. However, a more relevant comparison is to determine the total ADRC surface areas (i.e. hot selective surface plus photovoltaic surface) that would be required to achieve the same cooling rate as for the PDRC base case. To this end, Eqs. (1) through (8), (10) and (11) may be solved with qc,ADRC = qc,PDRC = 1897 W. At u∞ = 2 m/s and COP = 3, for example, the calculation yields Ẇ = 632 W, As = 2.79 m2 and Apv = 3.51 m2. Importantly, the presence of forced convection reduces the required total (heat rejection surface plus photovoltaic panel) surface area from At = As = 10 m2 for PDRC to At = As + Apv = 2.79 + 3.51 = 6.30 m2 for the ADRC concept. At u∞ = 0 m/s, the total ADRC surface area required to achieve the same cooling rate as for PDRC is At = 5.93 + 3.51 = 9.44 m2, still less than the total area required for PDRC. Finally, ADRC predictions associated with quiescent conditions and various COPs as well as solar irradiation values are presented in Fig. 6. The predicted values of qh and qc are relatively insensitive to GS

(Fig. 6a) due to the fact that most of the solar irradiation is reflected from the surface. Hence, the power required by the air conditioning unit is only slightly sensitive to the level of solar irradiation (Fig. 6b). To compensate for low levels of solar irradiation, however, the required photovoltaic surface area becomes large, as shown in Fig. 6c, demonstrating the need to power the system with non-solar sources during periods of low or no solar irradiation. Similar sensitivities of qc, qh, Ẇ and Apv to GS are noted for cases involving forced convection. 4. Discussion and conclusions A system-level model has been developed to predict the cooling performance of spectrally selective surfaces in a passive operating mode, as well as for a novel active, daytime radiative cooling concept. During ADRC, the spectrally selective surfaces are used in conjunction with established air conditioning and refrigeration hardware. The model predictions show that selective surfaces such as those recently proposed for PDRC could be more effectively incorporated with established air conditioning and refrigeration technologies operated in the ADRC mode. Several potential advantages of ADRC relative to PDRC are as follows.

• In contrast to the deteriorating ability of PDRC to cool a space or volume as the temperature of the space decreases, cooling rates

5000

4000

q

h

4000

3000

COP = 0.5

q , COP = 3 c

2

W (W)

q (W)

3000

.

1

2000

2 0.5

(a) 0

200

400

600

800

3

1000

1000

0

1

2000

0

1000

(b) 0

200

400

2

600

800

1000

2

G (W/m )

G (W/m )

S

S

50

0.5

30

1

pv

2

A (m )

40

20

2 COP = 3

10

0

(c) 0

200

400

600

800

1000

2

G (W/m ) S

2

Fig. 6. ADRC performance for As = 10 m , Tsky = 255 K, T∞ = 310 K, Ts = 325 K, Tc = 300 K, and u∞ = 0 m/s. (a) Heat rates. (b) Air conditioning power requirements. (c) Photovoltaic surface areas. 21

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T.L. Bergman

• •

•

•

•

provided by ADRC are relatively immune to the temperature of the volume to be cooled. ADRC can provide higher cooling rates than PDRC for the same cooling surface area. This advantage is more pronounced at higher COP. For the conditions considered here, ADRC conservatively increases cooling rates by 70% relative to PDRC. ADRC can require less surface area than PDRC to satisfy a specific cooling load, even when the area occupied by the ADRC photovoltaic panels is taken into account. For roof-mounted refrigeration and air-conditioning heat rejection surfaces and photovoltaic panels, for example, ADRC might be feasible when PDRC is not. This advantage is more pronounced at higher COP. For the conditions considered here, ADRC requires only about 65% of the total (heat rejection surface plus photovoltaic) surface area required by PDRC when forced convection (wind cooling) of the selective surface is accounted for. The cooling capacity of PDRC is adversely affected by heat transfer from the warm ambient to the selective surface, requiring insulation of the surface from heat gains due to convection and conduction. In contrast, ADRC cooling rates are improved by heat transfer from the hot selective surface to the ambient, minimizing or eliminating the need for insulation. In addition to the preceding advantages of ADRC over PDRC for air conditioning or refrigeration applications, ADRC increases the amount of heat lost from Earth to deep space relative to PDRC, beneficially impacting Earth’s energy balance and potentially reducing global temperatures. For the conditions considered here (Ts = 300 K and 325 K for PDRC and ADRC, respectively) heat losses from the selective surface to deep space are increased by approximately 40% by using the ADRC cooling approach instead of PDRC. ADRC offers the following advantages relative to conventional air conditioning and refrigeration systems that utilize convection to transfer heat from a condenser unit to the outside air. The ADRC concept relies on radiation as well as free or mixed convection, potentially eliminating the need for fan-cooled

•

•

condensers, reducing refrigeration and/or air conditioning capital as well as operating costs. In contrast to heat released from ground-level, fan-cooled condenser units, heat released from roof-mounted selective surfaces associated with ADRC is directed upward by radiation, and by convection to ambient air above the roof line. Therefore, roof-mounted ADRC surfaces will not raise temperatures of the ambient air at ground level as much as conventional air conditioning or refrigeration approaches, increasing human comfort outdoors and reducing cooling loads imposed on the infrastructure to be cooled, and on neighboring infrastructure. ADRC increases the amount of heat transferred from Earth to deep space relative to conventional cooling strategies, beneficially impacting Earth’s energy balance.

The model developed here uses straightforward energy balances and heat transfer rate equations to provide the initial predictions of the performance of the novel ADRC concept. More comprehensive modeling would be required to optimize ADRC for specific applications. More detailed descriptions of the radiation heat transfer would be desirable in order to predict transient ADRC performance over a broad range of microclimates and operating conditions. 5. Conflict of interest None. Acknowledgements Appreciation is extended to Professor Zhifeng Huang of Wuhan University and Professor Xiulin Ruan of Purdue University for providing the detailed heat flux data of Fig. A1. This research did not receive any specific grant from funding agencies in the public, commercial, or notfor-profit sectors.

Appendix Huang and Ruan (2017) calculate the net radiation heat flux from the same spectrally selective surface as described in Section 2.1 (ελ,1 = 0 for ≤ 2.5 μm and ελ,2 = 1 for λ > 2.5 μm) for various surface temperatures. In their calculations and as in this study, the solar irradiation is incident normal to the surface with GS = 900 W/m2, while convection as well as conduction exchange to or from the surface is neglected. In their detailed radiation model, (i) an actual, measured spectral distribution of GS is used, (ii) the directional distribution of atmospheric irradiation of the surface is accounted for, as is (iii) the water vapor content of the ambient air which has a specified air temperature of 300 K (Huang and Ruan, 2017). Using the

600 500

T

sky

net

2

q " (W/m )

400

= 245 K 255 K 265 K

300 200 100 0

Huang and Ruan, 2017 (solid line)

-100 -200 250

275

300

325

350

T (K) s

Fig. A1. Comparison of spectrally selective surface heat fluxes predicted by Huang and Ruan (2017) to those of the approximate model of this study (dashed lines) for various surface and sky temperatures. 22

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effective sky temperature model of Section 2.1 to account for spectral effects of the atmospheric radiation, the net radiation heat flux from the ′ ′ = qrad ′ ′ , atm−αS GS where Eq. (1) is used to determine the surface emissivity, Eq. (2) is used to calculate the solar absurface is determined byqnet

′ ′ , atm . sorptivity, and Eq. (3) is used to determine qrad

′ ′ associated with various surface and sky temperatures are provided in Fig. A1, along with values of the net radiation flux Predicted values of qnet reported by Huang and Ruan (2017). Discrepancies between the net radiation heat fluxes predicted by the two models are small, and are minimized when a sky temperature of Tsky = 255 K is specified. Despite the approximate nature of the effective sky temperature model, the predicted heat fluxes are, on average, in remarkable agreement with the benchmark (Huang and Ruan, 2017) predictions. Specifically, net radiation fluxes generated with the two models are in agreement to within 3.4% over the broad temperature range of interest in the parametric simulations of the study, 280 K < Ts < ∼ ∼ 330 K, with a maximum discrepancy of 4.6% at Ts = 280 K. Based on the good agreement with the benchmark data of Huang and Ruan, Tsky = 255 K is specified in the radiation model used in this study.

Lu, X., Xu, P., Wang, H., Yang, T., Hou, J., 2016. Cooling potential and applications prospects of passive radiative cooling in buildings: the current state-of-the-art. Renew. Sustain. Energy 65, 1079–1097. Moran, M.J., Shapiro, H.N., Boettner, D.D., Bailey, M.B., 2014. Fundamentals of Engineering Thermodynamics, eighth ed. John Wiley and Sons, Hoboken. Nilsson, T.M.J., Niklasson, G.A., 1995. Radiative cooling during the day: simulations and experiments on pigmented polyethylene cover foils. Sol. Energy Mater. Sol. Cells 37, 93–118. Raman, A.P., Anoma, M.A., Zhu, L., Rephaeli, E., Fan, S., 2014. Passive radiative cooling below ambient air temperature under direct sunlight. Nature 515, 540–544. Raman A.P., Fan S., Rephaeli E., 2017. Structures for Radiative Cooling. U.S. Patent 9, 709,349 B2. Vall, S., Castell, A., 2017. Radiative cooling as low-grade energy source: a literature review. Renew. Sustain. Energy Rev. 77, 803–820. Wong, K.V., 2017. Anthropogenic heat generation and heat exhaust to the ultimate sink. J. Energy Res. Technol. 139, 034701-1–3. Woodhouse, M., Jones-Albertus, R., Feldman, D., Fu, R., Horowitz, K., Chung, D., Jordan, D., Kurtz, S., 2016. On the Path to SunShot: The Role of Advancements in Solar Photovoltaic Efficiency, Reliability, and Costs. National Renewable Energy Laboratory, NREL/TP-6A20-65872, < http://www.nrel.gov/docs/fy16osti/65782. pdf > . Zhai, Y., Ma, Y., David, S.N., Zhao, D., Lou, R., Tan, G., Yang, R., Yin, X., 2017. Scalablemanufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling. Science 355, 1062–1066. Zhao, D., Tan, G., 2014. A review of thermoelectric cooling: materials, modeling and applications. Appl. Therm. Eng. 66, 15–24.

References Bao, H., Chen, Y., Wang, B., Fang, X., Zhao, C.Y., Ruan, X., 2017. Double-layer nanoparticle-based coatings for efficient terrestrial radiative cooling. Sol. Energy Mater. Sol. Cells 168, 78–84. Bergman, T.L., Lavine, A.S., 2017. Fundamentals of Heat and Mass Transfer, eighth ed. John Wiley and Sons, Hoboken. Chang, D.B., Pollack, S.A., Shi, L.-F., Jicha, A.J., 1995. Selective emissivity coatings for interior temperature reduction of an enclosure. U.S. Patent 5,405,690. Chen, Z., Zhu, L., Raman, A., Fan, S., 2016. Radiative cooling to deep sub-freezing temperatures through the 24-h day-night cycle. Nat. Commun. https://doi.org/10.1038/ ncomms13729. Chu, S., Cui, Y., Liu, N., 2017. The path towards sustainable energy. Nat. Mater. 16, 16–22. Eicker, U., Dalibard, A., 2011. Photovoltaic-thermal collectors for night radiative cooling of buildings. Sol. Energy 85, 1322–1335. Fernandez, N., Wang, W., Alvine, K., Katipamula, S., 2015. Energy Savings Potential of Radiative Cooling Technologies. U.S. Department of Energy Report, PNNL-24904. Granqvist, C.G., Hjortsberg, A., 1981. Radiative cooling to low temperatures: general considerations and application to selectively emitting SiO films. J. Appl. Phys. 52, 4205–4220. Huang, Z., Ruan, X., 2017. Nanoparticle embedded double-layer coating for daytime radiative cooling. Int. J. Heat Mass Transf. 104, 890–896. Kecebas, M.A., Menguc, M.P., Kosar, A., Sendur, K., 2017. Passive radiative cooling design with broadband optical thin-film filters. J. Quant. Spectrosc. Radiat. Transf. 198, 179–186.

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