Experimental Study of the Thermoelectric Conversion Characteristics of a Device Combining a TPCT and TGs

Abstract

In this paper, the thermoelectric conversion characteristics of a device combining a TPCT and TGs are studied. The experimental devices consist of four parts: TPCT heat transfer module, cooling and heat dissipation module, thermoelectric power generation module, and data collection module. The effects of different heating powers (100 W, 200 W, 400 W, and 600 W) and different liquid filling rates of the TPCT (10%, 25%, 35%, and 45%) on the heat transfer performance and the power generation performance of the device are studied. The research indicates that the impact of the liquid filling rate on heat transfer and power generation performance is less significant than that of heating power. As the heating power increases, both the heat transfer and power generation performance of the device will improve and is finally in a relatively stable state. The thermal resistance at the liquid filling rate of 10% is the smallest, roughly around 0.11 °C/W. At a heating power of 200 W, the TPCT at the liquid filling rate of 10% has the largest heat transfer efficiency, which is 83.36%. The maximum values of power generation efficiency and net power generation efficiency are 2.27% and 3.10%, respectively.

1. Introduction

Coalfield fires, which are the burning or overcast combustion of underground coal seams, are a widespread geological challenge worldwide. Coalfield fires cause great waste of coal resources and serious damage to the ecological environment. It is also a serious threat to human health and safety and hinders social and economic development [1]. Traditional means of coal fire management mainly include stripping, drilling, water injection, grouting, and covering loess, which are prone to ecological damage and have limited cooling effect, and the coalfield fire is not easily extinguished completely [2]. A large amount of water resources is wasted in the process of fire extinguishing, which easily causes groundwater pollution. About 1000 GW of waste heat energy from coalfield fires worldwide every year is wasted and not effectively utilized, which is equivalent to 2.5 times of the total power generation of 500 nuclear power plants worldwide and more than the sum of global water power generation [3]. If the waste heat resources can be recovered and effectively used, then the coalfield fire treatment process can be accelerated and water resources can be saved to avoid ecological damage and resource waste, which will produce huge ecological and environmental value and social and economic benefits.

In order to recover waste heat resources and convert them into renewable resources, a good solution is to apply two-phase closed thermosiphons (TPCTs). The TPCT has a simple structure, low cost, and high heat transfer efficiency. The heat can only be transferred from the bottom to the top of the TCPT in one direction, due to the effect of gravity [4]. TPCTs are used in many fields and have the advantages of excellent heat transfer performance, environmental adaptability, low economic cost, energy saving, and environmental protection [5]. In the field of permafrost ground temperature control and road snow melting, the excellent thermal conductivity of the TPCT, the absence of external power source and maintenance, and the good applicability to different engineering environments make it become an important method [6]. Studies have shown that TPCTs can reasonably solve the air–TPCT–soil coupled heat transfer problem of TPCT embankments [7]. It effectively attenuates the thermal effect of sunward slope, cools the subsurface permafrost, and ensures the stability of the permafrost foundation [8,9]. TPCTs are used to transfer the heat stored in the subsurface soil or groundwater to the road surface to melt snow and ice. It can overcome the drawbacks of traditional snow melting techniques, substantially increase the temperature of concrete pavements, and prove that the system can operate for a long time [10,11,12]. In industrial production, TPCTs are also widely used. In the nuclear industry, passive heat dissipation from TPCTs is used to remove decay heat from spent fuel pools in the event of a nuclear power plant blackout [13,14,15]. Adsorption chillers with a separated two-phase closed thermosiphon heating process allow the system to have fewer moving parts and reduced building size, while improving the performance factor and cooling power ratio of the cooling system [16]. The use of TPCTs can improve the fluid temperature distribution in the oilfield wellbore and can effectively transfer the heat contained in the high-temperature fluid at the bottom of the wellbore to the lower-temperature fluid in the upper part of the wellbore, increasing the oil production rate [17,18]. Energy-efficient technology for phosphate production was developed using two-phase closed thermosiphon [19]. A cryogenic TPCT was made using copper tubes, flexible bellows hoses with nitrogen fluid, and its heat transfer properties were used to design a thermally stable system for RED100 detectors that can provide heat transfer rates of up to 100 W in the temperature range of 100–80 K [20]. The application of TPCTs to the field of geothermal extraction has improved the efficiency of heat extraction [21]. The heat transfer performance of solar collectors was enhanced using TPCTs [5,22]. In the field of coalfield fires, researchers have also used TPCTs to remove heat sources and extract heat energy. Li et al. [23] established a coal pile–TPCT heat transfer model and used a TPCT to control the coal pile temperature below 80 °C, which had a significant effect on coal pile heat removal. Zhong et al. [24] used a TPCT to suppress heat production during coal spontaneous combustion, and the use of CuO nanofluidic material could improve the heat transfer performance of the TPCT by 27.9%. However, the study only considered the transfer of heat energy from coalfield fires, and further research is needed on heat utilization and heat conversion.

Therefore, after waste heat from coalfield fires is extracted and recovered, the next issue to be considered is to solve the problem of how waste heat from coalfield fires is utilized and converted, and thermoelectric power generation is a very suitable solution. Thermoelectric power generation uses the Seebeck effect of thermoelectric materials to directly convert thermal energy into electrical energy, which is a new green, environmentally friendly, and pollution-free power generation technology [25]. Currently, commercial thermoelectric power generation modules are generally composed of multiple PN galvanic arms connected in series, and the hot and cold ends are covered using ceramic sheets to form a temperature differential generator with multiple PN junctions [26]. Temperature differential generators (from AltaRock Energy, Inc., Sausalito, CA, USA) can convert low-taste heat into clean electrical energy and have the advantages of flexible installation, noiseless operation, environmental friendliness, high applicability, low maintenance cost, and long service life [27]. Therefore, thermoelectric power generation is also used in many fields. The combination of TGs with biomass burners can power small-scale electrical devices [28,29,30]. It is combined with solar energy for the co-production of solar thermal and electrical energy [31,32]. In the field of low-temperature geothermal utilization, it converts heat flow from the upper soil layer into electrical energy [33,34]. It is combined with small nuclear reactors to supply electrical energy to space probes [35,36]. In the automotive field, it recycles the heat energy from the exhaust of the car [37,38,39]. Using the function of TGs energized and cooled to dissipate heat for processor chips and electronic devices [40,41,42]. In the field of coalfield fire utilization, researchers have also applied thermoelectric power generation. Su et al. [1] concluded that thermoelectric power generation has the advantages of good heat source adaptation, easy assembly, and no location dependence by comparing a series of heat recovery modes of KC (Carina cycle) and ORC (Rankine cycle). It was proved to be practical in the field of coalfield fire utilization. Shi et al. [3] used the temperature difference between the heat transfer medium and the cooling medium to provide energy for thermoelectric power generation, and achieved a single-hole power generation power of 174.6 W in the Daquan Lake fire area in Xinjiang. Su et al. [2] carried out thermoelectric power generation model experiments, analyzed the main performance indexes of thermoelectric power generation, and designed a distributed thermoelectric power generation device, which can achieve a maximum output power of 700 W at a temperature difference of 80 °C. However, the study only considers the thermoelectric power generation technology for heat energy, and there is less research on heat transfer.

The above studies on the recovery and utilization of waste heat resources in coalfield fires have considered only TPCT heat transfer or thermoelectric power generation alone. Recently, the system combining TPCT and thermoelectric power generation technology has been studied and applied. Su et al. [43] studied the temperature gradient of the TPCT and the characteristics of temperature difference power generation. Deng et al. [44] established a thermal energy recovery system combining TPCT and thermoelectric power generation in the Sandaoba fire area in Xinjiang and evaluated the recovered heat. However, these studies do not consider the influence of TPCT heat transfer and temperature difference power generation together. Studies that consider how the heat transfer from the heat source and the TPCT parameters together affect the thermoelectric conversion performance of the system are lacking.

Coalfield fires are a global challenge, causing huge waste of resources and environmental problems. The vast heat resources from coalfield fires have great economic and ecological value [1]. The efficient heat transfer performance of two-phase closed thermosiphons (from Chenyi Heat pipe Company, Harbin, China) (TPCTs) and the direct power generation performance of thermoelectric generators (from Seebeck Company, Changsha, China) (TGs) are well suited for the recovery and utilization of waste heat resources in coalfield fire areas. It is necessary to study the recovery and utilization of waste heat resources from coalfield fires by studying TPCT heat transfer and thermoelectric power generation. Analyzing how different heat source heat transfers and TPCT parameters affect the system heat transfer performance and power generation performance, which is helpful to select the appropriate TPCT parameters for temperature level of heat sources for coalfield fires, will ensure that the thermoelectric conversion performance is optimal. This paper preliminarily investigates the thermoelectric conversion characteristics based on a two-phase closed thermosiphon and a temperature difference generator. By building an experimental setup, the effects of heating power (100 W, 200 W, 400 W, and 600 W) and liquid filling rate of the TPCT (10%, 25%, 35%, and 45%) on the heat transfer performance and power generation performance of the device are experimentally investigated. Combining a two-phase closed thermosiphon with thermoelectric power generation can bring out the advantages of each. It will have broad application prospects in the field of coalfield fire waste heat resource recovery and utilization.

2. Materials and Methods

2.1. Experimental Devices

Figure 1 shows the experimental devices of thermoelectric conversion based on a TPCT and TGs. The effect of the liquid filling rate of the TPCT and heating power on the heat recovery and utilization of the experimental device is studied and analyzed in terms of both heat transfer and power generation. The experimental devices consist of four parts: TPCT heat transfer module, cooling and heat dissipation module, thermoelectric power generation module, and data collection module.

2.1.1. TPCT Heat Transfer Module

The TPCT heat transfer module consists of a heating ring, a heating power controller and a TPCT. The heating power of the heater ring (from Safety Valley, Xuzhou, China) is in the range of 0–600 W and can be adjusted. The TPCT evaporation section is heated by heat conduction. The heating power controller can change the heating power of the heating ring by adjusting the voltage and current, and the adjustment range is 0–600 W. The parameters of TCPT are as follows: the length is 1000 mm; evaporation section is 500 mm; condensation section is 500 mm; outer diameter is 38 mm; thickness of TPCT wall is 3 mm; liquid filling ratio is 10%, 25%, 35%, and 45%; liquid filling medium is distilled water. The evaporation section of the TPCT is entirely located in the heating ring. The liquid in the evaporation section of the TPCT is heated to evaporate and liquefies in the condensation section when it is cold, releasing heat. Then, the condensing section transfers the heat to the thermoelectric power generation module by heat conduction.

2.1.2. Cooling and Heat Dissipation Module

The cooling and heat dissipation module consists of a water storage tank, a water pump and a heat sink. The water pump can increase the flow of cold water in the radiator, thus reducing the temperature of the cold end of the thermoelectric power generation module. There are channels inside the radiator that can circulate cold water, it has cooling fins arranged on the outer surface, and there are two cooling methods: water cooling and air cooling, which can enhance the cooling effect.

2.1.3. Thermoelectric Power Generation Module

The thermoelectric power generation module uses four TGs (from Seebeck Company, Changsha, China). The model number is TEG1–241-1.4–1.2. The two TGs on each side of the TPCT are connected in series and then in parallel. The thermoelectric power generation module is connected to the sliding resistor and then connected to the power meter. When the water in the cooling heat sink module flows through the heat sink, a temperature difference is created on both sides of the thermoelectric power generation module. Adjusting the radiator water flow can change the temperature of the condensing section of the TPCT, which can change the temperature difference of the temperature differential power module. The average of the temperatures measured by the two K-type thermocouples at the hot end of the differential temperature generation module is defined as the hot end temperature. The average of the temperatures measured by the two K-type thermocouples at the cold end is defined as the cold end temperature.

2.1.4. Data Acquisition Module

The data acquisition module consists of a PC processor, a temperature data acquisition device, nine K-type thermocouples, a power meter, and a flow meter. K-type thermocouple model is HH-K-24-SLE (from Zetian Company, Xuzhou, China), measuring temperature range is −73−704 °C, and accuracy is 0.5 °C. There are 13 thermocouples laid out, distributed on the surface of the TPCT wall and the hot and cold ends of the thermoelectric power generation assembly. The power meter is used to measure the open-circuit voltage, load voltage, and load power of the temperature difference generation module. The flow meter is used to measure the flow of cold water in the cooling heat sink module, its model is vortex flow meter MJ-A68-1 (from Zetian Company, Xuzhou, China), and its applicable flow range 0.2–6 L/min. Temperature, voltage, power, flow rate, and other data are uniformly processed by the PC processor.

2.1.5. Experimental Methods

To study and analyze the effect of the liquid filling rate of the TCPT and heating power on the heat recovery and utilization of the experimental devices, the heat transfer performance and power generation performance of TPCTs with four liquid filling rates (10%, 25%, 35%, and 45%) at different heating powers (100 W, 200 W, 400 W, and 600 W) are studied. The TPCT is heated for 50 min at four specific heating powers until the temperatures were steady. Then, the cooling module is turned on to observe the parameters of TCPTs and TGs under different temperature conditions. During the monitoring experiment, the temperature at different distances along the TCPT (10 cm, 30 cm, 50 cm, 70 cm, and 90 cm), cold and hot end temperature of TGs, ambient temperature, cooling water flow, open-circuit voltage of TGs, load current of TGs, and load power of TGs are monitored.

2.2. Principle and Calculation

During the two-phase closed thermosiphon heat transfer and thermoelectric conversion experiment, the main destination of the heat released from the heating source is two parts. One part of the heat is transferred to the condensing section of the TPCT through the evaporation section of the TPCT by heat absorption. The other part of the heat is released to the ambient atmosphere in the form of radiation and convection heat transfer at the wall of the evaporation section of the TPCT. Then, the heat that is transferred to the condensing section of the TPCT goes to three main parts. One part is converted into electricity by the temperature difference generator. One part is carried away by the radiator in the form of hot water. One part is released by the exposed condensing section of the TPCT in the form of radiation and convection heat transfer.

Therefore, in order to accurately calculate parameters such as TPCT heat transfer efficiency and thermoelectric efficiency, a series of calculations are required for the heat transfer process of the device. The heat transfer losses in the experimental heating process of the TPCT are radiation heat transfer losses and convective heat transfer losses. Because the convective heat transfer coefficient between the TPCT material and the air is very low, it is known that the main heat transfer loss is the radiation heat transfer loss.

2.2.1. Heat Transfer Loss

Radiation Heat Transfer Loss

TPCT radiation heat transfer losses include radiation heat transfer losses in the evaporation section and radiation heat transfer losses in the condensation section. The radiative heat transfer from the closed cavity consisting of two blackbody surfaces is:

$${\Phi }_{1,2}=A_1{E_{\mathrm{b}1}X}_{\mathrm{1,2}}-A_2{E_{\mathrm{b}2}X}_{\mathrm{2,1}}=A_1{X}_{\mathrm{1,2}}\left(E_{\mathrm{b}1}-E_{\mathrm{b}2}\right)=A_2{X}_{\mathrm{2,1}}\left(E_{\mathrm{b}1}-E_{\mathrm{b}2}\right)$$

(1)

${\Phi }_{1,2}$ is the radiation heat transfer. $A_1$ is the area of object 1. $A_2$ is the area of object 2. $X_{\mathrm{1,2}}$ and $X_{\mathrm{1,2}}$ are the angular coefficients of radiative heat transfer. ${ E}_{\mathrm{b}1}$ is the radiation force of object 1, $E_{\mathrm{b}1}=\sigma {T_1}^4$. $E_{\mathrm{b}2}$ is the radiation force of object 2, $E_{\mathrm{b}2}=\sigma {T_2}^4$.

$$X_{\mathrm{1,2}}={\displaystyle \frac{2}{\pi xy}}\{{\ln \left[{\displaystyle \frac{\left(1+x^2\right)\left(1+y^2\right)}{1+x^2+y^2}}\right]}^{{\displaystyle \frac{1}{2}}}-x\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}x+x\sqrt{1+y^2}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}{\displaystyle \frac{x}{\sqrt{1+y^2}}}-y\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}y+y\sqrt{1+x^2}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}{\displaystyle \frac{y}{\sqrt{1+x^2}}}\}$$

(2)

$\sigma$ is the Stephan–Boltzmann constant, which is the blackbody radiation constant. 5.67 × 10⁻⁸ W/(m²·K⁴).

TPCT radiation heat transfer is consistent with radiation heat transfer from a closed cavity consisting of two diffuse ash surfaces. The radiative heat transfer in the closed cavity consisting of two diffuse ash surfaces is:

$${\Phi }_{\mathrm{1,2}}={\displaystyle \frac{E_{\mathrm{b}1}-E_{\mathrm{b}2}}{\frac{1-{\epsilon }_1}{{\epsilon }_1{A}_1}+\frac{1}{A_1{X}_{\mathrm{1,2}}}+\frac{1-{\epsilon }_2}{{\epsilon }_2{A}_2}}}$$

(3)

Using A₁ as the calculated area, the above equation can be rewritten as:

$${\Phi }_{1,2}={\displaystyle \frac{A_1\left(E_{\mathrm{b}1}-E_{\mathrm{b}2}\right)}{\left(\frac{1}{{\epsilon }_1}-1\right)+\frac{1}{X_{\mathrm{1,2}}}+\frac{A_1}{A_2}\left(\frac{1}{{\epsilon }_2}-1\right)}}{={\epsilon }_{\mathrm{s}}A}_1{X}_{\mathrm{1,2}}\left(E_{b1}-E_{\mathrm{b}2}\right)$$

(4)

In Equation (5):

$${\epsilon }_{\mathrm{s}}={\displaystyle \frac{1}{1+X_{\mathrm{1,2}}\left(\frac{1}{{\epsilon }_1}-1\right)+X_{\mathrm{2,1}}\left(\frac{1}{{\epsilon }_2}-1\right)}}$$

(5)

${\epsilon }_1$ is the emissivity of object 1. ${\epsilon }_2$ is the emissivity of object 2. ${\epsilon }_{\mathrm{s}}$ is the emissivity of the system. When the radiating surface of object 1 is a flat or convex surface, $X_{\mathrm{1,2}}=1$, then:

$${\Phi }_{1,2}{={\epsilon }_{\mathrm{s}}A}_1\left(E_{\mathrm{b}1}-E_{\mathrm{b}2}\right)$$

(6)

The system emissivity is:

$${\epsilon }_{\mathrm{s}}={\displaystyle \frac{1}{\frac{1}{{\epsilon }_1}+\frac{A_1}{A_2}\left(\frac{1}{{\epsilon }_2}-1\right)}}$$

(7)

When the surface area $A_2$ is much larger than $A_1$, $A_1/A_2\to 0$. Surface 1 is a radiant heat transfer system with a non-concave surface. Then, Equation (4) is:

$${\Phi }_{1,2}{={\epsilon }_{1}A}_1\left(E_{\mathrm{b}1}-E_{\mathrm{b}2}\right)$$

(8)

In this experiment, the TPCT radiation heat transfer is in accordance with the description in Equation (8). Therefore, the TPCT radiation heat transfer loss is:

$$Q_2={\epsilon }_1{A}_1\times 5.67 \mathrm{W}/{\mathrm{m}}^2·K^4\left[{\left(T_1/100\right)}^4-{\left(T_2/100\right)}^4\right]$$

(9)

${\epsilon }_1$ is the TPCT wall emissivity, taken as 0.8.

The above can be obtained from the TPCT convection heat transfer loss being much smaller than the TPCT radiation heat transfer loss. Therefore, the TPCT heat transfer loss is taken as the TPCT radiation heat transfer loss value. TPCT heat transfer losses are:

$$Q_{\mathrm{s}}=Q_2$$

(10)

TPCT heat transfer power $Q_{\mathrm{c}}$ is the difference between heating power $Q_{\mathrm{j}}$ and TPCT heat transfer loss $Q_{\mathrm{s}}$:

$$Q_{\mathrm{c}}=Q_{\mathrm{j}}-Q_{\mathrm{s}}$$

(11)

Convective Heat Transfer Loss

TPCT convective heat transfer losses include convective heat transfer losses in the evaporation section and convective heat transfer losses in the condensation section. The convection between the TPCT and the air exists as natural convection and forced convection. From the equation ($Gr/{Re}^2\ge 10$) of judgment, we know that the effect of forced convection is negligible for natural convection. So, the TPCT convection heat transfer for the large space is natural convection heat transfer. The convective heat transfer between the air and the evaporative section of the TPCT conforms to the large space natural convective heat transfer with uniform wall temperature boundary conditions.

The experimental correlation equation for natural convection in large spaces is:

$${Nu}_{\mathrm{m}}={C\left(GrPr\right)}_{\mathrm{m}}^{\mathrm{n}}$$

(12)

${Nu}_{\mathrm{m}}$ is the number of $Nu$ consisting of the average surface heat transfer coefficient. The subscript $m$ indicates that the arithmetic average temperature of the boundary layer ($t_{\mathrm{m}}=(t_{\mathrm{\infty }}+t_{\mathrm{w}})/2$) is used for the qualitative temperature. $Pr$ is the Prandtl number. $Gr$ is the dimensionless Grashov number with H as the characteristic length: $Gr={\displaystyle \frac{\mathrm{g}{\alpha }_{\mathrm{V}}∆t{H}^3}{v^2}}$. $g$ is the acceleration of gravity. ${\alpha }_{\mathrm{V}}$ is the coefficient of volume change. Ideal gas: ${\alpha }_{\mathrm{V}}$ is the inverse of $T$. $∆t$ is the temperature difference. $∆t=t_{\mathrm{w}}-t_{\mathrm{\infty }}$. $t_{\mathrm{w}}$ is the wall surface temperature. $t_{\mathrm{\infty }}$ is the ambient temperature. The TPCT conforms to the following inequality for the vertical cylinder.

$${\displaystyle \frac{d}{H}}\ge {\displaystyle \frac{35}{{Gr}_{\mathrm{H}}^{1/4}}}$$

(13)

$d$ is the diameter of the TPCT. $H$ is the length of the evaporating section of the TPCT. The constant $C$ is 0.11 and the coefficient $n$ is 1/3 [45]. The $Nu$ number is composed of the average surface heat transfer coefficient.

$${Nu}_{\mathrm{m}}={C\left(GrPr\right)}_{\mathrm{m}}^{\mathrm{n}}$$

(14)

${Nu}_{\mathrm{m}}$ is also called the dimensionless number Nussle number with H as the characteristic length.

$${Nu}_{\mathrm{m}}={\displaystyle \frac{h_{\mathrm{H}}H}{\lambda }}$$

(15)

$h_{\mathrm{H}}$ is the surface heat transfer coefficient for convective heat transfer in the evaporation section of the TPCT. $\lambda$ is the thermal conductivity of the air fluid. $h_{\mathrm{H}}$ can be obtained from above. Newton’s formula for convective heat transfer in heat transfer:

$$Q_1=A_{\mathrm{Z}}{h}_{\mathrm{H}}∆T_1$$

(16)

$Q_1$ is the convective heat exchange between air and TPCT evaporation section. $A_{\mathrm{Z}}$ is the exterior area of evaporation section. $h_{\mathrm{H}}$ is the heat transfer coefficient of the surface of the TPCT evaporation section.

$$A_{\mathrm{Z}}=\pi d_{\mathrm{o}}{L}_1$$

(17)

$∆t$ is the temperature difference of convective heat exchange.

$$∆t=t_{\mathrm{w}}-t_{\mathrm{\infty }}$$

(18)

$d_{\mathrm{o}}$ is the diameter of the outer surface of the TPCT evaporation section. $L_1$ is the length of the evaporation section of the TPCT. The above can be obtained from the TPCT convection heat transfer loss $Q_1$ is much smaller than the TPCT radiation heat transfer loss $Q_2$. So, the TPCT heat transfer loss is taken as the TPCT radiation heat transfer loss value.

2.2.2. Thermal Resistance of TPCT

A typical TPCT is divided into three sections: the evaporation section, the adiabatic section, and the condensation section. The latent heat of phase change of the working medium is utilized by the TPCT. This allows for rapid heat transfer from the evaporative section to the condensing section. A schematic diagram of the structure of a TPCT is shown in Figure 1b. The heat transfer process consists of six interrelated phase processes.

Heat is transferred from the heating source to the evaporation section liquid through the wall of the TPCT.

• The liquid in the evaporation section is heated to evaporate and absorb heat.
• The evaporated vapor is transferred along the TPCT to the condensing section of the TPCT.
• Vapor in the condensing section of the wall of the tube is exothermic condensation.
• Heat is transferred from the vapor–liquid through the wall of the TPCT to the cold source.
• The liquid condensed in the condensing section wall flows back to the evaporating section due to gravity.

The thermal resistance per section of the TPCT in the heat transfer process is as follows Table 1.

Table 1. The thermal resistance per section of the TPCT in the heat transfer process.

Definition	Expressions
The heat transfer thermal resistance $R_0$ from the heating source to the outer wall of the evaporation section of the TPCT	$$\begin{array}{c}{R}_0={\displaystyle \frac{1}{\pi d_{\mathrm{e}}{l}_{\mathrm{e}}{h}_{\mathrm{o},\mathrm{e}}}}\end{array}$$ (19)
The thermal conductivity thermal resistance $R_1$ from the outer wall to the inner wall of the evaporation section of the TPCT	$$\begin{array}{c}{R}_1={\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{e}}}}ln{\displaystyle \frac{d_{\mathrm{e}}}{d_{\mathrm{i}\mathrm{e}}}}\end{array}$$ (20)
The liquid-vapor evaporative heat transfer thermal resistance $R_2$ of the medium inside the evaporation section	$$\begin{array}{c}{R}_2={\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{e}}{l}_{\mathrm{e}}{h}_{\mathrm{i},\mathrm{e}}}}\end{array}$$ (21)
The thermal resistance $R_3$ caused by the pressure drop in the vapor flow from the evaporation section to the condensation section of the TPCT	$$R_3\approx 0$$ (22)
The heat transfer resistance $R_4$ of the condensing section medium vapor–liquid condensation	$$\begin{array}{c}{R}_4={\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{c}}{l}_{\mathrm{c}}{h}_{\mathrm{i},\mathrm{c}}}}\end{array}$$ (23)
The thermal conductivity thermal resistance $R_5$ from the inner wall to the outer wall of the condensing section of the TPCT	$$\begin{array}{c}{R}_5={\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{c}}}}ln{\displaystyle \frac{d_{\mathrm{c}}}{d_{\mathrm{i}\mathrm{c}}}}\end{array}$$ (24)
The heat transfer thermal resistance $R_6$ between the outer wall of the condensing section of the TPCT and the heat sink	$$\begin{array}{c}{R}_6={\displaystyle \frac{1}{\pi d_{\mathrm{c}}{l}_{\mathrm{c}}{h}_{\mathrm{o},\mathrm{c}}}}\end{array}$$ (25)

$h_{\mathrm{o},\mathrm{e}}$ is the total surface heat transfer coefficient between the wall of the evaporation section of the TPCT and the heating source. $h_{\mathrm{o},\mathrm{c}}$ is the total surface heat transfer coefficient between the wall of the condensing section of the TPCT and the heat sink. $d_{\mathrm{e}}$ is the outside diameter of the evaporating section of the TPCT. $d_{\mathrm{c}}$ is the outside diameter of the condensing section of the TPCT. $d_{\mathrm{i}\mathrm{e}}$ is the inner diameter of the TPCT evaporation section. $d_{\mathrm{i}\mathrm{c}}$ is the inner diameter of the condensing section of the TPCT. $\lambda$ is the thermal conductivity of the TPCT material. $h_{\mathrm{i},\mathrm{e}}$ is the surface heat transfer coefficient of the TPCT evaporation heat transfer. $h_{\mathrm{i},\mathrm{c}}$ is the surface heat transfer coefficient of the TPCT condensation heat transfer.

Table 1. The thermal resistance per section of the TPCT in the heat transfer process.

Definition	Expressions
The heat transfer thermal resistance $R_0$ from the heating source to the outer wall of the evaporation section of the TPCT	$$\begin{array}{c}{R}_0={\displaystyle \frac{1}{\pi d_{\mathrm{e}}{l}_{\mathrm{e}}{h}_{\mathrm{o},\mathrm{e}}}}\end{array}$$ (19)
The thermal conductivity thermal resistance $R_1$ from the outer wall to the inner wall of the evaporation section of the TPCT	$$\begin{array}{c}{R}_1={\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{e}}}}ln{\displaystyle \frac{d_{\mathrm{e}}}{d_{\mathrm{i}\mathrm{e}}}}\end{array}$$ (20)
The liquid-vapor evaporative heat transfer thermal resistance $R_2$ of the medium inside the evaporation section	$$\begin{array}{c}{R}_2={\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{e}}{l}_{\mathrm{e}}{h}_{\mathrm{i},\mathrm{e}}}}\end{array}$$ (21)
The thermal resistance $R_3$ caused by the pressure drop in the vapor flow from the evaporation section to the condensation section of the TPCT	$$R_3\approx 0$$ (22)
The heat transfer resistance $R_4$ of the condensing section medium vapor–liquid condensation	$$\begin{array}{c}{R}_4={\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{c}}{l}_{\mathrm{c}}{h}_{\mathrm{i},\mathrm{c}}}}\end{array}$$ (23)
The thermal conductivity thermal resistance $R_5$ from the inner wall to the outer wall of the condensing section of the TPCT	$$\begin{array}{c}{R}_5={\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{c}}}}ln{\displaystyle \frac{d_{\mathrm{c}}}{d_{\mathrm{i}\mathrm{c}}}}\end{array}$$ (24)
The heat transfer thermal resistance $R_6$ between the outer wall of the condensing section of the TPCT and the heat sink	$$\begin{array}{c}{R}_6={\displaystyle \frac{1}{\pi d_{\mathrm{c}}{l}_{\mathrm{c}}{h}_{\mathrm{o},\mathrm{c}}}}\end{array}$$ (25)

$h_{\mathrm{o},\mathrm{e}}$ is the total surface heat transfer coefficient between the wall of the evaporation section of the TPCT and the heating source. $h_{\mathrm{o},\mathrm{c}}$ is the total surface heat transfer coefficient between the wall of the condensing section of the TPCT and the heat sink. $d_{\mathrm{e}}$ is the outside diameter of the evaporating section of the TPCT. $d_{\mathrm{c}}$ is the outside diameter of the condensing section of the TPCT. $d_{\mathrm{i}\mathrm{e}}$ is the inner diameter of the TPCT evaporation section. $d_{\mathrm{i}\mathrm{c}}$ is the inner diameter of the condensing section of the TPCT. $\lambda$ is the thermal conductivity of the TPCT material. $h_{\mathrm{i},\mathrm{e}}$ is the surface heat transfer coefficient of the TPCT evaporation heat transfer. $h_{\mathrm{i},\mathrm{c}}$ is the surface heat transfer coefficient of the TPCT condensation heat transfer.

$R_1, R_2, R_3, R_4,$ and $R_5$ are the thermal resistances inside the TPCT, and the total internal resistance is:

$$R=R_1+R_2+R_3+R_4+R_5={\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{e}}}}ln{\displaystyle \frac{d_{\mathrm{e}}}{d_{\mathrm{i}\mathrm{e}}}}+{\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{e}}{l}_{\mathrm{e}}{h}_{\mathrm{i},\mathrm{e}}}}+0+{\displaystyle \frac{1}{\pi d_{\mathrm{i}\mathrm{c}}{l}_{\mathrm{c}}{h}_{\mathrm{i},\mathrm{c}}}}+{\displaystyle \frac{1}{2\pi \lambda l_{\mathrm{c}}}}ln{\displaystyle \frac{d_{\mathrm{c}}}{d_{\mathrm{i}\mathrm{c}}}}$$

(26)

The heat transferred from the evaporation section to the surface of the condensation section per unit time is the TPCT heat transfer power $Q_{\mathrm{c}}$. It is the difference between the heating power $Q_{\mathrm{j}}$ and the TPCT heat transfer loss $Q_{\mathrm{s}}$.

$$Q_{\mathrm{c}}=Q_{\mathrm{j}}-Q_{\mathrm{s}}$$

(27)

$$Q_{\mathrm{c}}={\displaystyle \frac{{∆t}_{\mathrm{e}\mathrm{c}}}{R}}$$

(28)

$$R={\displaystyle \frac{{∆t}_{\mathrm{e}\mathrm{c}}}{Q_{\mathrm{j}}-Q_{\mathrm{s}}}}$$

(29)

$${\eta }_{\mathrm{c}}={\displaystyle \frac{Q_{\mathrm{c}}}{Q_{\mathrm{j}}}}\times 100\%$$

(30)

${∆t}_{\mathrm{e}\mathrm{c}}$ is the temperature difference between the surface of the evaporation section and the surface of the condensation section of the TPCT. $\eta$ is the heat transfer efficiency.

2.2.3. Thermoelectric Power Generation

As shown in Figure 1b, thermoelectric power generation uses the Seebeck effect of thermoelectric materials. It converts thermal energy directly into electrical energy, which is a new green, environmentally friendly, and pollution-free power generation technology. Copper, a good conductive metal, is connected to one end of the P-type thermoelectric material and the N-type thermoelectric material. The other end is connected with copper separately to form a PN junction, also known as a PN coupler arm. At this time, there is a high-temperature heat source at one end of the PN coupling arm to provide heat, forming the hot end. At the other end of the PN coupler arm, a low-temperature cold source dissipates energy, forming the cold end. This results in a temperature difference between the two ends of the PN junction. The holes (P-type thermoelectric material) and electrons (N-type thermoelectric material) at the high-temperature end of the PN coupler arm are driven by the temperature gradient and begin to diffuse toward the low-temperature end. This creates an electrical potential difference between the two ends of the PN coupler arm. Multiple PN coupler arms are connected to a load resistor, at which point a current is generated in the circuit. Due to the small electric potential that can be generated by a single PN coupler arm, multiple PN coupler arms are generally connected in series in commercial thermoelectric power generation modules today in order to obtain a larger output power. The hot and cold ends are covered with ceramic sheets to form a temperature differential generator with multiple PN junctions.

Thermoelectric materials are characterized by low resistance, low thermal conductivity, and high electrical conductivity. TGs composed of thermoelectric materials can generate DC voltage.

$$E=\alpha \left(T_{\mathrm{h}}-T_{\mathrm{c}}\right)={∆T}_{\mathrm{h}\mathrm{c}}$$

(31)

$$E=\alpha \left(T_{\mathrm{h}}-T_{\mathrm{c}}\right)={∆T}_{\mathrm{h}\mathrm{c}}$$

(32)

$E$ is the open-circuit electric potential of TGs. $\alpha$ is the Seebeck coefficient. $T_{\mathrm{h}}$ is the temperature of the hot end of TGs. $T_{\mathrm{c}}$ is the temperature of the cold end of TGs. ${∆T}_{\mathrm{h}\mathrm{c}}$ is the temperature difference between the hot end of TGs and the end of TGs.

The thermoelectric conversion efficiency of a thermoelectric material depends mainly on the euphoria factor ZT.

$$ZT={\displaystyle \frac{{\alpha }^2\sigma }{\lambda }}T$$

(33)

$\sigma$ is the electrical conductivity of the thermoelectric material. $\lambda$ is the thermal conductivity of the thermoelectric material. $T$ is the absolute temperature. A larger value of the thermoelectric optimum ZT indicates a better thermoelectric performance of the thermoelectric material.

When the load resistance $R_{\mathrm{L}}$ is the same as the internal resistance $R_{\mathrm{m}}$ of TGs, there is the maximum output power $P_{\mathrm{m}\mathrm{a}\mathrm{x}}$.

$$P_{\mathrm{m}\mathrm{a}\mathrm{x}}={\displaystyle \frac{E^2}{4R_{\mathrm{m}}}}$$

(34)

$${\eta }_{\mathrm{e}1}={\displaystyle \frac{P}{Q_{\mathrm{j}}}}\times 100\%$$

(35)

$${\eta }_{\mathrm{e}2}={\displaystyle \frac{P}{Q_{\mathrm{c}}}}\times 100\%$$

(36)

$P$ is the load power. $Q_{\mathrm{j}}$ is the heating power of heating source. $Q_{\mathrm{c}}$ is the heat transfer power of the evaporation section of the TPCT. ${\eta }_{\mathrm{e}1}$ is the power generation efficiency. ${\eta }_{\mathrm{e}2}$ is the net power generation efficiency.

Therefore, the open-circuit voltage E and load power P of TGs are important parameters to measure the thermoelectric conversion performance of the experimental device.

From Equation (29), it is known that the factors affecting the open-circuit voltage and load power of TGs are the Seebeck coefficient α and the temperature difference of TGs $T_{\mathrm{h}}-T_{\mathrm{c}}$. The Seebeck coefficient mainly depends on the nature of the thermoelectric material of TGs, while the main external factor is the temperature difference between the hot end and the cold end of TGs. Then, the temperature difference of TGs is mainly affected by the temperature of the evaporating section of the TPCT and the temperature of the condensing section of the TPCT. Therefore, it is necessary to study and analyze this.

3. Results and Discussion

3.1. Heat Transfer Performance

3.1.1. TPCT Heating and Isothermal Characteristics

Figure 2a–d shows the variation in temperature at different distances along the TCPT with time (increasing the heating power from 100 W to 600 W) at the liquid filling rates of 10%, 25%, 35%, and 45%, respectively. It is observed that the temperature at 10 cm, 30 cm, 50 cm, 70 cm, and 90 cm along the TCPT increases as the heating power increases. When the heating power is 100 W, the variation in temperature at 90 cm with time is relatively small, the heat transfer power of the TCPT is low and the heat cannot reach the top of TCPT. According to the heating power, the temperature rise process of TCPT can be divided into four stages. During each stage, the temperature of TCPT increases with time, and the rate of temperature increase gradually decreases. When the cooling and heat dissipation module is started, the temperature decreases quickly. When the heating power is changed, the temperature increases rapidly. The variations in temperature with different liquid filling rates are basically the same. With the increase in the heating power, the temperature of the TPCT increase. It shows that the heating power is the main factor affecting the temperature of the TPCT, and the liquid filling rate has a smaller effect on the temperature increase of the TPCT.

Figure 3a–d shows the variation in temperature with distance along the TCPT at different heating powers at the liquid filling rates of 10%, 25%, 35%, and 45%, respectively. There is a large temperature gradient in the evaporation section (from 0 cm to 50 cm), and there is a small temperature gradient in the condensation section (from 50 cm to 100 cm). As the wall of evaporation section absorbs heat and boils, there are a large number of bubbles, and the temperature distribution is more uneven. While the condensation section of the TPCT condenses and exerts heat, the temperature distribution is more uniform. It is observed that the temperature with distance along the TCPT increase as the heating power increase at all liquid filling rates. The temperature of the TCPT does not change obviously with the increase in the liquid filling rate. It can be concluded that the heating power is the main factor that affecting the temperature of TCPT and the liquid filling rate is a secondary factor. Finally, the temperature at each position of the condensation section tends to be consistent and stable at about 160 °C. It indicates that with the increase in heating power, the temperature consistency of evaporation section becomes weakening, and the temperature of the condensation section tends to be consistent and more average.

3.1.2. TPCT Heat Transfer Characteristics Analysis

The variation in the thermal resistance of the TPCT with heating power at different liquid filling rates is shown in Figure 4. It is observed that the thermal resistance of the TPCT decreases continuously with the increase in heating power. When the heating power is 100 W and 200 W, the rate of the variation in the thermal resistance is larger. When the heating power is 400 W and 600 W, the rate of the variation in the thermal resistance becomes smaller, consistent. The thermal resistance at the liquid filling rates of 10%, 25%, 35%, and 45% less variable, with some approximate value of 0.10 °C/W, 0.14 °C/W, 0.19 °C/W, and 0.18 °C/W, respectively. At the heating powers of 100 W, 200 W, 400 W, and 600 W, the thermal resistance of the TPCT at the liquid filling rate of 10% is the smallest, and with the increase in heating power, the thermal resistance does not change much, roughly around 0.11 °C/W. At the heating powers of 200 W–600 W, the thermal resistance of the TPCT with the 35% liquid filling rate is the largest; at the heating power of 100 W, the thermal resistance of the TPCT with the 25% liquid filling rate is the largest.

The variation in heat transfer loss of the TPCT with heating power at different liquid filling rates is shown in Figure 5. It is observed that the heat transfer loss has been increasing as the heating power increases. When the heating power is 100 W and 200 W, the difference in heat transfer loss between TPCTs with different liquid filling rates is small. It indicates that the liquid filling rate has less effect on the heat transfer loss at low heating power. But there is also a minimum point of heat transfer loss, the heat transfer loss of the TPCT with the 10% liquid filling rate is the smallest. When the heating power is 100 W and 200 W, the smallest heat transfer loss is 18.43 W and 33.28 W, respectively. When the heating power is 400 W and 600 W, the difference in heat transfer loss between TPCTs with different liquid filling rates is large. It indicates that the liquid filling rate has a more obvious effect on the heat transfer loss at high heating power. When the heating power is 400 W and 600 W, the smallest heat transfer loss is for the TPCT with the 25% liquid filling rate, and is 71.43 W and 119.48 W, respectively.

The variation in the heat transfer power of the TPCT with heating power at different liquid filling rates is shown in Figure 6. It is observed that that as the heating power increases, the heat transfer power keeps increasing. And the heating power and heat transfer power are roughly linear. When the heating power is 100 W and 200 W, the heat transfer power varies smoothly with the liquid filling rate, and the heat transfer power is basically the same at different liquid filling rates. At the heating power of 100 W, the heat transfer power of the TPCT at different liquid filling rates is about 82 W or less; at the heating power of 200 W, the heat transfer power is about 162 W or less. It means that the liquid filling rate has less influence on the heat transfer power at low heating power. Moreover, the heat transfer power of the TPCT at the liquid filling rate of 35% is the smallest, and the heat transfer power of the TPCT at the liquid filling rate of 10% is the largest at low heating power. When the heating power is 400 W and 600 W, the variation in heat transfer power with liquid filling rate is larger. It indicates that the liquid filling rate has a more obvious effect on the heat transfer power at high heating power. At high heating power, the TPCT at the liquid filling rate of 25% has the largest heat transfer power. At the high heating power of 400 W and 600 W, the largest heat transfer powers of the TPCT are 480 W and 328 W, respectively.

The variation in the heat transfer efficiency of the TPCT with heating power at different liquid filling rates is shown in Figure 7. It is observed that the heat transfer efficiency of TPCTs with different liquid filling rates shows a trend of first increasing and then decreasing as the heating power increases. TPCTs with liquid filling rates of 10%, 35%, and 45% exhibit the highest heat transfer efficiency at a heating power of 200 W, with efficiencies of 83.36%, 78.84%, and 77.71%, respectively. The TPCT with a liquid filling rate of 25% achieves the greatest heat transfer efficiency of 82.14% at a heating power of 400 W. It is observed that that the TPCT with the liquid filling rate of 10% has the largest heat transfer efficiency at the low heating powers of 100 W and 200 W, which are 81.57% and 83.36%, respectively. At the high heating powers of 400 W and 600 W, the TPCT with the liquid filling rate of 25% has the largest heat transfer efficiency, which is 82.14% and 80.09%, respectively. Therefore, the heat transfer efficiency of the TPCT is larger at low liquid filling rates. At the heating powers of 100 W, 200 W and 400 W, the TPCT with a liquid filling rate of 35% has the smallest heat transfer efficiency. At a heating power of 600 W, the heat transfer efficiency of the TPCT is essentially the same for a liquid filling rate of 35% and a liquid filling rate of 45%. Therefore, it can be considered that the smallest heat transfer efficiency of the TPCT at heating power (from 100 W to 600 W) is found in the TPCT at the liquid filling rate of 35%.

3.2. Power Generation Performance Analysis

3.2.1. Temperature Parameters Analysis

The variation in ${∆T}_{\mathrm{h}\mathrm{c}}$ with liquid filling rate at the heating powers of 100 W, 200 W, 400 W, and 600 W is shown in Figure 8. It is observed that that ${∆T}_{\mathrm{h}\mathrm{c}}$ increases as the heating power increases. When the liquid filling rate of the TPCT is 10%, 25%, and 35%, the ${∆T}_{\mathrm{h}\mathrm{c}}$ change curve is closer. When the liquid filling rate is 45%, ${∆T}_{\mathrm{h}\mathrm{c}}$ increases significantly. At the heating powers of 200 W, 400 W, and 600 W, the maximum ${∆T}_{\mathrm{h}\mathrm{c}}$ are 40.62 °C, 68.30 °C, and 90.03 °C, respectively, for the TPCT at the liquid filling rate of 45%. It shows that the heating power has a greater effect on ${∆T}_{\mathrm{h}\mathrm{c}}$ at higher liquid fill rates of the TPCT. It is observed that ${∆T}_{\mathrm{h}\mathrm{c}}$ shows a trend of decreasing and then increasing with the increase in the liquid filling rate of the TPCT. When the heating power is 100 W and 200 W, the variation in the temperature difference of TGs is smaller. When the high heating power is 400 W and 600 W, the variation is larger. It shows that at low heating power, the liquid filling rate has a smaller effect on the temperature difference of the power generator. At high heating power, the effect of the liquid filling rate on ${∆T}_{\mathrm{h}\mathrm{c}}$ is larger.

The variation in ${∆t}_{\mathrm{e}\mathrm{c}}$ with liquid filling rate at the heating powers of 100 W, 200 W, 400 W, and 600 W is shown in Figure 9. It is observed that ${∆t}_{\mathrm{e}\mathrm{c}}$ gradually increases as the heating power increases. As the liquid filling rate increases, ${∆t}_{\mathrm{e}\mathrm{c}}$ first increases and then decreases. At the heating powers of 200 W, 400 W, and 600 W, ${∆t}_{\mathrm{e}\mathrm{c}}$ at the liquid filling rate of 35% is the largest, which is 40.09 °C, 61.24 °C and 83.35 °C, respectively. At the heating power of 100 W, ${∆t}_{\mathrm{e}\mathrm{c}}$ at the liquid filling rate of 25% is the largest, which is 34.93 °C.

The variation in the evaporation section temperature with liquid filling rate at four heating powers is shown in Figure 10. It is observed that the evaporation section temperature of the TPCT increases gradually with the increase in heating power. When the heating power is greater than or equal to 400 W and the liquid filling rate is greater than or equal to 25%, the variation in the evaporation section temperature is roughly the same. It means that the evaporation section temperature of the TPCT is only proportional to the heating power at this time. When the heating power is 100 W and 200 W, the evaporation section temperature of the TPCT with the liquid filling rate of 25% is larger; when the heating power is 400 W and 600 W, the evaporation section temperature of the TPCT with liquid filling rates of 25%, 35%, and 45% tends to be the same. So, it means that in all heating power (from 100 W to 600 W), the evaporation section of the TPCT at the liquid filling rate of 25% has a higher temperature and better heating performance.

3.2.2. Power Generation Performance Indicators Analysis

Figure 11a–c shows the variation in open-circuit voltage, load current, and load power with heating power at the liquid filling rates of 10%, 25%, 35%, and 45%. It is observed that as the increase in heating power, the open-circuit voltage, load current, and measured load power increase. When the heating power is 200 W, 400 W, and 600 W, the values of power generation parameters, such as open-circuit voltage, load current, and load power, do not differ much for different liquid filling rates. It means that the open-circuit voltage, load current, and load power are less affected by the liquid filling rate and more affected by the heating power. However, when the heating power is 100 W, the value of the power generation parameter is larger for a 10% liquid-filled TPCT. This is because at low heating power, the TPCT with the lower liquid filling rate is easier to start and has better heat transfer characteristics. It is observed that with the increase in the liquid filling rate, when the heating power is 100 W and 200 W, the open-circuit voltage, load current, and load power show a trend of first decreasing and then increasing, and the TPCT with a liquid filling rate of 10% have the maximum values. When the high heating power is 400 W and 600 W, the open-circuit voltage, load current, and load power show a trend of first increasing and then decreasing, and the TPCTs with liquid filling rates of 25% and 35% have the maximum values.

Table 2. Power generation parameters at different heating powers.

Heating Power	Maximum Open-Circuit Voltage/V	Maximum Load Current/A	Maximum Load Power/W
100 W	3.51 (10%)	0.25 (10%)	0.47 (10%)
200 W	8.89 (10%)	0.61 (10%)	2.68 (10%)
400 W	16.43 (35%)	1.06 (25%)	8.13 (25%)
600 W	21.93 (35%)	1.37 (35%)	13.64 (35%)

shows the maximum values of open-circuit voltage, load current, and load power at different heating powers and liquid filling rates.

Figure 12a,b shows the variation in power generation efficiency and net power generation efficiency with heating power at the liquid filling rates of 10%, 25%, 35%, and 45%. It is observed that the power generation efficiency and net power generation efficiency increase as the heating power increases. When the heating power reaches 400 W, the increases in both power generation efficiency and net power generation efficiency become slower and gradually level off. It indicates that the heating power has more influence on the power generation efficiency and net power generation efficiency at the heating powers of 100 W and 200 W; the heating power has a smaller effect on the power generation efficiency and net power generation efficiency at the high heating powers of 400 W and 600 W. Finally, the power generation efficiency and net power generation efficiency converge to 2.08% and 2.68%. It is observed that with the increase in liquid filling rate, at the heating powers of 100 W and 200 W, the power generation efficiency and net power generation efficiency both show a trend of first decreasing and then increasing, and they have maximum values when the liquid filling rate is 10%. At the high heating powers of 400 W and 600 W, the power generation efficiency and net power generation efficiency both show a trend of first increasing and then decreasing, and they have maximum values when the liquid filling rates are 25% and 35%, respectively.

Table 3. Maximum power generation efficiency and maximum net power generation efficiency at different heating powers.

Heating Power	Maximum Power Generation Efficiency/%	Maximum Net Power Generation Parameters Under/%
100 W	0.4657 (10%)	0.5709 (10%)
200 W	1.3375 (10%)	1.6046 (10%)
400 W	2.0313 (25%)	2.6217 (35%)
600 W	2.2736 (35%)	3.1086 (35%)

shows the maximum values of power generation efficiency and net power generation efficiency at different heating powers and liquid filling rates.

4. Conclusions

The effects of heating power and liquid filling rate on heat transfer performance and power generation performance are studied. The following conclusions are drawn:

(1) The thermal resistance decreases as heating power increases, and the heat transfer power increases as heating power increases. The important indexes of power generation performance, for example, open-circuit voltage, load current, load power, power generation efficiency, and net power generation efficiency, increase as heating power increases. This shows that as the heating power increases, heat transfer performance and power generation performance of the device will also increase. As the heating power increases, the heat transfer loss increases and the heat transfer efficiency increases and then decreases. The power generation efficiency and net power generation efficiency increase as the heating power increases, and converge to 2.18% and 2.68%. This indicates that as the heating power increases, the heat transfer performance and power generation performance become slow to improve and finally stabilize at a relatively steady state.

(2) Overall, the effect of the liquid filling rate is smaller than that of the heating power for both heat transfer and power generation performance. At the low heating powers of 100 W and 200 W, the device with the TPCT at the lower liquid filling rate of 10% has better heat transfer performance and power generation performance. At the high heating powers of 400 W and 600 W, the device with the TPCT at the higher liquid filling rates of 25%, and 35% has better heat transfer performance and power generation performance.

(3) The thermal resistance of the TPCT at the liquid filling rate of 10% is the smallest, and with the increase in heating power, the thermal resistance does not change much, roughly around 0.11 °C/W. At a heating power of 200 W, TPCTs at liquid filling rates of 10%, 35%, and 45% have the maximum heat transfer efficiency, which is 83.36%, 78.84%, and 77.71%, respectively. At a heating power of 400 W, the TPCT at the liquid filling rate of 25% has the largest heat transfer efficiency, which is 82.14%.

The maximum values of power generation efficiency and net power generation efficiency are 2.27% and 3.10%, respectively.