# Fileset

[9781032529042_C008.pdf](https://mdr.nims.go.jp/filesets/ab9b9c2c-f571-4e45-b810-8e6db8dacd4d/download)

## Creator

[Ross Y. M. Wong](https://orcid.org/0000-0002-7556-3348), [Christopher Y. H. Chao](https://orcid.org/0000-0002-2974-0403), [Satoshi Ishii](https://orcid.org/0000-0003-0731-8428)

## Rights

This is an Accepted Manuscript of a book chapter published by Routledge/CRC Press in Thermal Plasmonics and Metamaterials for a Low-Carbon Society on 3 June 2024, available online: http://www.routledge.com/9781003409090 or http://www.crcpress.com/9781003409090[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Passive radiative cooling applications for thermal and electrical energy harvesting](https://mdr.nims.go.jp/datasets/4065d689-950a-4b41-bc66-9e1b5c09ffac)

## Fulltext

9781032529042_C008.indd140 DOI: 10.1201/9781003409090-88.1 � INTRODUCTIONPassive radiative cooling is a green technology without a carbon footprint that utilizes a sky-facing surface emitting thermal radiation through the bandwidth coincident with the infrared transparent atmospheric window lying within 8–13 μm of electromagnetic spectrum and self-preserving the temperature below ambient. It is deeply emerged in our daily life in which fog formation on land and plants under a nocturnal clear sky is a typical example. In 1978, with a titanium dioxide painted surface, it was the first time sub-ambient radiative cooling at daytime being reported in a scholarly research publication [1]. In 2014, thanks to escalating global concern on energy conservation and carbon neutrality, with a photonic radiative cooler composed of a bottom silver mirror and a top cascaded alternating silicon dioxide and hafnium dioxide 8–13 μm C h a p t e r  8Passive Radiative Cooling Applications for Thermal and Electrical Energy HarvestingRoss Y. M. WongNational Institute for Materials Science, Tsukuba, JapanChristopher Y. H. ChaoThe Hong Kong Polytechnic University, Hung Hom, Hong Kong, ChinaSatoshi IshiiNational Institute for Materials Science, Tsukuba, Japan9781032529042_C008.indd   140 15-02-2024   4.52.31 PMPassive Radiative Cooling Applications    ◾    141thermal emitter, Raman et al.’s demonstration on daytime radiative cooling, realizing a temperature reduction of 5°C and a radiative cool-ing power of 40 W/m2, drew intensive attention of the scientific com-munity [2]. Then tremendous spectrally selective radiative coolers with improved thermal performance, broad materials selection, and scalable manufacturing feasibility were suggested within a few years [3–12]. They are expected to evolve numbers of engineering applications, especially for thermal and electrical systems. Aiming to review our latest develop-ments on passive radiative cooling applications for thermal and electrical energy harvesting, this chapter is organized as follows. In Section 8.2 is a discussion of the analytical framework of thermo-photonic energy conversion for chilled water collection. Section 8.3 discusses one of the photo-thermoelectric energy conversion for electricity generation. In Section 8.4, is a discussion confronting the research challenge in passive radiative cooling. Last, Section 8.5 summarizes this chapter briefly. The advancement in radiative cooling materials is not discussed in this chap-ter because there have been a lot of published articles comprehensively reviewing the topic [13–15].8.2 � THERMO-PHOTONIC ENERGY CONVERSION FOR CHILLED WATER COLLECTIONA commercial chiller removes heat from chilled water via a vapor com-pression cycle, producing a cooling effect through a reversed Rankine cycle. A radiative-cooling-based chilled water system, simply integrable with a building’s heating, ventilation, and air-conditioning system via a heat exchange interface, can substitute a part of the cooling load with a chiller and directly save electricity consumption. From the 1990s to 2000s, radiative-cooling-based chilled water systems were suggested and stud-ied for nocturnal cooling capacity [16–21]. After Raman’s succession in daytime radiative cooling, sub-ambient water cooling up to 5 °C during the daytime was demonstrated with a copper-tube-embedded aluminum plate exchanger [22]. Then a kilowatt scale radiative cooled cold collection system, also called RadiCool, was developed to chill water up to 10.6 °C at noon [23, 24]. Besides sensible cooling, water condensate can be harvested at the peak rate of 50 mL/m2-hr through latent cooling [25, 26]. Building energy simulations and modeling predicted energy saving in office build-ings by 45–68 % relative to variable air volume HVAC system [27], cooling electricity saving in two-floor single-family houses by 26–46 % relative to 9781032529042_C008.indd   141 15-02-2024   4.52.31 PM142    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societysplit-type air conditioner [28], and indoor air temperature reduction up to 10 °C [29]. Unfortunately, chilling capacity of these radiative fluid cooling systems are bounded by a moderate radiative cooling power of 100 W/m2. To efficiently utilize this new form of renewable energy resource, it is espe-cially important to have a comprehensive understanding on their thermal and energy conversion performances, indicative by the fluid temperature reduction and energy conversion efficiency respectively.Fluid temperature reduction denotes the fluid temperature difference before and after cooling, and energy conversion efficiency represents the ratio of enthalpy converted by the working fluid to the cooling effect har-vestable from the sky [30]. To acknowledge the harvestable cooling effect, it is essential to consider energy balance of a radiative cooler subjected to a generic heat load q, which can be mathematically written as P T P T P h T T qArad w atm amb sun c amb w� � � � � � � �� �� � 0, (8.1)where Tw is the surface temperature, Tamb is the ambient temperature, hc is the coefficient of heat transfer between the surface and the environment, and A is the surface area. At an arbitrary temperature T,  P T I T d drad bb� � � � � � �� � � � �, cos ,�   (8.2)is the radiative heat flux emitted by the radiative cooling surface, P T I T d datm atm bb� � � � � � � ������� � �� � � � � � ��1 01,/cos , cos ,�  (8.3)is the radiative heat flux absorbed from the atmosphere, and,  P I dsun AM G� � � � �� � � �1 5. cos ,�   (8.4)is the radiative heat flux absorbed from the sun, where Ibb(λ, T) = 2hpc2/λ5(ehpc/λkbT − 1) is the blackbody radiance, c = 3 × 108 m/s is the speed of light, hp = 6.63 × 10−34 J-s is the Planck’s constant, kb = 1.38 × 10−23 J/K is the Boltzmann constant, θ is the zenith angle of spherical coordinate system, Ω is the solid angle extending the upper hemisphere of spheri-cal coordinate system, ψ is the zenith solar angle, λ is the wavelength, 9781032529042_C008.indd   142 15-02-2024   4.57.23 PMPassive Radiative Cooling Applications    ◾    143IAM1.5G is the air mass 1.5 global solar radiance, ε is the spectral emissivity of radiative cooling surface, and τatm, 0 is the zenith atmospheric spectral transmittance.When the surface temperature is raised to the ambient, the surface withstands the critical heat load that depends on ambient temperature only and equals the radiative cooling power in magnitude. Despite mea-suring the dischargeable electromagnetic energy, cooling power can be affected by materials properties, whereas harvestable cooling effect should be an intrinsic property of the sky as a heat dissipative thermal reservoir. Hence, cooling capacity should be determined by the ideal cooler capable in capturing the most cooling effect, performing as a spectrally selective blackbody emitter within 8–13 μm, but a perfect mirror elsewhere. Now energy conversion efficiency is well-defined as, ��thf p f f f c f hnet ideal amb� ��� �� �c Q T TP T, , ,,, (8.5)where ρf is the fluid density, cp, f is the specific heat capacity of fluid, Qf is the flow rate of fluid, Tf, h is the fluid temperature before cooling, Tf, c is the fluid temperature after cooling, and Pnet, ideal(Tamb) is the ideal radiative cooling power.8.2.1 � Energy Balance ModelTo formulate the analytical framework for fluid temperature reduction and energy conversion efficiency, it is necessary to consider the 1-dimensional heat transfer model of a radiative fluid cooling system specified as follow. As shown in Figure 8.1(a) schematically, A rectangular channel of length l, width w, and height τ is engraved on a radiative cooler of area A. It con-nects two reservoirs at distinct temperatures of Tf, h and Tf, c respectively at the ends. Working fluid of density ρf and specific heat capacity cp, f drifts at a flow rate Qf from the reservoir at Tf, h to the one at Tf, c. Under uniform surface temperature Tw and adiabatic reservoir surfaces assumptions, an overall energy balance equation can be expressed as P T P T P h T Tc QAT Trad w atm amb sun c amb wf p f ff h w� � � � � � � �� �� �� �� �� ,,1 eeh wlc Q�� � �fwf p f f� , ,0   (8.6)9781032529042_C008.indd   143 15-02-2024   4.59.38 PM144    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societywhere hfw is the fluid-wall interfacial heat transfer coefficient. In this equa-tion, fluid-wall interfacial heat transfer is entirely contributed by forced convection in the closed channel and, in this circumstance, hfw is depen-dent on the frontal area and mode of heating only and solvable by clas-sical heat transfer theory. Numerical values of Nusselt number Nufw, D, the dimensionless form of hfw equaling Nufw, D = hfwDH/κf, where κf is the thermal conductivity of fluid and DH is the hydraulic diameter, are avail-able in many heat transfer textbooks like ref. [31], ranging between 2.5 and 8.2 for fully developed laminar channel flow. Radiative fluid cooling performance is optimal upon satisfying the criteria of hfwwl/ρf cp, fQf > > 1. In this circumstance, eq. (8.6) can be further simplified by considering the system subjected to a small perturbation in fluid flow from Qf to Qf + dQf. The direct consequence is two-folded. First, Tw is shifted by dTw. Second, overall energy balance reacts in two aspects, in which the heat currents, Prad and hc(Tamb − Tw), are altered in response to the change in Tw. Then the differential energy response equation can be worked out by subtracting the energy balance equations at two different system statuses. And, recognizing the boundary conditions that saturation temperature reduction ΔT∞ equals the unloaded temperature reduction and saturation energy conversion efficiency, ηth, ∞ vanishes as Qf → 0, as well as ΔT∞ = 0 and ηth, ∞ = 1 as Qf → ∞, analytical expressions for ΔT∞ and ηth, ∞ can be obtained by integration as, �TP Tc QAE T T Ac Qh Ac� � �� ��� ��net ambf p f f amb ambf p f fcf p� �� �,, ,14 3ff fQ��������, (8.7)and, ���thnet ambnet ideal ambamb ambf p f f,,,� �� �� � �� ��P TP TE T T Ac Q14 3 hh Ac Qcf p f f� ,,�������� (8.8)respectively, where σ = 5.67 × 10−8 W/m2-K4 is the Stefan Boltzmann con-stant and E is the ratio of the change in emitted radiative heat flux by a grey-body to a blackbody, and Pnet(Tamb) is the radiative cooling power.9781032529042_C008.indd   144 15-02-2024   5.00.56 PMPassive Radiative Cooling Applications    ◾    145FIGURE 8.1  (a) one-dimensional heat transfer model; and (b) computational fluid dynamics simulation model for the passive radiative fluid cooling system; (c) a picture of the experimental setup for equivalent dissipative thermal reservoir experiment; a comparison of theoretical, simulated, and experimental results of (d) temperature reductions and efficiencies for flow rate between 2 μL/s and 1 mL/sRadiative coolingsurface (top)Radiative coolingsurface (top) hiddenHeat transfer interface(bottom)Heat transfer interface(bottom) hiddenMixed thermal b.c.(Continued )9781032529042_C008.indd   145 15-02-2024   5.01.18 PM146    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Society8.2.2 � Computational Fluid Dynamics Simulations ModelRadiative fluid cooling performance can be demonstrated by computa-tional fluid dynamics simulation. It involves two main procedures, includ-ing the meshing of computational domain and the iteration of discretized FIGURE 8.1  (Continued) (e) a picture of the experimental setup for outdoor field investigation on chilled water capacity; and (f) Daily profiles of measured system temperatures during outdoor field investigation on chilled water capacity. Part (c) is reprinted from International Journal of Heat and Mass Transfer, 174, Corrected radiative cooling power measured by equivalent dissipative thermal reservoir method, 121341, Copyright (2021), with permission from Elsevier. Parts (c) and (d) are reprinted from Renewable Energy, 180, Thermo-radiative energy conversion efficiency of a passive radiative fluid cooling system, 700 – 711, Copyright (2021), with permission from Elsevier. Parts (e) and (f) are reprinted from International Journal of Heat and Mass Transfer, 215, Field demonstrated extended Graetzian viscous dissipative thermo-photonic energy conversion with a blended MgO/PVDF/PMMA coated glass-PDMS micro-pillar heat exchanger, 124520, Copyright (2023), with permission from Elsevier.9781032529042_C008.indd   146 15-02-2024   5.01.19 PMPassive Radiative Cooling Applications    ◾    147governing equations under specified boundary conditions sequentially. As shown in Figure 8.1(b), the simulation model involves not only the fluid advancing space, but also the substrate for radiative cooling materi-als deposition, interconnected by a heat transfer interface. The model is decomposed into a finite number of elements with local refinement at the boundary faces and interface. For fluid sub-domain, the governing equa-tions are given by the mass, momentum, and energy conservation equa-tions which take the form of  �� �v 0,   (8.9)  �f ��� � � �� ���v v p ��,  (8.10)and,  � �f p f fc T T, ,��� � � �v 2  (8.11)respectively for a single species, viscous and constant properties fluid, where τ = μf(∇ v + ∇ vT) is the stress tensor, μf is the fluid viscosity, p is the hydrostatic pressure, v and vT are the fluid velocity vector and transpose of fluid velocity vector. Fluid velocity and temperature are specified at the inlet. Outflow boundary condition, where the gradients of flow variables are vanished, is employed at the outlet. And no-slip hydrodynamic bound-ary condition and adiabatic thermal boundary condition are applied on all surrounding walls. For solid sub-domain, mass and momentum trans-ports are negligible, and energy transport is driven by conduction only, where the heat conduction equation can be written as  �� �� � ��s T 0,  (8.12)where κs is the thermal conductivity of substrate. A mixed heat current, composed of a radiative current and a convective current, is specified at the radiative cooling surface. Thermally coupled wall condition is imposed at the fluid-wall heat transfer interface. An adiabatic wall boundary con-dition is set at the remaining walls. Finally, the governing equations are discretized by the second order upwind scheme, coupled with the SIMPLE algorithm, and solved by the finite element method. The relaxation factors are set in the range from 0.2 to 0.95. The discretized equations are iterated 9781032529042_C008.indd   147 15-02-2024   5.03.20 PM148    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societyuntil the normalized residues are reduced to 10−5 or below for mass and momentum conservation equation, and 10−9 or below for energy conser-vation equation.8.2.3 � Equivalent Dissipative Thermal Reservoir ExperimentFurthermore, radiative fluid cooling performance can be illustrated by equivalent dissipative thermal reservoir experiment. It makes use of the strong linear dependence of net radiative heat exchange between the radi-ative cooling surface and the environment when surface temperature and ambient temperature are slightly different. As such, fluid cooling perfor-mance can be examined under the replicated radiative cooling effect estab-lished by a linear free buoyant stream between the dummy radiative fluid cooling system and the equivalent dissipative thermal reservoir. As shown in Figure 8.1(c), the equivalent dissipative thermal reservoir at the effective temperature, constructed by a surface with the same area of dummy radi-ative cooling surface, was conducted to the cold side of a thermo-electrical cooling system. A copper plate, capping a heat exchanger, was channeled to the hot side. Coolant, kept at a constant temperature, was chilled and circulated by the refrigerative chillers. It took away residual heat pumped by the thermoelectric coolers upon execution. The two systems were mounted on a distance and orientation adjustable platform to set up the designated thermal boundary conditions. More details on the equivalent dissipative thermal reservoir experiment can be referred to ref. [32].Figure 8.1(d) compares the theoretical, simulated, and measured sur-face temperature reduction, fluid temperature reduction, and energy con-version efficiency. Saturation temperature reduction decreases with flow rate, whereas saturation energy conversion efficiency increases with flow rate. At small flow rate of 2 μL/s, temperature reduction approaches the unloaded value of 6.5 °C, but efficiency falls to 0 %. At a large flow rate of 1 mL/s, temperature reduction declines to 0 °C, but efficiency climbs to the ideal limit of 100 %. This inversed correlation can also be captured by sim-ulation and experiment. Simulated surface and fluid temperature reduc-tions come to the same point. And experimental results show that water can be chilled by 4.1 °C and cooling effect can be harvested by 212 mW, equivalent to the energy conversion efficiency of 14 %, whereas water can be weakly chilled by 1.5 °C and cooling effect can be harvested by 726 mW, equivalent to an elevated efficiency of 49 %. For flow rate over 20 μL/s, these tendencies are coherent with the theoretical prediction. For flow rate below 20 μL/s, simulated and experimental results are distinguishable 9781032529042_C008.indd   148 15-02-2024   5.03.20 PMPassive Radiative Cooling Applications    ◾    149from the analytical prediction. Despite the same simulated surface and fluid temperature reductions, the declining trends are not persistent with smaller flow rate and they plateau at 4.6 °C. Also, measured surface and fluid temperature reductions are not convergent. When the flow rate is 12.4 μL/s, fluid temperature reaches the bottom of 4.1 °C, higher than the saturation temperature reduction by 0.3 °C, but surface temperature reduction drops with flow rate continually, significantly lower than the saturation temperature reduction by 3 °C. As a consequence, energy con-version efficiency is lower than the saturation value.8.2.4 � Outdoor Field Investigation of Chilled Water CapacityFurthermore, an outdoor field investigation of chilled water capacity was conducted with a wafer-sized radiative cooling blend coated glass-polydimethylsiloxane (glass-PDMS) micro-pillar heat exchanger [33]. The heat exchanger was composed of a micro-pillar patterned polydimethyl-siloxane (PDMS) slab and a glass substrate. The PDMS slab was prepared by silicon stamping method [34, 35], in which the silicon master mask was fabricated by sequential micro-fabrication processes. PDMS, prepared by mixing the elastomer and curing agent in 10:1 was poured onto the pat-terned mask, baked in the oven for curing and lifted off from the mask after solidification. Lastly, a micro-porous radiative cooling blend was sprayed-coated on the opposite face. The blend was selected by recogniz-ing the complementary thermal emissive property of poly(vinylidene-flu-oride) and poly(methyl-methacrylate) through Maxwell-Garnett effective medium theory [36] and appraising the excellent solar reflective property of large energy bandgap dielectric materials [37–40]. Fourier transform mid-infrared spectrometry and UV/Vis/NIR spectrometry reveal high sky window emissivity and solar reflectivity.As the experimental setup shown in Figure 8.1(e), the chilled water sys-tem, driven by a peristaltic pump, circulated water through the micro-pillar heat exchanger, water heating tube, and water reservoir at a constant flow rate of 6.3 μL/s. Besides, a radiative cooler with the same blend coated on a glass substrate was installed for radiative cooling power measure-ment. All components were well-insulated from conduction, convection, and radiation. Surface temperature of the radiative heat exchanger, water temperatures before and after cooling, as well as ambient temperature, were measured and their daily profiles were depicted in Figure 8.1(f). Beginning from sunset, the system arrived at different pseudo-steady tem-peratures at mid-night when the ambient temperature was 15.7 °C. Surface 9781032529042_C008.indd   149 15-02-2024   5.03.20 PM150    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societytemperature of the radiative heat exchanger lay at 7.7°C, and it chilled water from 17.1°C to 14.5°C, equivalent to surface and water temperature reductions by 8.0°C and 2.6°C respectively. At noon of the second day, ambient temperature climbed to 23.0°C. Surface temperature of the radia-tive heat exchanger remained near ambient at 22.8°C, and it chilled water from 24.2°C to 22.8°C, equivalent to surface and water temperature reduc-tions by 0.2°C and 1.4°C respectively. At nighttime, cooling power was measured by loading the blend-coated radiative cooler to ambient tem-perature. Just before the measurement, ambient temperature and surface temperature of the radiative cooler were 15.0°C and 6.0°C respectively. This denoted an unloaded surface temperature reduction of 9.0°C. During the measurement, ambient temperature declined slightly from 15.9°C to 14.1°C and surface temperature followed the same trend. Averaged tem-peratures differed by 0.3°C due to thermal control error. In this scenario, it gave a cooling power of 131 W/m2 on per area basis. Meanwhile, the radiative heat exchanger arrived at a surface temperature of 9.4°C and chilled water by 2.3°C. Hence, estimated cooling efficiency with these fig-ures was 5.9 %.Compared to the temperature reduction and efficiency predicted by Equations (8.7) and (8.8), measured values are significantly lower even though the system satisfies the saturation criteria, perhaps because, at such a small flow rate, axial heat conduction, neglected in the one-dimen-sional heat transfer model, can be comparative to the convective and interfacial heat currents. The interplay among these heat currents causes a loss of interfacial heat transfer, but an increase in internal viscous dissipa-tion. As a result, it degrades overall chilled water capacity by passive radia-tive cooling in this flow regime.8.3 � PHOTO-THERMOELECTRICAL ENERGY CONVERSION FOR ELECTRICITY GENERATIONPhoto-thermoelectrical generation is an equally important engineering application of passive radiative cooling technology. At daytime, in-site photo-electrical energy conversion can be simply realized by a photovol-taic cell. Nowadays, with a new anti-reflection coating, a concentrated multi-junction tandem solar cell made of III-V compounded semi-conductors recorded the state-of-art solar-electrical energy conversion efficiency of 47.6 % [41]. At nighttime, similar direct renewable energy conversion technology was overlooked until recent attempts on photo-thermoelectricity generation enabled by radiative cooling. It makes use 9781032529042_C008.indd   150 15-02-2024   5.03.20 PMPassive Radiative Cooling Applications    ◾    151of the heat dissipative radiative cooling coating to set up a temperature gradient between the hot and cold sides of a Peltier module and extract electrical work between the ambient and universe. Passive radiative-cool-ing based thermoelectrical energy harvesting has potential applications in various aspects, including building space cooling [42, 43], and powering wearable electronics [44, 45].8.3.1 � Energy Balance ModelTheoretically, system thermal performance, indicated by cold-sided tem-perature TTE, c and hot-sided temperature TTE, h, can be acknowledged by solving the energy balance equations for the Peltier module of area A, comprising N p-n junctions with an individual Seebeck coefficient Spn, thermal conductance Kpn and electrical resistance Rpn, connected to an external load of resistance Re. For the cold side, P T P T P h T T P T Trad TE c atm amb sun c amb TE c cond TE h TE,, , , ,� � � � � � � �� �� ccseebeck TE c joule� �� � � � �P T P, 0   (8.13)and, for the hot side,  � �� �� � � � � � � �h T T P T T P T Pc amb TE h cond TE h TE c seebeck TE h joule, , , ,, 00,  (8.14)where Pcond = NKpn(TTE, h − TTE, c)/A is the conductive heat flux, Pseebeck = NSpnTI/A is the Seebeck effect, Pjoule = NI2Rpn/2A is the joule heating, and I = NSpn(TTE, h − TTE, c)/(NRpn + Re) is the thermoelectrical current. In eq. (2.1), Prad, Patm and Psun are given by Equations (8.2), (8.3) and (8.4) respec-tively and hc(Tamb − TTE, c) is the non-radiative heat load from the environ-ment. Hence, system electrical performance, denoted by thermoelectrical power output Pe, is coupled with the difference in TTE, h and TTE, c via I, and given by [46, 47] PN S T T RNR Repn TE h TE c epn e��� ��� �2 2 22, , . (8.15)An outdoor field investigation of the black-paint coated commercial thermoelectric module realized a two-sided temperature difference up to 2 °C and generated a thermoelectrical power of 25 mW/m2 at the maximum 9781032529042_C008.indd   151 15-02-2024   5.04.17 PM152    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societypower point, in which the field investigative result validates the theoretical model [48]. Predicted thermoelectrical performance is divergent and highly sensitive to the input system parameters, in which Zhao et al. estimated a moderate output power density of 291 mW/m2 [47], whereas Fan et al. fore-casted a much larger optimal value of 2.2 W/m2 [46].8.3.2 � Laboratory Testing on Thermo-Electricity GenerationA laboratory testing comparing thermo-electricity generation by Peltier modules combined with a selective thermal emitter and a blackbody ther-mal emitter was set up for duplicating thermo-electricity generation [49]. As shown in Figure 8.2(a), the selective thermal emitter was an e-beam evaporated 100 nm aluminum film on a glass with the glass side facing top, and the blackbody thermal emitter was a blackbody paint-sprayed glass with the blackbody paint facing top. Figure 8.2(b) shows their spec-tral emissivity and reflectivity from visible to mid-infrared wavelengths. FIGURE 8.2  (a) Pictures of the selective and blackbody thermal emitters; (b) measured spectral emissivity and reflectivity of the selective and blackbody thermal emitters from visible light to mid-infrared wavelengths; (c) An illustrative diagram on the experimental conditions for laboratory testing(Continued )9781032529042_C008.indd   152 15-02-2024   5.04.17 PMPassive Radiative Cooling Applications    ◾    153FIGURE 8.2  (Continued) (d) A comparison of the thermoelectrical voltage generated under abovementioned three experimental conditions; (e) Thermograph; and (f) measured temperature difference and thermoelectrical voltage of the selective and blackbody thermal emitters under field investigation. Reprinted from Applied Physics Letters, 117, Ishii S, Dao TD, Nagao T, Radiative cooling for continuous thermoelectric power generation in day and night, 013901, with permission from AIP Publishing.9781032529042_C008.indd   153 15-02-2024   5.04.18 PM154    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon SocietyThe glass/aluminum emitter has a high reflectivity in the optical range, but a high emissivity in the mid-infrared range.A blackbody-painted Peltier module and a solar simulator were used to imitate the universe and the sun. As illustrated in Figure 8.2(c), three experimental conditions, simulating a standalone radiative cooling effect, combined radiative cooling and solar heating effect, and combined radia-tive cooling, solar heating, and conductive heating effect, were trialed. Figure 8.2(d) compares the thermoelectrical voltage generated under abovementioned three experimental conditions. Where there is radiative cooling only, the two samples generated similar voltage. When there are both radiative cooling and solar heating, the one with selective thermal emitter generated positive voltage, whereas the one with the blackbody thermal emitter generated negative voltage with a larger absolute magni-tude. Solar heating overwhelmed radiative cooling, resulting in a larger temperature difference and voltage. However, when the samples were heated at the bottom, the former generated a larger voltage than the latter. Top-sided radiative cooling and bottom-sided conductive heating maxi-mized the temperature difference and voltage. When the bottom-sided temperature increased from room temperature to 50 °C, thermoelectrical voltage of the one with a selective thermal emitter increased from 3.8 to 50 mV, whereas the one with the blackbody thermal emitter changed from −15 to 33 mV only. This indicated that a selective thermal emitter could take advantage of bottom-sided heating from waste heat in practice for enhanced radiative-cooling based thermo-electricity generation.8.3.3 � Outdoor Field Investigation of Thermo-Electricity GenerationThen, an outdoor field investigation was conducted to investigate the performance. The selective thermal emitter was radiatively cooled all the time, and the top of the thermoelectricity generator is always cooler than the bottom, thus maintaining continuous thermoelectricity generation. In contrast, the black-paint emitter has a high emissivity across the entire spectrum. The blackbody thermal emitter was radiatively cooled at night-time but heated by sunlight at daytime. Thus, after sunrise, the top surface temperature increased gradually, and reached the same bottom face tem-perature gradually. Without vanished voltage, continuous thermoelectric-ity generation acted as the overwhelming advantage of radiative-cooling based electrical energy harvesting. Figure 8.2(e) shows the thermograph of two devices under field investigation taken in day. As can be seen, 9781032529042_C008.indd   154 15-02-2024   5.04.18 PMPassive Radiative Cooling Applications    ◾    155the radiative cooling surface was at a temperature lower than the back-ground, whereas the blackbody was at a higher temperature. Figure 8.2 (f) shows the measured temperature difference and thermoelectrical voltage during field investigation. Note that the temperature difference is posi-tive/negative when the emitter surface is cooler/hotter than the ambient temperature At nighttime, top-to-bottom temperature differences were approximately 2–4 °C for both devices. Consequently, they produced sim-ilar thermoelectrical voltage up to 20 mV. At daytime, the temperature difference arrived at 5 °C for the selective thermal emitter, whereas, with a higher top face temperature due to solar heating, it reached a larger value of −15 °C for the blackbody thermal emitter. Hence, the thermoelectricity generator installed by the blackbody thermal emitter generated a larger voltage, up to 60 mV, because solar heating by the blackbody absorber is stronger than radiative cooling by the selective radiative cooler. Moreover, from 1pm to 5pm, the sky was cloudy and inferred from the lower solar irradiance. During this period, the device with a selective thermal emitter recorded a larger thermoelectrical voltage than the one with a blackbody thermal emitter. Furthermore, it generated nearly constant thermoelectri-cal voltage regardless of weather change.Later, it was shown that reducing parasitic losses, controlling emitter area and thermal resistance of the thermoelectric generator, and stacking multiple thermoelectric generators are all effective ways to boost the power density. Also, a measured power density exceeding 100 mW/m2, represent-ing over 2-fold improvement over the previous results, was demonstrated experimentally [50]. Also, a new kind of thermoelectrical energy converter based on the spin Seebeck effect, in which the temperature gradient and the thermoelectrically generated electric field are perpendicular, was sug-gested for energy harvesting from solar heating and radiative cooling simultaneously [51]. The Spin Seebeck effect induced voltage is propor-tional to the length of the device, which is perpendicular to the tempera-ture gradient. This means that voltage and power can be increased by simply elongating the device length without forming multitude of serial p-n junctions, as is the case with a conventional thermoelectric device. And, this simplifies the device architecture. A prototype, comprising paramagnetic gadolinium gallium garnet substrate, ferrimagnetic yttrium iron garnet insulator, paramagnetic platinum metal, and blackbody paint light absorber, demonstrated the simultaneous harvesting of radiative cooling and solar heating in the outdoors.9781032529042_C008.indd   155 15-02-2024   5.04.18 PM156    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Society8.4 � RESEARCH CHALLENGE IN PASSIVE RADIATIVE COOLINGGeographical variation in the passive radiative cooling performance poses one of the top research challenges in low latitude hot and humid regions. The radiative cooling resource map for the contiguous United Stated showed that the southwestern area had the highest cooling potential of 70 W/m2, whereas the southeastern had the lowest potential of 30 W/m2 [52]. Similar maps for China identified that the northwestern area had the highest cooling potential of 70–90 W/m2, whereas the southeastern had the lowest potential of 10–40 W/m2 [53, 54]. An investigation of the impact of humidity, cloudiness, and aerosol concentration on radiative cooling performance compared the cooling potential at Stanford and Hong Kong, where the estimated values were 61 W/m2 and 25 W/m2 respectively due to climatic difference [55]. Besides, higher solar intensity in Singapore, where the predicted cooling power limit was 30 W/m2, was identified as the major cause of degraded radiative cooling performance [56]. As such, despite plenty of groundbreaking field investigative reports from North America, some comparative studies conducted elsewhere failed to achieve sub-ambient daytime radiative cooling [57–61]. In Shanghai, where the ambient temperature and relative humidity were above 24 °C and 50 % respectively, nano-particle based solar reflecting thermal radiators were tested, but they remained 3–10 °C above ambient at daytime [57]. In the subtropical city, Hong Kong, Raman’s photonic radiative cooler was tested in vacuum and non-vacuum enclosures, but none can replicate sub-ambient daytime radiative cooling [2, 58]. Then a modified titanium oxide photonic radiative cooler and a bio-inspired polymeric radiative cooler were tested with and without shade, and only the shaded ones accom-plished sub-ambient daytime radiative cooling [59, 60]. In the tropical country, Singapore, Raman’s photonic radiative cooler and an enhanced specular reflective film were assessed. It was concluded that high solar intensity and humidity counteracted the radiative cooling effect [2, 61].8.4.1 � Empirical Sky Temperature ModelsContrary to mainstream deterministic energy balance-based analysis of the variance in radiative cooling performance arising from climatic fac-tors, a new approach by means of probabilistic regression modeling was suggested to establish the correlation between radiative cooling perfor-mance and corresponding weather conditions [62]. It is advantageous in tolerancing the uncertainties arising from time varying and uncontrolled 9781032529042_C008.indd   156 15-02-2024   5.04.18 PMPassive Radiative Cooling Applications    ◾    157atmospheric uncertainties abundant in field investigation. Meteorological variables like ambient temperature, relative humidity, and cloudiness, quantifying the downwelling atmospheric thermal radiation from the sky, can be lumped into a single parameter of sky temperature. Sky tempera-ture Tsky can be viewed as the equivalence of atmospheric thermal inten-sity Isky in absolute temperature scale, convertible by the Stefan-Boltzmann equation of I Tsky sky� � 4 , where σ = 5.67 × 10−8 W/m2-K4 is the Stefan-Boltzmann constant. And sky emissivity εsky is defined by Tsky via εsky = (Tsky/Tamb)4. As εsky ranges from 0 to 1, Tsky is always lower than Tamb. εsky can be measured by a pyrometer experimentally, simulated by an atmo-spheric radiative transfer model numerically, and a sky emissivity model empirically. A pyrometer produces an output voltage by scanning in situ infrared radiance within 4.5–100 μm, but it requires careful calibration to eliminate background radiation from buildings and vegetations. An atmospheric radiative transfer model evaluates the atmospheric spectral emissivity within 0.2–100 μm line-by-line upon comprehensive specifica-tion of absorbing gases, aerosol, water vapor, cloud characteristics, vertical temperature, and humidity profiles, as well as various secondary atmo-spheric variables [63, 64]. In contrast, an empirical model is rather simple, correlating εsky with fundamental meteorological variables measurable by the observatory.Since the 1910s, plenty of sky temperature models, falling into two cat-egories regarding clear and cloudy skies, have been suggested. Under a clear sky, suspended water vapors act as the primary source of down-welling atmospheric thermal radiation. In 1932, Brunt formulated one of the earliest clear sky temperature models, expressing clear sky emissivity εsky c,  as  �sky c w, ,� �a a p1 212   (8.16)where a1 = 0.52 and a2 = 0.065 are the empirical constants, and pw is the vapor pressure [65]. Afterwards, various parametric forms were suggested, and published models were also recalibrated. These reports revealed the difficulty in universal sky temperature modeling because the models were established with localized and biased meteorological data drawn from one or several weather stations. A recent revisit on this topic might have ana-lyzed the most comprehensive meteorological and radiation data, collected from seven stations of the Surface Radiation Budget Network in the United 9781032529042_C008.indd   157 15-02-2024   5.05.05 PM158    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon SocietyStates, located at Goodwin Creek (Mississippi), Bondville (Illinois), Penn State University (Pennsylvania), Fort Peck (Montana), Sioux Falls (South Dakota), Boulder (Colorado), and Desert Rock (Nevada). The meteoro-logical dataset, covering climatic diversity in the northern hemisphere, were used to recalibrate Brunt’s model with renewed empirical constants of a1 = 0.62 and a2 = 0.056 [66]. Under a cloudy sky, clusters of liquid phase water and solid phase ices absorb and emit longwave radiation more vigorously than gaseous phase vapors. To cater for additional heat load imposed by clouds, clear sky emissivity ought to be corrected by a factor regarding cloud fraction. A new empirical form of cloudy sky emissivity εsky was suggested as  � � �sky sky c c c� �� ��, ,1 1 32 4 5b f b fb b b  (8.17)where b1 = 0.78, b2 = 1, b3 = 0.38, b4 = 0.95 and b5 = 0.17 are the empirical constants, ϕ is the relative humidity, and fc is the cloud fraction [66]. In the expression, εsky, c can be calculated with recalibrated Brunt’s clear sky emissivity by Equation (3.1). When fc = 0, it represents the clear sky condi-tion, and εsky, given by Equation (3.2), is reduced to εsky, c. Hence, cloudy sky temperature model is applicable for all sky conditions.8.4.2 � Correlations Between Sky Temperature Difference and Surface Temperature ReductionOutdoor field investigations were conducted for photonic radiative and polymeric radiative coolers. For each kind of radiative cooler, one was shadowed by an external shade, and one was exposed to direct sunlight. During the investigations, surface temperatures and site ambient temper-ature were measured. Meanwhile, ambient temperature, relative humid-ity, cloud fraction, and solar intensity were collected from neighboring weather stations.In total, 70 sets of field investigative results were gathered at nighttime, whereas 35 sets were gathered at the peak solar radiance. Then tempera-ture measurements were time averaged. And Figure 8.3(a)–(d) shows the scatterplots of the response variable of surface temperature reduction against predictor variable of sky temperature difference for different mate-rials at nighttime. Surface temperature reduction, as a cardinal indicator of radiative cooling performance, is a reasonable selection for the response variable. Also, sky temperature difference, which is the difference between 9781032529042_C008.indd   158 15-02-2024   5.05.26 PMPassive Radiative Cooling Applications    ◾    159(Continued )FIGURE 8.3  Scatterplots of surface temperature reduction at nighttime against sky temperature difference and bivariate regression lines for (a) shaded polymeric radiative cooler; (b) unshaded polymeric radiative cooler; (c) shaded photonic radiative cooler; and (d) unshaded photonic radiative cooler. Scatterplots of surface temperature reduction at daytime against sky temperature difference, bivariate and multi-variate regression lines for (e) shaded polymeric radiative cooler; (f) unshaded polymeric radiative cooler. 9781032529042_C008.indd   159 15-02-2024   5.05.27 PM160    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societysky temperature and ambient temperature, can be an appropriate choice for the predictor variable. It is because, from an energy balance consider-ation, net radiative heat exchange by the radiative cooler results from out-fluxing emission proportional to the fourth power of surface temperature and inflowing absorption proportional to the fourth power of sky tem-perature. For small differences among ambient temperature, sky tempera-ture, and surface temperature, they can be expressed as a Taylor expansion about ambient temperature, and thus, net radiative heat exchange can be scaled with a single, lumped meteorological variable of sky temperature difference. From a statistical perspective, each data-pair scatters about the best fitted line. Supposed to be linear, the best fitted lines, based on opti-mal intercept coefficient and slope coefficient, are plotted in the same fig-ure for reference. Variance of surface temperature reduction and R2 value estimate the reliability of the regression model, where the former repre-sents the amount of variability inherent in the regression model, and the latter interprets the proportion of variation in surface temperature reduc-tion predictable from the sky temperature difference. The variances after normalization are approximately the same of −0.18 for all specimens, which means climatic factors impact on expected radiative cooling per-formance, but do not alter the random deviation, and R2 values lie within 0.63 and 0.7, which denotes a substantial linear correlation between sur-face temperature reduction and sky temperature difference for nighttime radiative cooling performance.FIGURE 8.3  (Continued) (g) shaded photonic radiative cooler; and (h) unshaded photonic radiative cooler. Reprinted from Renewable Energy, 211, Wong RYM, Tso CY, Jeong SY, Fu SC, Chao CYH, Critical sky temperatures for passive radiative cooling, 214–226, Copyright (2023), with permission from Elsevier.9781032529042_C008.indd   160 15-02-2024   5.05.27 PMPassive Radiative Cooling Applications    ◾    161At daytime, solar absorption imposes an additional heat load on the radiative coolers. Figure 8.3(e)–(h) plots the corresponding scatterplots under the peak solar intensity. Repeating the bivariate linear regression model for data analysis, variances and R2 values lie within statistically valid ranges for shaded radiative coolers, whereas they appear as tremen-dous departures between measured datasets and regressed equations, and associated random errors are magnified enormously, but R2 values are reduced dramatically, questioning the linear coupling between sky tem-perature difference and surface temperature reduction. Therefore, it is essential to revise the model by introducing an extra predictor variable regarding solar heat load. Obviously, sky temperature difference and solar intensity are not mutually independent variables, but solar intensity should be regarded as a single variable function of sky temperature differ-ence, and its explicit form ought to be pre-determined otherwise. Beer-Lambert law states that [67, 68] spectral radiative extinction traversing a thin layer of medium is proportional to local spectral intensity, number density and extinction cross section of extinctive particles, as well as medium thickness. For the atmosphere composed of multi-component gases and suspended particulates, the contribution of extinction cross sec-tion by each species is additive and the integral form of Beer-Lambert law can be written as  I s I e s jK N s ds� ��, , .� � � � ���� � � � �� �0j j  (8.18)Constituent gases, like nitrogen, oxygen, and argon, occupy permanent fractions in the atmosphere, whereas suspended particulates, like aerosols, water vapors, and clouds, are time and space varying in concentration. Complicated extinction mechanism and comprehensive specification of number density and extinction coefficient for each atmospheric constituent throughout the optical path do not facilitate practical implementation of Beer-Lambert law. In many circumstances, it is essential to recognize these changes with respect to climatic parameters like sky temperature rather than their absolute values. Because of a small variation in sky temperature, the term, ∑jK Nj j, in the Beer-Lambert equation at any sky temperature can be expressed as a Taylor’s expansion about a reference sky temperature. And the contributions from water vapors and clouds become the only terms dynamic with sky temperature. Further neglecting spatial variations 9781032529042_C008.indd   161 15-02-2024   5.06.02 PM162    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societyin extinction cross-sections of vapors and clouds yields the territorial solar intensity written as I T I eT T K N T KSsun sky sunsky sky v v sky c�� �� � ��� �� ������� � � � �� �00 / NN T dsc sky/�� � �, where Isun0� �  represents the solar intensity at Tsky0� �, which can be as high as 1140 W/m2 at low-to-mid altitude areas [69]. Admittedly, a constant extinction cross-section assumption may not stand because water vapors are spec-trally selective solar absorbers, in which the atomic arrangement of water molecule permits three fundamental vibration modes of symmetry, bend-ing, and anti-symmetry, responsible for multiple solar and near-infrared absorption bands at 940 nm, 1.1 μm, 1.38 μm and 1.87 μm [70]. The inte-gral, −∫S(Kv∂Nv/∂Tsky + Kc∂Nc/∂Tsky)dś , denotes the exponential declining rate of solar intensity with respect to sky temperature difference. In a semi-empirical treatment, it can be determined by surveying the historical mete-orological data pairs of the peak solar intensity against the sky temperature difference, and appraising the slope at any arbitrary sky temperature differ-ence is supposed to be the linear interpolation of two limiting characteristic rates. Hence, the integral can be simplified as γ1 + 2γ2ΔTsky, where γ1 and γ2 are the empirical model constants. They can be determined by minimizing the root-of-squared error between collected dataset and modeling equa-tion. as such, I T I e T Tsun sky sunsky sky�� �� � � � � � �0 0 1 22� � � and the multivariate regres-sion equation becomes � �� �T T e T Tw skysky sky,0 0 1 20 1 22� � �� �� � �  � � � . Compared to bivariate regression model, it provides a better fit with scattered data pairs in Figure 8.3(f)–(j), features decreased variances, as well as increased R2 values, and improves overall interpretability of the statistical model. For shaded radiative coolers, variances range from 1.1 °C to 1.4 °C and R2 val-ues range from 0.69 to 0.79. The refinement is the least notable because, without the action of direct solar illumination, the bivariate regression model has rationalized radiative cooling performance. For exposed radia-tive coolers and silicon wafer, the advancement is more significant, reveal-ing the crucial role of solar heat load on cooling performance. Even the polymeric radiative cooler feature reasonably high solar reflectivity vari-ance is reduced to 2.0 °C, and R2 value is more than doubled, valuing 0.11. The small random uncertainty affirms the reliability of the regression model, whereas the feeble correlation stems from the counter-interaction of radiative cooling and solar heating. For photonic radiative cooler, variance is 3.0 °C and R2 value is 0.58. The multivariate regression model reduces the random uncertainty but reinforces the correlation between sky tempera-ture difference and surface temperature reduction.9781032529042_C008.indd   162 15-02-2024   5.07.30 PMPassive Radiative Cooling Applications    ◾    163Under a subtropical hot and humid climate, sub-ambient passive radia-tive cooling is possible providing reconcilable materials with sky window emissivity and solar reflectivity higher than the benchmarked polymeric radiative cooler. A few alternative solution strategies to subtropical and tropical radiative cooling were also proposed. Providing external shading can be the simplest way to block incoming solar radiation and lower sur-face temperature [59, 60]. In Hong Kong, a radiative cooler with superior spectral selectivity, comprising a solution-derived silicon oxynitride layer sandwiched between a reflective substrate and a self-assembly monolayer of silicon dioxide microspheres narrowband emitter, realized sub-ambient cooling of up to 5 °C in autumn and 2.5 °C in summer [71]. In Singapore, a switchable solar heater radiative cooler with engineered porous struc-ture, enabling the device to serve as an efficient solar reflector and infrared emitter in dry state, as well as an efficient solar heater in wet state, yielded a nighttime cooling power of 61.2 W/m2 and daytime heating power of 720 W/m2 [72]. These strategies create a new opportunity for the development of novel and multi-functional radiative cooling materials.8.5 � SUMMARY AND CONCLUSIONSThis chapter reviews passive radiative cooling applications in thermal and electrical energy harvesting. They are important because of plenty of smart and green technological applications toward a carbon neutral built environment. For thermal energy harvesting, chilled water collection by circulating water through a radiative heat exchanger is the simplest form, but it raises critical concerns on thermal and energy conversion performances. A study on a passive radiative fluid cooling system in a controlled environmental facility revealed that water temperature reduc-tion and energy conversion efficiency are always inversely correlated, in which temperature reduction increases with decreasing flow rate but efficiency increases with increasing flow rate. This poses a fundamental difficulty in collecting chilled water in an energy efficient manner. For electrical energy harvesting, thermoelectricity by creating temperature difference through heat dissipation with radiative cooling materials at the cold side can be generated continuously day and night. It demands on the development of high-performance radiative cooling-based thermo-electricity generator delivering power density approaching the theoretical upper limit. However, it must be emphasized that performance of radia-tive cooling-based devices and systems rely on the weather conditions 9781032529042_C008.indd   163 15-02-2024   5.07.30 PM164    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Societyheavily. Sky temperature modeling unveils that, the higher the thermal emissivity, the larger is the surface temperature reduction at nighttime, and heavy solar heat load can be absorbed by the radiative coolers at day-time even they feature reasonably high solar reflectivity. Therefore, hot and humid climates are not favorites for passive radiative cooling. This complicates the applications in tropical and subtropical regions, where the cooling demand is the heaviest, though a few overcoming schemes were suggested. Nonetheless, advancement in passive radiative cooling materi-als and applications will not be stopped and will continuously steer a new shape of our community and society.REFERENCES  [1] Harrison, A. W., Walton, M. R. (1978). Radiative cooling of TiO2 white paint. Solar Energy, 20, 185–188.  [2] 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.  [3] Chen, Z., Zhu, L., Raman, A., Fan, S. (2016). Radiative cooling to deep sub- freezing temperatures through a 24-h day-night cycle. Nature Communi­cations, 7, 13729.  [4] Kou, J., Jurado, Z. Chen, Z., Fan, S., Minnich, A. J. (2017). Daytime radiative cooling using near-black infrared emitters. ACS Photonics, 4, 626–630.  [5] Hossain, M. M., Jia, B., Gu, M. (2015). A metamaterial emitter for highly efficient radiative cooling. Advanced Optical Materials, 3, 1047–1051.  [6] Zou, C., Ren, G., Hossain, M. M., Nirantar, S., Withayachumnankul, W., Ahmed, T., Bhaskaran, M., Sriram, S., Gu, M., Fumeaux, C. (2017). Metal-loaded dielectric resonator metasurfaces for radiative cooling. Advanced Optical Materials, 5, 1700460.  [7] Yu, N., Mandal, J., Overvig, A., Shi, N. N. (2016). Systems and Methods for Radiative Cooling and Heating, US patent: WO2016205717A1.  [8] Zhai, Y., Ma, Y., David, S. N., Zhao, D., Lou, R., Tan, G., Yang, R., Yin, X. (2017). Scalable manufactured randomized glass-polymer hybrid metamate-rial for daytime radiative cooling. Science, 355, 1062–1066.  [9] Mandal, J., Fu, Y., Overvig, A. C., Jia, M., Sun, K., Shi, N. N., Zhou, H., Xiao, X., Yu, N., Yang, Y. (2018). Hierarchically porous polymer coatings for highly efficient passive daytime radiative cooling. Science, 362, 315–319. [10] Peoples, J., Li, X. Y., Lv, Y. B., Qiu, J., Huang, Z. F., Ruan, X. L. (2019). A strat-egy of hierarchical particle sizes in nanoparticle composite for enhancing solar reflection. International Journal of Heat Mass Transfer, 131, 487–494. [11] Li, X., Peoples, J., Huang, Z., Zhao, Z., Qiu, J., Ruan, X. (2020). Full daytime sub-ambient radiative cooling in commercial-like paints with high figure of merit. Cell Reports Physical Science, 10, 100221.9781032529042_C008.indd   164 15-02-2024   5.07.30 PMPassive Radiative Cooling Applications    ◾    165 [12] Li, X., Peoples, J., Yao, P., Ruan, X. (2021). Ultrawhite BaSO4 paints and films for remarkable daytime subambient radiative cooling, ACS Applied Mater. Interfaces, 13, 21733–21739. [13] Zhao, B., Hu, M., Ao, X., Chen, N., Pei, G. (2019). Radiative cooling: A review of fundamentals, materials, applications, and prospects. Applied Energy, 236, 489–513. [14] Sun, J., Wang, J., Guo, T., Bao, H., Bai, S. (2022). Daytime passive radia-tive cooling materials based on disordered media: A review. Solar Energy Materials and Solar Cells, 236, 111492. [15] Xie, B., Liu, Y., Xi, W., Hu, R. (2023). Colored radiative cooling: Progress and prospects. Materials Today Energy, 34, 101302. [16] Ali, A. H. A., Taha, I. M. S., Ismail, I. M. (1995). Cooling of water flowing through a night sky radiator. Solar Energy, 55, 235–253. [17] Erell, E., Etzion, Y. (1999). Analysis and experimental verification of an improved cooling radiator. Renewable Energy, 16, 700–703. [18] Saitoh, T. S., Fujino, T. (2001). Advanced energy-efficient house (Harbeman house) with solar thermal photovoltaic and sky radiation energies (Experimental results). Solar Energy, 70, 63–77. [19] Meir, M. G., Rekstad, J. B., Lovvik, O. M. (2002). A study of a polymer-based radiative cooling system. Solar Energy, 73, 403–417. [20] Dimoudi, A., Androutsopoulos, A. (2006). The cooling performance of a radiator based roof component. Solar Energy, 80, 1039–1047. [21] Tevar, J. A. F., Castano, S., Marijuan, A. G., Heras, M. R., Pistono, J. (2015). Modelling and experimental analysis of three radioconvective panels for night cooling. Energy and Buildings, 107, 37–48. [22] Goldstein, E. A., Raman, A. P., Fan, S. (2017). Sub-ambient non-evaporative fluid cooling with the sky. Nature Energy, 2, 17143. [23] Zhao, D., Aili, A., Zhai, Y., Lu, J., Kidd, D., Tan, G., Yin, X., Yang, R. (2019). Subambient cooling of water: Toward real-world applications of daytime radiative cooling. Joule, 3, 111–123. [24] Aili, A., Zhao, D., Lu, J., Zhai, Y., Yin, X., Tan, G., Yang, R. (2019). A kw-scale, 24-hour continuously operational, radiative sky cooling system: Experimental demonstration and predictive modelling. Energy Conversion and Management, 186, 586–596. [25] Zhou, M., Song, H., Xu, X., Shahsafi, A., Qu, Y., Xia, Z., Ma, Z., Kats, M. A., Zhu, J., Ooi, B. S., Gan, Q., Yu, Z. (2021). Vapor condensation with day-time radiative cooling. Proceedings of National Academy of Science, 118, 2019292118. [26] Haechler, I., Park, H., Schnoering, G., Gulich, T., Rohner, M., Tripathy, A., Milionis, A., Schutzius, T. M., Poulikakos, D. (2021). Exploiting radiative cooling for uninterrupted 24-hour water harvesting from the atmosphere. Science Advances, 7, 3978. [27] Wang, W., Fernandez, N., Katipamula, S., Alvine, K. (2018). Performance assessment of a photonic radiative cooling system for office buildings. Renewable Energy, 118, 265–277.9781032529042_C008.indd   165 15-02-2024   5.07.30 PM166    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Society [28] Zhang, K., Zhao, D., Yin, X., Yang, R., Tan, G. (2018). Energy saving and economic analysis of a new hybrid radiative cooling system for single-family houses in the USA. Applied Energy, 224, 371–381. [29] Jeong, S. Y., Tso, C. Y., Zouagui, M., Wong, Y. M., Chao, C. Y. H. (2018). A numerical study of daytime passive radiative coolers for space cooling in buildings. Building Simulation, 11, 1011–1028. [30] Wong, R. Y. M., Tso, C. Y., Chao, C. Y. H. (2021). Thermo-radiative energy conversion efficiency of a passive radiative fluid cooling system. Renewable Energy, 180, 700–711. [31] Incropera, F. P., Dewitt, D. P., Bergman, T. L., Lavine, A. S. (2006). Fundamentals of Heat and Mass Transfer (6th edition), John Wiley & Sons, United States of America. [32] Wong, R. Y. M., Tso, C. Y., Chao, C. Y. H. (2021). Corrected radiative cool-ing power measured by equivalent dissipative thermal reservoir method. International Journal of Heat and Mass Transfer, 174, 121341. [33] Wong, R. Y. M., Tso, C. Y., Fu, S. C., Chao, C. Y. H. (2023). Field demonstrated extended Graetzian viscous dissipative thermo-photonic energy conversion with a blended MgO/PVDF/PMMA coated glass-PDMS micro-pillar heat exchanger, International Journal of Heat and Mass Transfer, 215, 124520. [34] Xia, Y., Whitesides, G. M. (1998). Soft lithography. Annual Review of Materials Science, 28, 153–184. [35] Whitesides, G. M., Ostuni, E., Takayama, D., Jiang, X., Lngber, D. E. (2001). Soft lithography in biology and biochemistry. Annual Review of Biomedical Engineering, 3, 335–373. [36] Wong, R. Y. M., Tso, C. Y., Fu, S. C., Chao, C. Y. H. (2022). Maxwell-Garnett permittivity optimized micro-porous PVDF/PMMA blend for near unity thermal emission through the atmospheric window. Solar Energy Materials and Solar Cells, 248, 112003. [37] Grum, F., Luckey, G. W. (1968). Optical sphere paint and a working standard of reflectance. Applied Optics, 7, 2289–2294. [38] De Sousa Meneses, D., Brun, J., Echegut, P., Simon, P. (2004). Contribution of semi-quantum dielectric function models to the analysis of infrared spec-tra. Applied Spectroscopy, 24, 100658. [39] Kelly-Gorham, M. R. K., DeVetter, B. M., Brauer, C. S., Cannon, B. D., Burton, S. D., Bliss, M., Johnson, T. J., Myers, T. L. (2017). Complex refractive index measurement for BaF2 and CaF2 via single-angle infrared reflectance spectroscopy. Optical Materials, 72, 743–748. [40] Palik, E. D. (1991). Handbook of Optical Constants of Solids (Volume 2), Elsevier, United States of America. [41] Best Research-Cell Efficiencies, https://www.nrel.gov/pv/assets/pdfs/best-research-cell-efficiencies.pdf, accessed in May 2023. [42] Zhao, D., Yin, X., Xu, J., Tan, G., Yang, R. (2020). Radiative sky cooling-assisted thermoelectric cooling system for building applications. Energy, 190, 116322. [43] Kwan, T. H., Gao, D., Zhao, B., Ren, X., Hu, T., Dabwan, Y. N. (2021). Integration of radiative sky cooling to the photovoltaic and thermoelec-tric system for improved space cooling. Applied Thermal Engineering, 196, 117230.9781032529042_C008.indd   166 15-02-2024   5.07.30 PMPassive Radiative Cooling Applications    ◾    167 [44] Liu, Y., Hou, S., Wang, X., Yin, L., Wu, Z., Wang, X., Mao, J., Sui, J., Liu, X., Zhang, Q., Liu, Z., Cao, F. (2022). Passive radiative cooling enables improved performance in wearable thermoelectric generators. Small, 18, 2106875. [45] Khan, S., Kim, J., Roh, K., Park, G., Kim, W. (2021). High power density of radiative-cooled compact thermoelectric generator based on body heat har-vesting. Nano Energy, 87, 106180. [46] Fan, L., Li, W., Jin, W., Orenstein, M., Fan, S. (2020). Maximum nighttime electrical power generation via optimal radiative cooling. Optics Express, 28, 25460. [47] Zhao, B., Pei, G., Raman, A. P. (2020). Modelling and optimization of radia-tive cooling based thermoelectric generators. Applied Physics Letters, 117, 163903. [48] Raman, A. P., Li, W., Fan, S. (2019). Generating light from darkness. Joule, 3, 2679–2686.  [49] Ishii, S., Dao, T. D., Nagao, T. (2020). Radiative cooling for continuous thermo-electric power generation in day and night. Applied Physics Letters, 117, 013901. [50] Omair, Z., Assawaworrarit, S., Fan, L., Jin, W., Fan, S. (2022). Radiative-cooling based nighttime electricity generation with power density exceeding 100 mW/m2. iScience, 25, 104858. [51] Ishii, S., Miura, A., Nagao, T., Uchida, K. (2021). Simultaneous harvesting of radiative cooling and solar heating for transverse thermoelectric generation. Science and Technology of Advanced Materials, 22, 441–448. [52] Li, M., Peterson, H. B., Coimbra, C. F. M. (2019). Radiative cooling resource maps for the contiguous United States. Journal of Renewable and Sustainable Energy, 11, 036501. [53] Zhu, Y., Qian, H., Yang, R., Zhao, D. (2021). Radiative sky cooling potential maps of China based on atmospheric spectral emissivity. Solar Energy, 218, 195–210. [54] Chen, J., Lu, L., Gong, Q. (2021). A new study on passive radiative sky cooling resource maps of China. Energy Conversion and Management, 237, 114132. [55] Huang, J., Lin, C., Li, Y., Huang, B. (2022). Effect of humidity, aerosol, and cloud on subambient radiative cooling. International Journal of Heat and Mass Transfer, 186, 122438. [56] Han, D., Fei, J., Li, H., Ng, B. F. (2022). The criteria to achieving sub-ambient radiative cooling and its limits in tropical daytime. Building and Environment, 221, 109281. [57] Bao, H., Yan, C., Wang, B., Fang, X., Zhao, C. Y., Ruan, X. (2017). Double-layer nanoparticle-based coatings for efficient terrestrial radiative cooling. Solar Energy Materials and Solar Cells, 168, 78–84. [58] Tso, C. Y., Chan, K. C., Chao, C. Y. H. (2017). A field investigation of passive radiative cooling under Hong Kong’s climate. Renewable Energy, 106, 52–61. [59] Jeong, S. Y., Tso, C. Y., Ha, J. Y., Wong, Y. M., Chao, C. Y. H., Huang, B., Qiu, H. (2019). Field investigation of a photonic multi-layered TiO2 passive radia-tive cooler in sub-tropical climate. Renewable Energy, 146, 44–55. [60] Jeong, S. Y., Tso, C. Y., Wong, Y. M., Chao, C. Y. H., Huang, B. (2019). Daytime passive radiative cooling by ultra emissive bio-inspired polymeric surface. Solar Energy Materials and Solar Cells, 206, 110296.9781032529042_C008.indd   167 15-02-2024   5.07.30 PM168    ◾    Thermal Plasmonics and Metamaterials for a Low-Carbon Society [61] Han, D., Ng, B. F., Wan, M. P. (2020). Preliminary study of passive radiative cooling under Singapore’s tropical climate. Solar Energy Materials and Solar Cells, 206, 110270. [62] Wong, R. Y. M., Tso, C. Y., Jeong, S. Y., Fu, S. C., Chao, C. Y. H. (2023). Critical sky temperatures for passive radiative cooling. Renewable Energy, 211, 214–226. [63] Berk, A., Conforti, P., Kennett, R., Perkins, T., Hawes, F., van den Bosch, J. (2014). MODTRAN 6: A major upgrade of the MODTRAN radiative trans-fer code. 2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 1–4. [64] Berk, A., Acharya, P. K., Bernstein, L. S., Anderson, G. P., Lewis, P., Chetwynd, J. H., Hoke, M. L. (2008). Band model method for modeling atmospheric propagation at arbitrarily fine spectral resolution. US patent no: 7433806. [65] Brunt, D. (1932). Notes on radiation in the atmosphere I. Quarterly Journal of the Royal Meteorological Society, 58, 389–420. [66] Li, M., Jiang, Y., Coimbra, C. F. M. (2017). On the determination of atmo-spheric longwave irradiance under all-sky conditions. Solar Energy, 144, 40–48. [67] Liou, K. N. (2002). An Introduction to Atmospheric Radiation, 2nd edition. Elsevier, United States of America. [68] Wallace, J. M., Hobb, P. V. (2006). Atmospheric Science. An Introductory Survey, 2nd edition. Elsevier, Canada. [69] Meinel, A. B., Meinel, M. P. (1976). Applied Solar Energy. An Introduction. Addison-Wesley, United States of America. [70] Liou, K. N., Yang, P. (2016). Light Scattering by Ice Crystals, Fundamental and Applications, Cambridge University Press, United Kingdom. [71] Lin, C., Li, Y., Chi, C., Kwon, Y. S., Huang, J., Wu, Z., Zheng, J., Liu, G., Tso, C. Y., Chao, C. Y. H., Huang, B. (2022). A solution-processed inorganic emitter with high spectral selectivity for efficient subambient radiative cooling in hot humid climates. Advanced Materials, 34, 2109350. [72] Fei, J., Han, D., Ge, J., Wang, X., Koh, S. W., Gao, S., Sun, Z., Wan, M. P., Ng, B. D., Cai, L., Li, H. (2022). Switchable surface coating for bifunctional pas-sive radiative cooling and solar heating. Advanced Functional Materials, 32, 2203582.9781032529042_C008.indd   168 15-02-2024   5.07.30 PM