Modified phase change materials used for thermal management of a novel solar thermoelectric generator

Energy Conversion and Management 208 (2020) 112459

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Modified phase change materials used for thermal management of a novel solar thermoelectric generator

T

⁎

Xiaohang Luoa,b, Quangui Guoa,b,c, , Zechao Taoa,c, Yanjuan Lianga,b, Zhanjun Liua,c a

Key Laboratory of Carbon Materials, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, China Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China c Corporation of Foshan Zhongke Siwei Thermal Management Technologies, Foshan 528300, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Thermal management Phase change materials Paraffin Expanded graphite Solar thermoelectric generator

How to produce electricity safely and without pollution is an important issue to our world. The solar thermoelectric generator can realize direct solarelectric energy conversion. However, the output power of the traditional solar thermoelectric generator is instability because of the instantaneity of the solar energy. In this paper, the paraffin/expanded graphite phase change materials were used in the solar thermoelectric generator to realize the thermal management of the solar energy. Expanded graphite improves the thermal conductivity and the anti-leakage ability of the paraffin; therefore, the prepared phase change materials have higher thermal response speed and wider application than the pure paraffin. As a result, when the temperatures of the phase change materials with different melting points (50 °C, 60 °C, 70 °C, and 80 °C) enter their own phase transition regions, the open circuit voltages of the corresponding systems also enter the stable output platforms. This verifies the excellent thermal management performance of the phase change materials on solar thermoelectric generator. In addition, the output voltage is considerable and the maximum value is 2.697 V for 80 °C PCMs. When the solar irradiation disappears, the latent heat of paraffin can still keep the system operating. Meanwhile, a mathematical model with high accuracy was also proposed.

1. Introduction Solar energy is the most readily available clean thermal energy [1,2]. The land and the oceans on the earth receive 51% (89 PW, 1 PW = 1015 W) of the whole incoming solar irradiation energy [3]. The solar thermoelectric generator (STEG) can convert solar energy into electric energy directly via Seebeck effect. The temperature difference between solar energy and ambient temperature is the power to drive the thermoelectric module (TEM) in the STEG. This technology has the advantages of all solid-state operation, no moving components and harmful working fluids, long lifespan, no maintenance, non-pollution, no scale effect, and noiseless working which has attracted much attention [4,5]. Many researchers have focused on the STEG for a long time [6–18]. Telkes [6] used a flat-plate glazed solar collector to assemble a STEG firstly in 1954. Xiao et al. established some multi-stage STEG models consisted of low- and medium- temperature thermoelectric materials. Their research determined that the reasonable thermal design can improve the performance of the STEG [10]. Zhang et al. [12] prepared a solar thermoelectric co-generator system based on two domestic

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evacuated tubular solar collectors by adding the TEMs to the heat pipes in solar collectors. This system could generate electric energy and hot water simultaneously. Sun et al. [17] researched the daily performance of a practical STEG under realistic condition and proposed a simulation module simultaneously. These works have confirmed that the STEG is a promising technology to produce electric energy using solar energy. However, the solar irradiation intensity is inherently time-varying due to the influence of the revolution and rotation of the earth and the variation of the atmospheric layer [19]; therefore, the output power of the traditional STEG is floating. For example, the electric power of the STEGs designed by Zhang et al. [12] and Sun et al. [17] varied greatly in one day. This instability has a negative effect on the use of the STEG for us. In order to solve this problem, we urgently need a thermal storage technology to manage the solar energy to prevent the thermal fluctuation. The phase change materials (PCMs) can absorb or release a large amount of heat during the phase transition, while the temperature can be kept at around the phase transition point. According to this characteristic of the PCMs, we can make the solar energy be converted and stored in the PCMs to eliminate the thermal fluctuation. When the

Corresponding author at: Key Laboratory of Carbon Materials, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, China. E-mail address: [email protected] (Q. Guo).

https://doi.org/10.1016/j.enconman.2019.112459 Received 19 November 2019; Received in revised form 28 December 2019; Accepted 31 December 2019 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

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Fig. 1. DSC curves of a) 50 °C paraffin and PCMs, b) 60 °C paraffin and PCMs, c) 70 °C paraffin and PCMs, and d) 80 °C paraffin and PCMs. Table 1 The properties of the pure paraffin and corresponding PCMs. Properties

50 °C paraffin

50 °C PCMs

60 °C paraffin

60 °C PCMs

70 °C paraffin

70 °C PCMs

80 °C paraffin

80 °C PCMs

Melting point (°C) Latent heat (J/g) Density (g/cm3) Specific heat (J/g•K) Thermal diffusivity (mm2/s) Thermal conductivity (W/m•K)

54.9 228.0 0.90 1.83 0.12 0.20

48.3 165.8 0.99 1.79 6.31 11.18

62.2 221.5 0.89 2.06 0.14 0.26

61.6 161.1 0.95 1.91 6.42 11.65

72.8 223.5 0.92 1.83 0.15 0.25

72.0 160.6 0.97 1.63 6.41 10.13

87.1 229.7 0.91 1.76 0.13 0.21

81.2 163.5 0.96 1.67 6.40 10.26

will increase the time necessary for thermal storage and recycling. And the leakage problem of the liquid paraffin leads to the fact that the researchers must use containers to encapsulate the paraffin, which will increase the thermal resistance and the economic cost; therefore, the pure paraffin cannot be used in the STEG directly. In order to use paraffin successfully for thermal management to the solar energy in the STEG, the problems of low thermal conductivity and liquid leakage must be solved. Adding the high thermal conductivity fillers into paraffin matrix is a common way, such as carbon nanotubes [22], graphene [23], carbon fiber [24], and nanoparticles [25], etc. But this method can only improve the thermal conductivity of the paraffin, and has no effect to prevent the liquid leakage. Saturating the paraffin into the porous media such as expanded graphite (EG) has aroused increasing concern nowadays. The high thermal conductivity of EG can increase the thermal conductivity of paraffin by an order of magnitude. And the EG also can prevent the leakage of liquid paraffin due to its capillary force [26–32]. According to the literatures, there are no studies have used the modified PCMs to improve the performance stability of the STEG under the realistic condition. In this paper, the paraffin/EG composites with different melting points (50 °C, 60 °C, 70 °C, and 80 °C) were prepared and tested. Then a novel STEG was devised by combining these PCMs

Table 2 Specifications of the CP14, 127, 045 thermoelectric module. Parameters

Value

Thermoelectric Material

Bismuth Telluride semiconductor material 127 40 × 40 × 3.3 81.5 8.5 16.4 1.75 80

P-N junctions (couples) Length × Width × Thickness (mm) Pmax (W) Imax (A) Vmax (V) Internal Resistance (Ω) Maximum Operating Temperature (°C)

phase transition undergoes, a stable heat source is provided to the TEMs in the STEG. PCMs is divided into three categories: the organic PCMs, the inorganic PCMs, and the eutectic PCMs [20]. Among them, the paraffin (belongs to the organic PCMs) which has the advantages of high latent heat, broad melting temperature range, great chemical stability, non-corrosive, and large scale commercialization is the most widely used PCMs [21]. However, the paraffin has two drawbacks which are the low thermal conductivity and the leakage problem when the solid phase turns to the liquid phase. The low thermal conductivity 2

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Fig. 2. a) Schematic diagram of the STEG, b) partial enlarged detail of the STEG, c) image of the test system, and d) detailed image of the STEG.

Fig. 4. T-t curves of the pure paraffin and PCMs.

Fig. 3. Image of the T-t experiment.

and hot sides of the TEM must be large enough, and the maximum operating temperature of the selected TEM is set as 80 °C; therefore, we chose four kinds of paraffin (Shang Hai Joule Wax Co., Ltd., China) with different melting points of 50 °C, 60 °C, 70 °C, and 80 °C. Each kind of paraffin was completely melted in a vacuum drying oven (DZF-6050, Hang Zhou Ruijia Precision Scientific Instruments Co., Ltd., China) firstly, and then the EG (Inner Mongolia Ruisheng graphite new material Co., Ltd., China, ρ = 0.235 g/cm3) was fully immersed in the liquid paraffin. After 6 h of vacuum infiltration, the samples were removed from the oven. The mass ratio of the paraffin and EG was 7:3. When the PCMs was completely solidified in the air, the PCMs was broke into particles with a size of 1–3 mm using a universal mechanical crusher (HW-20B, Beijing Huanya Tianyuan Machinery Technology Co., Ltd.,

with the evacuated tubular solar collectors (ETSC), micro-channel heat pipe (MCHP), TEMs, and the heat fins. Furthermore, in order to verify the thermal management effect of these modified PCMs on the designed STEG, we tested the open circuit voltage of this STEG under the realistic condition. In addition, we also established a mathematical model according to the realistic heat transfer process to predict the output power of this designed STEG.

2. Experimental The modified PCMs were prepared by a vacuum penetration method. Considering that the temperature difference between the cold 3

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Fig. 5. Comparison of anti-leakage ability between the pure paraffin and PCMs.

Fig. 6. Variation of the solar irradiation on March 25, 2019.

layer of thermal conductive silicone grease to reduce the thermal contact resistance. The hot sides were attached to the MCHP, while the cold sides were located on the pedestals of the heat fins. The specifications of the chosen TEM are shown in Table 2. The thermal contact resistance will also decrease with the increase of the joint pressure on the contact surfaces [33]; therefore, the pedestals of the heat fins, TEMs and MCHP were bound tightly by self-locking nylon bands to make a greater contact between each other. Finally, we connected these two TEMs in the type of electrically in series. The schematic diagrams of the novel STEG are shown in the Fig. 2. An automatic digital recorder (measurement accuracy: ± 0.2%, SKA8000, Xiamen SIKI Automation Equipment Co., Ltd., China.) was used to record the temperatures of the ambient environment, the hot and cold sides of TEM, and the open circuit voltage of the novel STEG. Recorded the instantaneous values every two seconds to ensure the accuracy of the experiment. The corrected K-type thermal-couples were used to measure the temperatures. The solar irradiation intensity was

China). Phase transition temperature, latent heat, and specific heat of the pure paraffin and PCMs were measured by a differential scanning calorimetry (DSC, 200 F3 MAIA, Netzsch, Germany). The DSC curves of the chosen paraffin and corresponding PCMs are shown in Fig. 1. Thermal diffusivity of the pure paraffin and PCMs were determined by a Netzsch apparatus (LFA427, Germany) based on laser flash technique. The properties of the pure paraffin and PCMs are illustrated in Table 1. Apparently, the thermal conductivities of the PCMs are 41 to 56 times higher than that of pure paraffin. We filled the crushed PCMs into the ETSC (Quan De Fu solar heater Co., Ltd., China, length: 620 mm, external diameter: 70 mm, internal diameter: 58 mm), then an aluminum MCHP (Nan Jing Re Er Electronic Technology Co., Ltd., China, length × width × thickness: 500 × 40 × 3 mm) was inserted into the middle of PCMs. Set aside a length of 5 cm of MCHP outside of the ETSC to install the TEMs. Both sides of MCHP can install the TEMs. The cold and hot sides of these two TEMs (CP14, 127, 045, Laird Technologies) were evenly coated with a

4

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Fig. 7. Temperature variation curves of the different PCMs used in the STEG on March 25, 2019.

Fig. 8. Curves of the Thot, Tcold, and ΔT of the TEM in the STEG used a) 50 °C PCMs, b) 60 °C PCMs, c) 70 °C PCMs, and d) 80 °C PCMs; e) curve of the ambient environment temperature on March 25, 2019.

3. Mathematical model of the STEG

measured every hour by a solar power meter (measurement accuracy: ± 10 W/m2, TES-1333, TES Electrical Electronic Corp.). The experimental site was in Taiyuan, Shanxi Province, China (longitude: 112.55, latitude: 37.87). The angle between the ETSC and the ground was 30°. The test time was from 8: 00 to 21: 00 on March 25, 2019 and September 21, 2019.

3.1. Description of the heat transfer process In this section, the mathematical model is established according to the realistic heat transfer process in the STEG. When the STEG is under 5

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Fig. 9. The open circuit voltage curves of the STEG used different PCMs: a) overall contrast, b) 50 °C, c) 60 °C, d) 70 °C, and e) 80 °C on March 25, 2019.

percent [33]. Therefore, the thermal contact resistance between all contact surfaces is neglected.

the light, the system starts to operate. Firstly, the solar energy is converted into the thermal energy by the ETSC, and followed, the thermal energy is absorbed and stored by the PCMs in the forms of sensible heat and latent heat, and then the thermal energy is conducted through the MCHP to the TEMs which are attached on the condenser of the heat pipe. The cold sides of the TEMs are cooled by heat fins with natural air cooling. This creates a temperature difference between the two sides of TEMs. In order to simplify the calculation, the following assumptions are applied to the heat transfer process:

3.2. Model The energy balance equation for ETSC can be expressed as follows,

Qsolar = Q in + Qconv + Q rad

(1)

Qsolar = A a Is τα

(2)

Qconv = h e A(Te − Ta)

(1) Only the steady state is considered for all energy balance equations. (2) The properties of the materials in the system are independent with temperature. (3) The increasing of the pressure on the solid contact surface can create a greater contact area, thus reducing the contact thermal resistance. Simultaneously, the use of thermal grease can markedly reduce the thermal contact resistance, perhaps as much as 75

Q rad =

εe σ A(T e4

−

T a4)

(3) (4)

where Qsolar is the solar energy absorbed by the ETSC, Qin is the available thermal energy translated by the ETSC, Qconv is the convection heat loss from the outer surface of the ETSC to the ambient environment, Qrad is the radiation heat loss from the outer surface of the ETSC to the ambient environment, A, Aa, Is, τ, α, he, εe, σ, Te and Ta are 6

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Fig. 10. The output power curves of the STEG used different PCMs: a) overall contrast, b) 50 °C, c) 60 °C, d) 70 °C, and e) 80 °C on March 25, 2019.

there is no heat conducted from PCMs to the ETSC. As a result, the heat transfer efficiency of PCMs can be defined as

the outer surface area of the external tube, the area of the absorbing surface of the ETSC, the solar irradiation, the transmissivity of the tubular glass, the solar absorptivity of the absorbing coating, the convective heat transfer coefficient between the external tube surface and ambient environment, the emissivity of external tube, the StefanBoltzmann constant, the temperature of the external tube surface and the ambient environment temperature, respectively. According to the Eqs. (1) – (4), we can obtain the solar energy conversion efficiency of the ETSC,

ηs =

4 A a Is τα − h e A(Tsur − Ta) − εe σ A(T sur − T a4) Q in = Qsolar A a Is τα

ηP = 1

(6)

Then the heat is conducted to the hot sides of the TEMs by MCHP. Applying the energy balance to the MCHP, the equation can be expressed as below,

(5)

Qin is subsequently absorbed and stored by the PCMs which are filled in the ETSC. The PCMs is sealed in the inside tube and the heat is conducted from the inside tube to the PCMs when phase transition undergoes; therefore, the convection heat loss and the radiation heat loss between PCMs and environment are non-existent, meanwhile,

EPCMs = Econd + Econv + Erad

(7)

EPCMs = Q in

(8)

Econv = hhp Ahp (Tp − Ta)

(9)

Erad = εhp σ Ahp (T P4 − T a4)

(10)

where EPCMs is the heat absorbed and stored by the PCMs, Econd is the heat conducted through the MCHP, Econv is the convection heat loss from the MCHP to the ambient environment, Erad is the radiation heat 7

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Fig. 11. Variations of a) the environment temperature, b) the temperature of the different PCMs, c) the Thot, Tcold, and ΔT of the TEM used 50 °C PCMs, d) the Thot, Tcold, and ΔT of the TEM used 60 °C PCMs, e) the Thot, Tcold, and ΔT of the TEM used 70 °C PCMs, f) the Thot, Tcold, and ΔT of the TEM used 80 °C PCMs, g) the open circuit voltage of the STEG used different PCMs, and h) the output power of the STEG used different PCMs during the test period of no solar irradiation on March 25, 2019.

loss from the MCHP to the ambient environment, hhp, Ahp, εhp and TP stand for the convective heat transfer coefficient between the MCHP and ambient environment, the area of the MCHP exposed to the ambient environment, the emissivity of the MCHP and the temperature of the MCHP exposed to the ambient environment, respectively. The heat transfer efficiency of the MCHP can be express as

ηP =

Q in − hhp Ahp (Tp − Ta) − εhp σ Ahp (T P4 − T a4) Econd = EPCMS Q in

V = α ΔT

(12)

ΔT = Thot − Tcold

(13)

α = NαPN

(14)

where α is the Seebeck coefficient of a single TEM, αPN is the Seebeck coefficient of a single p-n junction, N is the number of p-n junctions in a TEM, Thot is the temperature of the hot side, Tcold is the temperature of the cold side, and ΔT is the temperature difference between the hot side and cold side. The heat rate absorbed by a single TEM is

(11)

When the heat reaches the hot sides of the TEMs, the temperature gradient appears, and the Seebeck effect begins to work. The open circuit voltage produced by a single TEM is

QH = α Thot I + Kin ΔT −

8

1 RinI2 2

(15)

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Lc = L +

t 2

(21) 1

m=

hf P h (2z + 2t) ⎤2 ≈ =⎡ f ⎥ ⎢ k f Af kf tz ⎦ ⎣

2hf (Whenthez > > t) kf t

ΔTf = Tf − Ta

(22) (23)

where hf is the convective heat transfer coefficient between the fin and ambient environment, kf is the thermal conductivity of the fin, Af is the cross-sectional area of the fin and P is the perimeter of the fin. L, z, t, and Tf are the length of a piece of fin, the width of a piece of fin, the thickness of a piece of fin, and the temperature at the bottom of the fin, respectively. The electrical power production of the STEG can also be expressed as

2P = QH − NQ loss

(24)

where N is the number of the fins.

Fig. 12. Image of the reassembled STEG.

4. Results and discussion The heat rate dissipated by a single TEM is

QC = α Thot I + Kin ΔT +

1 RinI2 2

4.1. Effect of the EG on the thermal response ability of the PCMs. (16)

In order to reach the phase transition temperature as soon as possible for the PCMs and make the hot side of the TEM has a stable temperature rapidly, the PCMs must have a fast thermal response to the heat. We had set up a group of comparative test to verify the thermal response ability of the PCMs. Placed 200 ml of pure 80 °C paraffin and 200 ml of EG/80 °C paraffin composite in a vacuum oven (Fig. 3). Two K-type thermal-couples were inserted into these two samples to record the temperature variation. The onset temperature of the vacuum oven was the environmental temperature and the terminal heating temperature was set as 90 °C. The samples were heated in the condition of vacuum. The T-t curves are illustrated in Fig. 4. It is evident that the temperature of the PCMs has been reached the solid-liquid phase transition temperature platform in 180 min, while the pure paraffin takes 420 min to reach this platform. When the paraffin is infiltrated into the EG and is wrapped by the microporous of the EG, the paraffin is segregated into some tiny parts and the heat transfer area is increased. The heat is rapidly transferred to these tiny paraffin blocks through the EG network which has a high thermal conductivity, then these tiny paraffin blocks melt speedily and synchronously. Thus the thermal response ability of PCMs is enhanced. However, when the heat is conducted in the pure paraffin, the external paraffin is melted firstly, and then the heat is transferred to the internal paraffin. The low thermal conductivity of the pure paraffin results in a long heat transfer process and a slow temperature rising rate.

where I is the current, Kin is the thermal conductance of the TEM and Rin is the internal electrical resistance of a single TEM. Calculation of electrical power production of a single TEM is based on the open circuit voltage and the internal electrical resistance, it can be described as below,

P=

V2open (17)

Rin

In accordance with the Eqs. (15)–(17), the power generation efficiency of the whole STEG is defined as

ηT =

2P QH

(18)

However, it is difficult to obtain the QH from the Eq. (15). So we can use another form to represent the QH as QH = Econd . In this condition, the ηT can be expressed as

ηT =

2V2open 2P = 4 Econd Rin [A a Is τα − h e A(Tsur − Ta) − εe σ A(T sur − T a4) − hhp Ahp (Tp − Ta) − εhp σ Ahp (T P4 − T a4)] (19)

Finally, the heat is released into the ambient environment by the fins. The heat loss from each piece of fin is

Q loss = (tanhmL c) hf Pkf Af ΔTf

4.2. The anti-leakage effect of the PCMs

(20)

If there is no sealed vessel, the liquid paraffin will overflow after the

Fig. 13. Variation of a) the solar irradiation and b) the environment temperature on September 21, 2019. 9

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Fig. 14. Curves of a) the temperature variation of the PCMs, b) the Thot, Tcold, and ΔT variation of the TEM, c) the open circuit voltage, and d) the output power of the STEG used 80 °C PCMs on September 21, 2019.

ETSC; therefore, the PCMs in ETSC was gradually heating-up. With the increasing of the solar irradiation intensity, there is a rapidly upward tendency for the temperature of all kinds of PCMs in the initial time. Then the temperatures of 50 °C PCMs and 60 °C PCMs reach their respective phase transition temperature platforms until the ETSC is not exposed to the sunlight, while the temperatures of 70 °C PCMs and 80 °C PCMs do not reach the corresponding phase transition temperature platforms as that of 50 °C PCMs and 60 °C PCMs. This phenomenon demonstrates that the thermal energy which is converted from the solar energy is sufficient to ensure that the PCMs undergoes solid–liquid phase transition and offset the heat transmitted to the TEMs by MCHP in the case of 50 °C PCMs and 60 °C PCMs. For 70 °C PCMs and 80 °C PCMs, the melting points are higher than that of 50 °C PCMs and 60 °C PCMs. The heat is stored in the PCMs in the form of sensible heat until the temperature reaches the melting point, hence the 70 °C PCMs and 80 °C PCMs need more thermal energy than 50 °C PCMs and 60 °C PCMs to reach the solid–liquid phase transition points. The phase transition of paraffin is not at a fixed temperature point, but in a temperature range. From the temperature curve of the 70 °C PCMs, it can be seen that the temperature has been exceed 70 °C during the period of the highest solar irradiation intensity. For 80 °C PCMs, the maximum temperature is 73.1 °C. Combining with Fig. 1, there are still a part of paraffin undergoes solid–liquid phase transition in 70 °C PCMs and 80 °C PCMs. Fig. 8 (a)–(d) are the curves of the hot side temperature (Thot), cold side temperature (Tcold), and the temperature difference between these two sides (ΔT) of a TEM used in the STEG integrated with different PCMs on March 25, 2019. Fig. 8 (e) is the ambient environment temperature curve. It is clear from the Fig. 8 that the variation tendencies of the Thot in these four cases are consistent with the temperature variations of the corresponding PCMs as shown in Fig. 7, respectively. Therefore, for the STEG used 50 °C PCMs and 60 °C PCMs, the TEMs have a very stable heat sources when these two kinds of PCMs enter into their respective phase change platforms. For the STEG used 70 °C PCMs and 80 °C PCMs, the stability of Thot is not as good as that of 50 °C PCMs and 60 °C PCMs, but the fluctuation of Thot is in a small range after the initial rising period. The Tcold is mainly influenced by the Thot and the ambient environment. PCMs endows the STEG with a stable heat source and the

solid-liquid phase transition, which causes a great inconvenience for us to use the pure paraffin directly. In this section, we chose 80 °C pure paraffin and 80 °C PCMs to verify the anti-leakage ability of the PCMs. Put 10 g of pure paraffin and 10 g of PCMs on the centers of the filter papers whose diameters are 18 cm, respectively. Placed a piece of white paper under these two filter papers. Then put the samples in a vacuum oven. The temperature of vacuum oven was set as 90 °C. The adsorption of the filter papers was observed at 0 h, 3 h, 6 h, 12 h, and 24 h as shown in Fig. 5. Obviously, the filter paper under the pure paraffin sample has been contaminated by the liquid paraffin entirely at 3 h, and the white paper under the filter paper has also been stained with the liquid paraffin. As the heating time continues, the area of the white paper stained by the liquid paraffin becomes larger and larger. At 24 h, the pure paraffin sample has almost completely melted. While the filter paper around the PCMs sample does not appear the situation of impregnating by the liquid paraffin in 24 h test period. When we remove the samples from the filter papers after 24 h, we can see that only the part of filter paper under the PCMs sample have a slight liquid paraffin impregnating. The results indicate that the designed PCMs has few leakage of the liquid paraffin in the 24 h when the phase transition undergoes, and its antileakage ability is excellent. 4.3. Performance comparison of the novel STEG integrated with different PCMs In this section, we chose four kinds of PCMs with different phase transition temperatures (50 °C, 60 °C, 70 °C, and 80 °C, respectively) to validate the thermal management effect on the novel STEG. The solar irradiation intensity during the test time is illustrated in Fig. 6. It can be clearly seen that the solar irradiation intensity increased progressively from 8:00, and reached the maximum (1071.5 W/m2) at 13:00, then decreased gradually. At 17:47, the experimental site where the STEG was placed was no longer exposed to the sunlight due to the obscuring of the surrounded taller buildings. Under the condition of Fig. 6, the temperature variation profiles of the four chosen PCMs used in the novel STEG on March 25, 2019 are presented in the Fig. 7. When the STEG was placed under the sunlight, the solar energy was started to be converted into the thermal energy by 10

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Fig. 15. Variations of a) the environment temperature, b) the temperature of the 80 °C PCMs, c) the Thot, Tcold, and ΔT of the TEM used 80 °C PCMs, d) the open circuit voltage of the STEG used 80 °C PCMs, and e) the output power of the STEG used 80 °C PCMs during the test period of no solar irradiation on September 21, 2019.

environment temperature is fluctuant; therefore, we can get the variation curves of the ΔT which are relatively stable and slow rising when solid-liquid phase transition occurs. The total open circuit voltages (V) of the novel STEG integrated with different PCMs on March 25, 2019 are shown in Fig. 9. We can clearly see that the V of all cases are stable and rising slowly during the phase change of the PCMs. This is consistent with the variation of the ΔT. When the solar irradiation disappeared, V decreased. The two TEMs are symmetric in the STEG, and we define Vopen as the open circuit voltage of a single TEM; therefore, the V equals to twofold of the Vopen. V is closely linked with ΔT according to the Seebeck effect (Vopen = αΔT). If we associate Fig. 8 with Fig. 9, it is evident that the ΔT is the smallest, and the V is the smallest yet in the case of 50 °C PCMs, while for 80 °C PCMs, the ΔT is the largest, and the V is also the largest. The average V corresponding to the phase transition temperature platform of the STEG used 50 °C PCMs is 1.544 V and the average V of that of 80 °C PCMs is 1.790 V. Meanwhile, the maximum V is 2.116 V. According to Eq. (17), we can calculate the output power of the system as shown in Fig. 10. The square of Vopen in the equation amplifies the fluctuation of data. The maximum output power of the STEG with 80 °C PCMs is 1.279 W. It is worth noticing that the designed STEG still has output electricity more than three hours when the solar irradiation disappears in all cases as shown in Fig. 11, which is mainly due to the latent heat of the PCMs. From Fig. 7, we can see that the decrease of the solar

irradiation intensity has led to a decline of the temperature of PCMs in the ETSC during the test time in the afternoon, but a part of the PCMs is still in the state of phase transition at this time because of the widely phase transition temperature range of the paraffin. When the solar irradiation disappears, the photothermal conversion of the ETSC is terminated immediately and the STEG lost the heat source of solar energy. However, the latent heat stored in the paraffin which still undergoes phase transition begins to play an important role at this time. In addition, a small amount of the sensible heat stored in the PCMs also plays a certain role. Meantime, the vacuum interlayer inside the ETSC has a good heat preservation effect on the PCMs, so the PCMs can continue to maintain a relatively high temperature for a long time. All of this ensure that the thermal energy still can be provided to the TEMs from the PCMs constantly and the STEG still has the output electricity continuously under the condition of no sunlight as shown in Fig. 11(c), (d), (e), (f), (g), and (h). Nevertheless, this part of the thermal storage is consumed gradually and the continuous reduction of the environment temperature caused by no sunlight will lead to the fast heat dissipation of the whole system as the test time goes on, so the variation of the temperature of PCMs shows a gradually and slowly downward tendency without the external thermal energy supplement from the time of the solar irradiation just disappears to the end of the test as shown in Fig. 11(b). As a result, the output electricity of the STEG changes same as the variation of the temperature of PCMs in the ETSC, which also 11

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Fig. 16. Comparison between the experimental open circuit voltage and calculated open circuit voltage of the STEG used a) 50 °C PCMs, b) 60 °C PCMs, and c) 80 °C PCMs.

of the output power of the STEG. Meanwhile, the output power of the novel STEG can be kept at a high level for a long time. And the latent heat of the PCMs can make the STEG continue to output the electricity without light more than three hours.

shows a trend of slow decrease and has no stop during this period of more than three hours as shown in Fig. 11(g) and (h). Under the above solar irradiation intensity and environment temperature, the temperatures of 70 °C PCMs and 80 °C PCMs did not reach the corresponding phase transition temperatures; therefore, in order to further explore the potential of this novel STEG, we reassembled a device again (as shown in Fig. 12). On the basis of the previous structure, we turned the support plate of the STEG into a mirror to enhance the light on the back of the ETSC. This time, we directly tested the thermal management effect of 80 °C PCMs on this novel STEG on September 21, 2019. We did not choose the summer with the strongest solar irradiation intensity and hot weather, which is due to the fact that the maximum operating temperature of the selected TEM is 80 °C. In summer, the TEM will be damaged if the temperature of the PCMs in the ETSC is too high. We can see that the solar irradiation intensity and environment temperature on September 21, 2019 were higher than that on March 25, 2019 when compared Fig. 13 with Fig. 6, and coupled with the reflection of the mirror to sunlight; the temperature of 80 °C PCMs in the ETSC entered the corresponding phase transition temperature region. The higher temperature of the PCMs leads to a higher output power of the STEG as shown in Fig. 14. In Fig. 14(c), the maximum V of the STEG reaches 2.697 V, and when the 80 °C PCMs enters the phase transition platform, most of the measured V float between 2 V and 2.697 V. Meanwhile, the maximum output power is 2.08 W as shown in Fig. 14(c). As we can see from the results in Fig. 15 which is similar to the conclusions on March 25, 2019, the use of PCMs enables the STEG to have continuous output electricity for a long time when there is no solar irradiation. At the end of the test, the system's open circuit voltage is still 0.178 V as shown in Fig. 15(d). These results have a great advantage over the current studies on STEG. In general, the utility of the PCMs is helpful to improve the stability

5. Comparison of the realistic experiment and mathematic model In this section, we verify the accuracy of the mathematical model which was established according to the realistic heat transfer process in the STEG, and the parameter Vexp/Vthe is used to evaluate the accuracy as shown in Fig. 16. Among them, Vexp is the experimental V and Vthe is the theoretical V calculated by the mathematical model. When the PCMs undergo phase transition, the latent heat will have the thermal management effect to the STEG; therefore, we choose the Vexp every one minute during 13:00–15:00 to compare with the corresponding Vthe. In this period, the temperatures of 50 °C PCMs, 60 °C PCMs, and 80 °C PCMs have entered their respective phase transition temperature regions and the realistic solar irradiation intensity is about 1000 W/m2. According to the equations in the mathematical model, we calculate that the values of the Vthe in the case of 50 °C PCMs, 60 °C PCMs, and 80 °C PCMs are 1.575 V, 1.566 V, and 2.523 V under the solar irradiation of 1000 W/m2, respectively. The results in Fig. 16 show that most of the Vexp/Vthe values are between 0.90 and 1.10 in the case of 50 °C PCMs, 60 °C PCMs. For the STEG used 80 °C PCMs, almost all Vexp/Vthe values are in 0.80–1.00. Hence, the realistic values are in good agreement with the calculated values. These results show that the mathematical model for the designed STEG has a high accuracy and can provide a good guidance for the design of STEG. 6. Conclusion A novel STEG based on the EG/paraffin composites, ETSC, MCHP, 12

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TEMs, and heat fins was designed and the thermal management effects of the modified PCMs with different melting points (50 °C, 60 °C, 70 °C, and 80 °C) on this STEG were investigated in this study. The ETSC which has been commercialized could efficiently convert the solar energy into the thermal energy, and the thermal energy would be stored by the modified PCMs in the forms of sensible heat and latent heat. When the phase transition occurred, the instantaneous solar energy will be rapidly transformed into a stable heat source to the TEMs through the MCHP which could turn low heat flux to high heat flux at a nearly constant temperature. As highlighted here, the porous structure and high thermal conductivity of the EG could well solve the problems of the paraffin which are liquid leakage and low thermal conductivity. The results show that the output power of this novel STEG will become stable if the PCMs enter the phase transition temperature region. Simultaneously, the values of the output voltages were at a high level and it increased with the rise of melting points. The maximum V was 2.697 V in the case of 80 °C PCMs on September 21, 2019. Even in the case of 50 °C PCMs, the average V in the stable output region was still as large as 1.544 V. When the light disappeared, the latent heat of the PCMs could also make the STEG continue to have the output power until the latent heat was exhausted. We hope that this design will open up the paths for the application of the high performance PCMs in the STEG.

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CRediT authorship contribution statement Xiaohang Luo: Writing - original draft, Methodology, Data curation, Software. Quangui Guo: Conceptualization, Resources, Writing review & editing, Validation. Zechao Tao: Investigation, Funding acquisition, Formal analysis. Yanjuan Liang: Supervision, Visualization. Zhanjun Liu: Project administration. 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. Acknowledgement This work was supported by the Youth Innovation Promotion Association CAS (Grant No. 2017205) and sponsored by Foshan Xincheng Government (Grant No. 2K-2017-016). References [1] Parida B, Iniyan S, Goic R. A review of solar photovoltaic technologies. Renew Sust Energ Rev 2011;15:1625–36. [2] Sudharshan KY, Praveen Kumar V, Barshilia Harish C. Performance evaluation of a thermally concentrated solar thermo-electric generator without optical concentration, Sol Energy Mat Sol. Cell 2016;157:93–100. [3] Smil V. General energetics: energy in the biosphere and civilization. 1st ed. New York: John Wiley & Sons; 1991. [4] Champier Daniel. Thermoelectric generators: a review of applications. Energ Convers Manage 2017;140:167–81. [5] He W, Zhang G, Zhang XX. Recent development and application of thermoelectric generator and cooler. Appl Energy 2015;143:1–25.

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