Performance analysis of the sky radiative and thermoelectric hybrid cooling system

Energy 200 (2020) 117516

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Performance analysis of the sky radiative and thermoelectric hybrid cooling system Trevor Hocksun Kwan , Bin Zhao , Jie Liu , Gang Pei * Department of Thermal Science and Energy Engineering, University of Science and Technology of China, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 January 2020 Received in revised form 29 February 2020 Accepted 30 March 2020 Available online 4 April 2020

In this paper, the radiative sky cooler (RSC) and thermoelectric cooler (TEC) are integrated to form the RSC-TEC hybrid cooling system that can reduce the TEC required power consumption and increase the system’s cooling capacity over a standalone RSC. Specifically, a feasibility study is conducted to evaluate the design and working conditions that allow this system to have superior performance; For example, the TEC module type and number, RSC surface area and radiative emissivity value, solar absorption coefficient and air convective heat transfer coefficient have been parametrically swept to assess their effects on the system’s cooling capacity and the TEC power saving coefficient, a metric to define the degree of TEC power consumption reduction due to the RSC. The analyzes have been conducted through a non-dimensional steady-state mathematical model of the hybrid system that cools an enclosed space. Results demonstrate that a 0.1 m2 RSC could reduce the required power consumption of a TEC module (size 4 cm by 4 cm) by up to 10%. Moreover, increasing the RSC surface area further improved the TEC power saving coefficient, but the solar absorption coefficient had to be under 0.02 to maintain a reasonable TEC power saving coefficient. © 2020 Elsevier Ltd. All rights reserved.

Keywords: Hybrid cooling system Parametric analysis Power savings Radiative sky cooler Thermoelectric cooler

1. Introduction Cooling energy is a fundamentally important component of everyday living such as for personal comfort/health and food preservation. This is especially true in warmer regions such as near the equator where it is virtually impossible to find a natural or passive cooling source. Unfortunately, the production of cooling energy by active means is often very energy intensive, thus motivating researchers and engineers to develop an efficient, economic and compact cooling energy device. Although the vapor compression cycle (VCC) has been the most successful and widely used cooling technology for over a century [1], this technology also has some drawbacks including the involvement of environmentally harmful refrigerants and the involvement of moving parts which leads to the need for frequent maintenance. Even today, researchers are still determining ways to improve the VCC technology, as reviewed by Park et al. [2], where example aspects include implementing high-grade energy compensation ratio concept by Dehu et al. [3] or including an ejector into the cycle [4].

* Corresponding author. E-mail addresses: [email protected] (T.H. Kwan), [email protected] (B. Zhao), [email protected] (J. Liu), [email protected] (G. Pei). https://doi.org/10.1016/j.energy.2020.117516 0360-5442/© 2020 Elsevier Ltd. All rights reserved.

Therefore, alternative to the VCC, other cooling technologies have also been developed and these include the radiative sky cooler (RSC) and thermoelectric cooler (TEC). The RSC is one that utilizes the principle of heat radiation into the cold outer space, and it does so by having a high transparency for thermal radiation in midinfrared wavelength bands (i.e. the atmospheric window, within 8e13mm) [5]. The key advantage of the RSC over the VCC is that it obtains the cooling energy passively which means it does not need a device to power its operation, and the RSC is also fully solid-state. Unfortunately, the RSC also has several major disadvantages such as having a very low cooling density (under 100W=m2 in many practical cases [6,7]) and the inability for a conventional design to operate during the daytime. Therefore, many researchers have undertaken extensive researches to improve the RSC’s cooling performance in many aspects with one being that of materials design. For example, Yang et al. [8] developed a dual-layer structure RSC which experimentally achieved a 0.99 solar reflectance and a radiative emittance of 0.9 in the mid-infrared region, thus their RSC design was highly suitable for daytime radiative cooling. In another study by Jeong et al. [9], multi-layered titanium oxide was proposed as another RSC material, which could achieve a 0.94 solar reflectance, mid-infrared radiative emittance of 0.84 and operate normally even when the air relative humidity (RH) was up to 0.7.

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Nomenclature

Abbreviations COP e Coefficient of Performance RH e Relative Humidity RSC e Radiative Sky Cooling TEC e Thermoelectric Cooling Variables ARSC

a i εr εsky

gS hair K

l 4save pH2 O

e Radiative sky cooler surface area (m2 ) - Seebeck coefficient (W/K) e TEC operating current (A) e radiative emissivity (ranges from 0 to 1) e sky radiative emissivity (ranges from 0 to 1) - Solar absorptivity of the radiative sky cooling material (ranges from 0 to 1) e Convective heat transfer coefficient of air (W/(mK)) e Thermal conductance (W/K) e Thermal conductivity (W/(mK)) e TEC power saving coefficient (ranges from 0 to 1) e Partial pressure of water (Pa)

Alternatively, the study by Wong et al. [10] proposed integrating the RSC with an asymmetric electromagnetic transmission window (AEMT), where the latter material allows outgoing radiative transmission by the RSC but reflects incoming solar irradiation. Alternative to materials design, other researchers have also applied the RSC technology to real-world applications, such as to a “Nightcool” building in Parker and Sherwin’s study [11] to reduce the space cooling requirement by the primary cooling device. The economic feasibility of the RSC technology in a two-floor single family house in several cities in USA was also studied by Zhang et al. in Ref. [12], and it was found there that this system increased the cooling system’s average coefficient of performance (COP) by more than 39.4%. Besides these studies, other applications have also been considered such as the usage of RSCs on a building’s attic [13] and demonstrating the all-day operation of a 1 kW-scaled RSC device [14]. Moreover, another innovative concept that has been recently introduced is developing a device that integrates the RSC’s function at night time and solar energy utilization at daytime by Hu et al. [15] and Zhao et al. [5]. Specifically, the study by Hu et al. collected solar energy as heat during the daytime whereas the study by Zhao et al. involved a PV panel to produce power. Also, the thermoelectric cooler (TEC) is another type of cooling energy device which operates under the Peltier effect principle to produce the cooling energy, and it can be seen as being another type of heat pump. The TEC can also operate in the reverse direction to convert heat to electricity via the Seebeck effect, which is known as the thermoelectric generator or TEG [16]). The TEC attracts wide research interest because it does not involve moving parts, operates without noise and does not emit any pollutants [17]. However, the TEC also has its drawbacks; For example, the COP and the specific volume power density are relatively low compared to other counterpart technologies such as the previously mentioned vapor compression cycle (VCC), as demonstrated in the comparative analysis by Hermes et al. [18]. Thus, the TEC is most often used for small scale applications, such as cooling of portable electronic devices [19], CPUs or items in small portable refrigerators [17,19]. Conversely, the indoor cooling of buildings is almost always achieved by using the VCC [2].

pH2 OðsÞ PTEC QH QL Qa Qr Qs qc qcðNo TECÞ

s T Tamb Tsky Tdew

e Saturation partial pressure of water (Pa) e TEC power consumption (W) e Heat transfer at the TEC’s hot side (W) e Heat transfer at the TEC’s cold side (W) e Convective heat transfer (W) e Radiative sky heat transfer (W) e Solar heat (W) e Cooling capacity of the RSC-TEC hybrid system (W/ m2 ) e Cooling capacity of a standalone RSC device (W/ m2 ) e Electrical Conductivity (S/m) e Enclosed cooling space temperature (K) e Ambient temperature (K) e Sky temperature (K) e Dew-point temperature (K)

Constants Patm ¼ 105 Pa e Atmospheric pressure d ¼ 5:67  108 W=ðm2 KÞ e Stefan Boltzmann constant

Therefore, to suitably apply the TEC to the building cooling application, either a separate device is required for support or the TEC should be utilized in a unique way. For example, Irshad et al. [20] proposed to integrate the photo-voltaic (PV) wall to the TEC, which has two useful purposes; The first is to provide the power required by the TEC; The second is to act as an extra thermal insulation layer against the solar irradiation. Therefore, the cooling ability to the building room by TEC operation has greatly increased over adopting the TEC via conventional means (e.g. supply the power from the grid). In another study, Zhao et al. [21] proposed that, instead of cooling the entire building space, thermal comfort could also be achieved by developing localized thermal envelopes around the individual occupants, thus lowering the cooling energy requirement for the building itself. Therefore, Zhao et al. developed a portable TEC energy conversion unit that can provide such a thermal envelope and showed that an average of only 24.6 W cooling power is required by each occupant. Most recently, Xia et al. [22] proposed to integrate the thermoelectric device (TEG) to the RSC, where the TEG utilizes the temperature difference between the ambient and the produced cooled space by the RSC to generate power. Although this system could effectively generate power silently and without any moving parts, the reported output power was only in the order of nano-Watts, which indeed is too low for any practical applications. In an alternative study, Zhao et al. [23] integrated the RSC to the TEC application for buildings, where the RSC was specifically used to dissipate heat from the TEC’s hot side. Nevertheless, such an implementation limits heat dissipation at the TEC hot side to only by RSC operation and eliminates other options such as convective air cooling, which in turn limits the total cooling capacity of the TEC itself. In contrast to placing the RSC at the TEC hot side, this paper performs a feasibility study of setting the RSC and TEC to both provide their cooling energy to the target object. This implementation can not only enable a higher cooling capacity over a standalone RSC by TEC operation, it also reduces the required TEC power consumption for achieving a specified cooling requirement by RSC operation. Furthermore, rather than focusing on a specific design size, a feasibility study is conducted to determine the design

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choices and working conditions that the RSC-TEC hybrid system can suitably operate or cannot operate with; For example, design variables such as the type of TEC module and number as well as RSC surface area have been explored to evaluate their influences on the system’s TEC power saving coefficient and overall cooling capacity. Furthermore, the commonly known environmental impacts on the RSC such as solar absorption and air convective heat transfer have also been included in the study, where the corresponding coefficients have been parametrically swept to assess the working conditions in which RSC-TEC hybrid system is acceptable for normal operation. These characteristics have been calculated through a non-dimensional steady-state mathematical model for the RSC-TEC hybrid system that cools an enclosed space, and its TEC model was verified with in house obtained experimental data. The remainder of this paper is structured as follows. Section 2 presents the mathematical model and related equations of the RSC-TED hybrid system. Section 3 then presents a validation model that proves the model of Section 2 is accurate and reliable. Section 4 presents the case study that this paper will analyze and the list of parameters that are set as constants. Section 5 analyzes the simulation results and Section 6 concludes this paper.

2. System modelling 2.1. Radiative sky cooler model Fig. 1 shows the overall system structure and a generalized heat balance model of the proposed RSC-TEC hybrid cooling system. Here, cooling is given to an internal space, where the RSC is shown on the top surface and faces the sky direction and the TEC is located on the opposite side. The RSC produces cooling via radiation to the outer space environment as the variable QR . In addition to this, other parasitic effects such as input solar radiation during daytime operation (QS ) and convective heat transfer into the ambient environment (Qa ) are also included to study their influences on the RSC-TEC system’s hybrid cooling ability. Meanwhile, the TEC consumes power (PTEC ) to produce cooling energy to the enclosed space via the variable QL , and it dissipates the gathered heat back into the ambient environment as QH : To maintain calculation simplicity and perform reasonable comparative analyzes, the following assumptions are imposed on the mathematical model of the RSC-TEC system: 1. A steady-state analysis is conducted. 2. Heat and cooling energy loss to the environment via the enclosed space walls and the TEC lateral faces are neglected. 3. During TEC operation, the TEC hot side is assumed to be 8 K higher than the ambient environment (i.e. TH ¼ Tamb þ 8). This

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is used to account for the thermal resistance effect between the TED hot side and the ambient temperature. 4. The RSC and TEC cold side surface temperatures are assumed to be equal to the enclosed space. 5. Temperature is assumed to be uniform across the RSC and TEC surfaces and volumes, implying a non-dimensional analysis is conducted. By the principle of conversation of energy, the total cooling power available by the hybrid system is calculated as follows:

Qs þ Qr þ Qa þ QL ¼ QCðTotalÞ

(1)

where the SRC provides cooling energy via radiative dissipation:

  4 Qr ¼ εr dARSC T 4  Tsky

(2)

where εr is the radiative emissivity of the RSC material which is assumed to be a constant in this paper, ARSC is the RSC’s surface area and d is the Stefan Boltzman’s constant. Also, T is the enclosed cooling space temperature and Tsky is the sky temperature which is defined as follows (adopted from Ref. [24]):

1 Tsky ¼ εsky Tamb 4

(3)

where εsky is the emissivity of the sky. In this paper, εsky has been estimated based on empirical formulas from a previous publication, where the adopted formula is as follows (adopted from Ref. [24]):

εsky ¼ 0:77 þ 0:0062ðTdew  273:15Þ

(4)

where Tdew is the dew point temperature of atmospheric air above the RSC which is defined as follows:

Tdew ¼

5179   pH2 O 20:519  loge 7:6  1013

(5)

where pH2 O is the partial pressure of water.

pH2 O ¼ RH  pH2 OðsÞ

(6)

where RH denotes the relative humidity of the air, and the water saturation pressure pH2 OðsÞ has been defined by the following relationship (adopted from Ref. [25]):

pH2 OðsÞ ¼ Patm  10K K ¼  2:1794 þ 0:02953ðT  273:15Þ  9:1387  105 ðT  273:15Þ2 þ 1:4454  107 ðT  273:15Þ3

(7)

(8)

Meanwhile, the input solar irradiation during daytime operation is defined as follows:

Qs ¼ gs IARSC

(9)

where gs denotes the solar absorptivity of the RSC material and I denotes the irradiance size. Also, the convective heat transfer from the RSC to the ambient environment is defined as follows:

Qa ¼ hair ARSC ðT  Tamb Þ Fig. 1. Overall structure of the RSC-TEC hybrid cooling system.

where hair is the convective transfer coefficient of air.

(10)

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2.2. TEC model The widely known energy equilibrium TEC model described in Ref. [17] is adopted here, and the model equations are shown below:

  1 QH ¼ n aiTH þ KðTH  TÞ  i2 R 2

(11)

  1 QL ¼ n aiT þ KðTH  TÞ þ i2 R 2

(12)

where PTECðRSCÞ denotes the TEC power consumption when an RSC is included, and PTECðNo RSCÞ denotes the TEC power consumption when the RSC is excluded (i.e. TEC by itself). As the value of 4Save increases towards a theoretical maximum of 1, this indicates that the RSC is providing a major contribution in reducing the required TEC power consumption. Conversely, if the value of 4Save is 0 (i.e. PTECðRSCÞ ¼ PTECðNo RSCÞ ) then this indicates that the RSC has not contributed to reducing the TEC’s power consumption. Indeed, negative values of 4Save indicates that the RSC is negatively affecting the TEC’s operation and thus shall be avoided in practice. Finally, the total cooling capacity of the overall system is also defined:

QCðTotalÞ

where QL denotes the contribution of cooling energy to the enduser and QH denotes the heat that is dissipated at the hot side. Also, n is the number of thermo-couples in the thermoelectric module, a is the Seebeck coefficient, K is the thermo-couple leg’s thermal conductance and R is the electrical resistance of a single thermo-couple leg. All of these parameters are material and module specification related. By defining an operating current i, these two equations can be solved and subsequently the TEC power consumption is evaluated as follows:

Indeed, to justify the use of the RSC-TEC hybrid system, the value of qc should be higher than when the TEC is not included, which is defined as:

PTEC ¼ QH  QL

where QRSC ¼  Qs þ Qr þ Qa .

(13)

In terms of material properties, the Seebeck coefficient, electrical conductivity and thermal conductivity will vary with respect to the thermocouple’s operating temperature [17]. However, because this paper studies the TEC when it operates in a relatively small temperature range about the natural ambient condition, constant values have been assumed. Initially, the values were extracted from Ref. [26] were used but they were further adjusted to closely match the data obtained by the validation experiment (which will be presented in the next subsection). The final values are obtained as: a ¼ 4:5313  104 V=K, s ¼ 1:7150  105 S=m and l ¼ 3:162 W=ðm KÞ. 2.3. Performance metrics A number of metrics have been defined to assess the improvements to the TEC performance through RSC integration. First, the effective coefficient of performance (COP) of the TEC after an RSC (hence based on the hybrid system) is defined:

COPRSCTEC ¼

QCðTotalÞ PTEC

(14)

noting that QCðTotalÞ equals the total cooling energy that is contributed by both the RSC and TEC. An improvement is shown when this parameter’s value is higher than that of the COP obtained by a standalone TEC:

COPTEC ¼

QL PTEC

(15)

Another performance metric is the power saving coefficient, which quantifies the degree of which TEC power consumption is reduced due to the inclusion of the RSC. When evaluating this performance metric, both PTECðRSCÞ and PTECðNo RSCÞ are compared under identical working conditions (e.g. same ambient temperature, cooling space temperature, total output cooling power, etc.). The TEC power saving coefficient is defined as follows:

4Save ¼ 1 

PTECðRSCÞ PTECðNo RSCÞ

(16)

qc ¼

ARSC þ ATEC

qcðNo TECÞ ¼

QRSC ARSC

(17)

(18)

2.4. Solving the model The following procedure is used to couple together the RSC and TEC models and hence evaluate the characteristics of the overall RSC-TEC hybrid system: 1. Input the constant working conditions and design parameter values. 2. Solve the radiative sky cooler model to obtain QRSC ¼  Qs þ Q r þ Qa . 3. Calculate the TEC cooling power requirement as: QL ¼ QCðTotalÞ  QRSC . 4. Solve the TEC model to obtain PTEC . 5. Evaluate the performance metrics values based on the obtained data from steps 2 and 4. 3. Model validation To ensure that the adopted TEC simulation model and relevant material property values are accurate, an experimental platform is developed to obtain the TEC module’s output characteristics. The experimental results are then compared with those from the simulation model under the same working conditions, where the two results should be similar or ideally be identical. In the experiment, two TEC1-12715 modules are connected in series, where the cold side is attached to an electric heater and the hot side is attached to an actively air-cooled heat sink. The electric heater at the cold side is used to measure the “cooling” energy produced by the TEC after the temperatures reach a steady state. Temperature measurements are made by a DS18b20 temperature sensor with ± 0:5 C accuracy for the TEC hot side, and by a digital multi-meter and its manufacturer supplied thermo-couple for the TEC cold side. The overall experimental platform’s schematic has been graphically illustrated in Fig. 2. In the experiment, the electric heater at the TEC cold side is set to output a constant heat of 40 W, and the cooling fan at the TEC hot side is set to a constant speed. The TEC supply voltage is then varied within the range of 10 Ve20 V with steady-state measurements taken at 2 V increments. Based on these imposed experimental conditions, it was found that the TEC cold side temperature would vary from 26:5 C to 28 C and the hot side correspondingly varies

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4. Study case Table 1 lists the working conditions that have been imposed in this paper. The selected parameters are set to represent a portable cooling box application, where the required cooling power may be up to 30 W and the box be placed in a hot environment of up to 310 K. A limit of 30 W was chosen because higher values lead to significant difficulties in practically managing heat dissipation at the TEC hot side. The RSC surface area, type of TEC and number of TEC modules are all parametrically swept to assess their influences on the performance metrics that were defined in Section 2.3. Initially, solar irradiation and convective heat transfer with the surrounding air has been neglected to obtain the ideal case results, but their effects are later included in different case studies.

5. Results 5.1. Typical target cooling power Fig. 2. Schematic of the experimental platform for validating the TEC model’s accuracy.

from 37:75 C to 49:56 C. Fig. 3 shows the subsequent experimental results and also compares them to those obtained by the TED simulation model. Clearly, according to Fig. 3(a) and (b), the TEC power consumption and corresponding COP curves are closely matched between the experiment and simulation for most temperature difference values. A significant discrepancy has been noticed at the higher temperature differences value beyond 18 K. This may have occurred due to slight misestimations on the thermo-couple material properties at varying temperature differences. Nevertheless, the discrepancies are not huge and remain within 5% for temperature difference values below 12 K, values of which are primarily used in this paper.

Initially, the target cooling power value is set at 20 W and the cooling space temperature is varied. By setting the RSC surface area at 0.1 m2 and adopting a single TEC1-12715 module, the contribution of cooling power, TEC power consumption and TEC’s COP are plotted in Fig. 4 (a), (b) and (c) respectively. By observing Fig. 4 (a), the RSC’s contribution to the cooling power decreases from 7.5 W to 2.5 W as the cooling space temperature is further lowered from the ambient. In doing so, the TEC cooling power contribution progressively increases to compensate for the reduction in RSC cooling power. Obviously, the RSC alone is unable to achieve the required 20 W cooling power, and it rather is more suitable as a supplementary cooling device to reduce the TEC’s required cooling power contribution. Clearly, according to Fig. 4 (b), at all cooling space temperatures, including the RSC has reduced the required TEC power consumption over the case of when RSC is excluded from the cooling system. The magnitude of reduction appears to be quite constant at a value of 0.75 W for the studied temperature range. According to Fig. 4 (c),

Fig. 3. Comparison between the experimental and simulation data as a function of the temperature difference between the TEC hot and cold sides (a) TEC power consumption (b) Heating coefficient of performance.

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T.H. Kwan et al. / Energy 200 (2020) 117516 Table 1 List of the working conditions that are imposed in this paper’s study. Parameter

Value

Ambient temperature (Tamb ) Target cooling power (QCðTotalÞ Þ

310 K 10 We30 W

Atmospheric relative humidity (RH) RSC Mid Infra-red Emissivity RSC Surface Area (ARSC ) Primary TEC product Primary TEC’s thermocouple length Primary TEC’s thermocouple cross-section dimensions Secondary TEC product Secondary TEC’s thermocouple length Secondary TEC’s thermocouple cross-section dimensions

0.2 0.9 0.1 m2 or 0.2 m2 TEC1-12715 (4 cm by 4 cm module) 1 mm 1.2 mm by 1.2 mm TEC1-12730 (6 cm by 6 cm module) [27] 1.3 mm 2.4 mm by 2.4 mm

Fig. 4. Performance comparison of the TEC with and without the RSC’s assistance (a) Contribution of cooling power between the two components (b) TEC power consumption comparison (c) Effective COP comparison.

the effective COP after including the RSC is clearly higher than that without it, and the COP improvement appears to be much more significant when the cooling space temperature is higher. 5.2. Varying target cooling power and temperature To obtain a broader understanding of the RSC-TEC hybrid cooling system’s performance, both the temperature and cooling power have been varied, and a colored contour plot that shows the TEC power saving coefficient w. r.t these two parameters have been given in Fig. 5 and Fig. 6. Specifically, Fig. 5(a) and (b) show the cases when two different TEC modules (TEC1-12730 and TEC112715) are adopted, and Fig. 6 shows the case when the RSC area or number of adopted TEC modules are varied. According to Fig. 5(a) and (b), a region in which the TEC power saving coefficient registers values very close to 1 exists when at cooling temperatures is very close to the ambient (308 Ke310 K) and at lower cooling powers. Indeed, as the cooling space temperature progressively drops towards 300 K and as the total cooling

power increases, the power saving coefficient variable will drop towards 0, implying the RSC’s contribution to reducing the TEC power consumption diminishes with respect to these two parameters. By comparing Fig. 5(a) and (b), clearly the region with higher power saving coefficient values occupies a larger area when the TEC1-12715 module is adopted. For example, when observing the contours regions in which the power saving coefficient is around 0.5, the TEC1-12715 case in Fig. 5 (b) intersects at around 306 K at the temperature axis and 20 W at the cooling power axis. However, for the TEC1-12730 case, the power saving coefficient peaks at 0.24 even under the best-case scenario. These results suggest that applying the RSC to a smaller TEC module results in larger contributions to reducing the TEC’s required power consumption. A likely reason for this observation is because a smaller TEC module (i.e. with a smaller surface area) needs to consume more power to produce the same level of cooling power over a larger TEC module, thus leading to higher contributions to power reduction when the smaller TEC is used. Therefore, the TEC1-12715 module has been used in subsequent the analyzes

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Fig. 5. Comparison of the TEC power saving coefficient that is obtained between two modules as a function of temperature and total cooling power (a) TEC1-12730 (b) TEC1-12715.

Fig. 6. Color plots showing how the TEC power saving coefficient is influenced by the operating temperature and the total cooling power under different RSC and TEC sizes. In (b), (2S, 1P) refers to 2 series connected TEC modules with 1 parallel string. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

of this paper, including Fig. 6, where this figure compares the contour plots of the 4save parameter under the case when two TEC112715 modules are used and when a larger RSC surface area is adopted. Clearly by observing Fig. 6 (c) and comparing it to (a) and (b), increasing the RSC surface area has very significantly increased the total cooling power versus operating temperature region in which the power saving coefficient remains at values above 0.6. The increase in the contribution is because of the increased RSC cooling power output from increasing its surface area, thus the required TEC cooling power and hence the power consumption has decreased. Conversely, between Fig. 6(a) and (b), increasing the number of TEC modules did not have a significant effect on the power saving coefficient color plot. In fact, the size of the region with a high power saving coefficient has mildly dropped for the

case of Fig. 6 (b), indicating that the RSC cannot provide as much contribution to power saving when a larger TEC is included. This observation is consistent with that observed in Fig. 5, where a smaller TEC1-12715 module achieved higher power savings than the larger TEC1-12730 module. Overall, these results suggest that maximizing the TEC power saving coefficient is best achieved by adopting a larger RSC versus TEC surface area ratio. 5.3. Varying solar absorption and convective coefficient Fig. 7 shows how varying the solar absorption coefficient (in (a)) and air convective transfer coefficient (in (b)) affects the TEC power saving coefficient, where the total cooling power was set at 20 W in these curves. Analogously, a region in which the TEC power saving coefficient is at a large value also exists in these color plots. Based

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Fig. 7. Variation of the TEC power saving coefficient in terms of the RSC’s solar emissivity and air convective coefficient.

on Fig. 7 (a), as the solar absorption increases, the power saving coefficient dramatically drops and even becomes negative at values beyond 0.05, indicating the RSC is conversely increasing the TEC power consumption. Moreover, as the cooling temperature drops decreases, the solar absorption coefficient has an even stronger negative effect on the power saving coefficient. In fact, the effects of the solar absorption coefficient is only shown up to 0.08 in Fig. 7 (a) because the power saving coefficient will always be negative at any value beyond this. Clearly, the solar absorption coefficient has a really strong effect on the hybrid system’s performance, and in practice, the value shall at least be below 0.05 to justify the use of this system during daytime operation. In other words, adopting the RSC-TEC system during daytime operation requires a very strict design process for minimizing the side effect of solar irradiation and hence may not be suitable in practice. In contrast to the solar absorption, the air convective coefficient appears to have a smaller effect on the TEC power saving coefficient. For example, when the cooling temperature is 308 Ke310 K, the power saving coefficient hardly changes and remains quite constant near 0.5. However, a lower cooling temperature influences the power saving coefficient more significantly, and a zero-crossing contour is found between 300 K and 306 K. The reason for the drop in power saving coefficient is simply because of the higher temperature difference between the ambient air and the RSC surface, leading to higher “cooling” losses by convection. Overall, because the convective air coefficient only has negative effects on the power saving coefficient, measures to minimize or eliminate it would certainly be an appropriate design choice to improve the RSC-TEC system’s performance. Suggestions for minimizing the air coefficient include isolating the RSC surface from the flowing air or by placing the RSC in a vacuum environment.

5.4. Varying convective coefficient and emissivity together Fig. 8 shows the effects on the power saving coefficient from simultaneously varying both the radiative emissivity and the air convective coefficient, where two temperature difference values were selected for comparison. Unsurprisingly, larger emissivity values and lower air convective coefficient values result in TEC larger power saving coefficients. More specifically, based on the contour line curves in Fig. 8 (a), the air convective coefficient causes a larger negative impact on the power saving coefficient performance at lower radiative emissivity values. The impact is even larger when the ambient versus cooling space temperature difference is changed to 7 K as of Fig. 8 (b), air convective coefficients being over 6 W/(m K) will always result in negative power saving ratios, regardless of the radiative emissivity value. Overall, it is shown that creating a vacuum-sealed environment for the RSC is certainly a valuable choice to eliminate the negative impact caused by the air convective coefficient, and this is especially true when a larger cooling space to ambient temperature difference is required. Indeed, the best operating point in both Fig. 8(a) and (b) is when the radiative emissivity value is 1 and the convective air coefficient value is zero. The corresponding maximum theoretical power saving coefficient values are 0.35 and 0.2, respectively. Therefore, as the RSC surface of 0.1 m2 is reasonably compatible with the TEC, the RSC-TEC integration concept is well justified. 5.5. Cooling capacity influence Fig. 9 shows how the system’s overall cooling capacity (as qc ) is affected by varying the RSC area and TEC power consumption. It is noted that when the TEC is not included, the RSC yielded a constant

T.H. Kwan et al. / Energy 200 (2020) 117516

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Fig. 8. Effect of varying the radiative emissivity and air convective coefficient on the power saving coefficient. In both graphs, Q C ¼ 20 W and ARSC ¼ 0:1 m2 .

total cooling capacity became less than the case when the TEC is not included is because the TEC’s surface area was included in the total cooling capacity calculation. Overall, it is shown that the TEC’s contribution to increasing the RSC’s cooling capacity is better achieved when used with a smaller RSC surface area and a higher TEC power consumption. 6. Conclusion

Fig. 9. Color plots showing how the system’s cooling capacity is influenced by TEC power consumption and RSC surface area. The temperature difference is constant at 6 K and, without the TEC, the RSC’s cooling capacity was 43.695 W= m2 . (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

43.695 W/m2 cooling capacity and is independent of the surface area size. Clearly, according to Fig. 9, the cooling capacity is at an extremely high value of up to 1100 W/m2 when the RSC surface area is small (<0.05 m2) and the TEC power consumption is beyond 8 W. However, as the RSC surface area increases and the TEC’s contribution is low, the cooling capacity dramatically drops (e.g. a minimum value of 34.56 W/m2 was recorded at 0.3 m2 and 1 W TEC power consumption). This result is normal because, while the TEC’s contribution to cooling power remains constant, the RSC’s surface area has been increased. Also, the reason that a recorded minimum

This paper has combined the radiative sky cooler (RSC) and thermoelectric cooler (TEC) to form a hybrid cooling system that can reduce the required TEC power consumption and increase the cooling capacity over a standalone RSC. A steady-state mathematical model for cooling an enclosed space through the proposed hybrid system is introduced, and its TEC model was verified with in house obtained experimental data. The effect of the TEC module type and number, RSC surface area, solar absorption and air convective transfer coefficient have all been explored to evaluate their influences on the system’s TEC power saving coefficient (quantitively defined in (16)) and the overall system cooling capacity. The primary findings of this paper include: 1. Under a target of 20 W total cooling power, including an RSC can reduce the TEC’s power consumption, and the improvement rate could be over 10%, depending on the temperature difference between the ambient environment and the cooling space. 2. Overall, adopting a larger RSC area greatly improves the TEC power saving ratios by increasing the total cooling power versus temperature region size in which this parameter remains at high values (e.g. above 0.6). Conversely, adopting a larger TEC module reduces this region size. 3. The solar absorption coefficient needed to be under 0.02 to achieve a reasonable TEC power saving coefficient for a temperature difference of up to 10 K. Thus, utilizing the RSC-TEC hybrid cooling system for daytime operation is a very challenging task, but is possible based on solar reflectance data of

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state of the art RSC materials, such as by Yang et al. [8] who reported a reflectance value of 0.99 (i.e. absorption value of 0.01). 4. The air convective coefficient has a significant influence on the TEC power saving coefficient when the cooling temperature is over 5 K from the ambient (potentially dropping below 0 when the coefficient is over 3 W/(m2 K). Therefore, isolating the RSC surface from flowing ambient air is a recommended design practice. 5. The TEC enabled a higher system cooling capacity over a standalone RSC when its power consumption is increased and when the RSC surface area is smaller. Once the RSC surface area is beyond 0.25 m2, a single TEC module has a very small contribution to the system cooling capacity. Future work includes building an experimental platform to demonstrate the RSC-TEC hybrid system operating all night in a real environment. It is expected that the work of this paper can serve as a valuable guideline for the experiment, and the encounterable challenges may include maintaining a uniform temperature distribution in the cooling space by the RSC-TEC system and building a sustainable power subsystem for the TEC component. Another work may be to integrate the RSC at both the cold side and hot side of the TEC to improve the total performance of the system. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Trevor Hocksun Kwan: Conceptualization, Data curation, Formal analysis, Writing - original draft, Investigation, Methodology, Visualization. Bin Zhao: Writing - review & editing, Project administration, Resources, Software. Jie Liu: Writing - review & editing, Validation. Gang Pei: Funding acquisition, Supervision. Acknowledgments This research was sponsored by the National Natural Science Foundation of China (NSFC 5171101721, NSFC 51776193). References [1] Kharagpur, Vapour compression refrigeration systems, accessed on 2020/2/ 27; Available from: https://nptel.ac.in/content/storage2/courses/112105129/ pdf/RAC%20Lecture%2014.pdf.

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