An approach to improve the efficiency of cooling enhancement of a thermoelectric refrigerator through the use of phase‐change materials

In this study, a technique is suggested to enhance the temperature difference for cooling and energy efficiency of thermoelectric cooler (TEC) used in cooled detectors when subjected to high current conditions. Embedding a structure for storing heat during phase change is the basis of this method at the heat sink. A simulation model was created for a common two‐stage series TEC with an asymmetrical design, which is coupled with a structure for storing heat through phase change. The research examined how phase transition heat storage impacts the coefficient of performance (COP) and refrigeration temperature difference across various phase‐change substances, heat transfer coefficients at the hot end, currents, and the height of the phase‐change material (PCM). The findings suggest that the suggested approach of combining PCM with TEC can efficiently lower the cold end temperature of TEC by a maximum of 20 K, enhance the temperature gap by a maximum of 16 K, and preserve the consistency of the optimized quantity across various hot end heat transfer coefficients. During the phase‐change process of PCMs, the COP of TECs integrated with PCM is found to increase by an average of 2%–3% compared to TECs without PCM integration. Under the maximum current operating condition, the cryogenic temperature can be optimized to a minimum of 238 K. In summary, the proposed method of integrating phase‐change heat storage with TECs provides a promising solution for improving their cooling performance and energy efficiency in cooled detectors under high current conditions. Additional investigation can be conducted to explore the practical application of this approach and enhance the design parameters for various uses.


| INTRODUCTION
2][3][4][5] The principle is that when the current passes, cooling occurs at the electrical connection of two different types of thermoelectric particles.][8][9] However, as the temperature difference between the hot and cold ends of the TEC increases, the Fourier heat conduction and the Seebeck potential in the thermoelectric particles increase, which has a negative effect on the performance of the TEC.Therefore, strengthening the heat dissipation of the hot end of the TEC has become a major research hot spot in the optimization of TEC. 10 At present, the heat dissipation methods of the hot end of the TEC are enhanced using fin heat dissipation, circulating fluid heat dissipation, efficient radiator heat dissipation, and nanofluid heat dissipation.In the field of fin heat dissipation, Cai and colleagues 11,12 conducted a study on the differences, advantages, and disadvantages of three typical heat exchangers in a thermoelectric setup.They also considered the power consumed by auxiliary equipment to improve thermoelectric performance.The results demonstrated the net power output performance of thermoelectric devices with three different types of heat exchangers.Air cooling heat exchangers exhibited the minimum auxiliary power consumption, while heat pipe cooling heat exchangers showed the highest effectiveness.However, it should be noted that the heat pipe cooling heat exchanger had the highest cost of US$15.12/(W/K).In the field of circulating fluid heat dissipation, Huang et al. 13 used circulating fluid heat dissipation to conduct relevant experimental studies on thermoelectric refrigeration and studied the influence of heat transfer coefficient at the hot end on refrigeration performance.The results show that when the optimal current of 7 A is determined, the heat load is lower than 57 W, and the integration of water cooling device and TEC helps to improve the refrigeration performance of TEC by 4%.In the field of high-efficiency radiators, Lee et al. 14 studied the heat dissipation effect of the hot end heat pipe through simulation and experiment, and the results show that the heat transfer coefficient of the hot end can reach 5400 W/(m 2 K).In the nanofluid heat dissipation study, Mohammadian et al. 15 numerically studied the single-phase heat transfer and pressure drop of Al 2 O 3 water nanofluids in micro-pin-fin heat exchangers located on both sides of the hot spot module to enhance heat transfer of circulating fluids.The effects of nanofluid volume fraction and nanoparticle diameter on coefficient of performance (COP) and total entropy were studied.The results show that at low Reynolds number, the addition of low-fraction nanoparticles to the base fluid of the thermal surface heat exchanger will increase the COP of the TEC by 3%.At high Reynolds number, the addition of nanoparticles to the hot end base fluid of the TEC will increase the COP by 2% and reduce the total entropy by 3%.
Phase-change material (PCM) has the advantages of high fusion heat, small volume change during phase change, nontoxic, noncorrosive, and ideal phase-change temperature.High fusion heat makes PCM melt and solidify at the phase-change point to store and release a large amount of heat, making the integration of PCM and TEC a new research hot spot in the thermal management of thermoelectric refrigeration devices. 16an and Zhao 17 proposed a TEC system integrated with PCM for space cooling.The PCM stores cold and hot energy at night and is used as a radiator to reduce the hot side temperature, thereby improving the performance efficiency of the system.The results show that the average system cooling COP increases by 56% (from 0.5 to 0.78) due to the addition of PCM.Li et al. 18 studied the effect of thermoelectric cooling device with PCM on patients with multiple sclerosis.It combines the heat pump delivery capacity of the thermoelectric device and the heat storage capacity of the PCM.The properties of three different PCMs were studied experimentally.The results show that PCM-OM37 with a power input of 3 W can provide the required 10°C temperature in 20 min.Wang et al. 19 studied the performance of PCM TECs for aerospace applications.Compared with the case without PCM, the temperature of TEC with PCM is controlled at the required temperature, and the COP is increased by more than 100%.Caroff et al. 20 studied and optimized the structure of the TEC of the double-sided cooling motordriven power module combined with the PCM heat storage solution and found that the best architecture for this application is TEC with a thermal resistance of about 1 K/W, coupled to a 5 K/W radiator that integrates 17 cm 3 paraffin (T fusion = 100-110°C) to keep the insulated-gate bipolar transistor (IGBT) temperature at 110°C during 60 s overload.By increasing the target IGBT temperature, the volume of PCM can be significantly reduced: during the 60 s overload, only 5 cm 3 of paraffin is available for the IBGT temperature of 125°C.Manikandan et al. 21studied the PCM system attached to the TEC radiator and concluded that the implementation of PCM on the radiator can increase the COP of TEC by 30% and reduce the temperature of the hot side from 52°C to 32°C and the cold side from 25°C to 12°C.Selvam et al. 22 considered more conditions and parameters to reduce the temperature of the cold end.They studied the effects of applying current pulses and filling the radiator part with a PCM.The results show that the cooling temperature of the TEC decreases from −14.5°C to 17.5°C when using PCM and applying the current pulse.
Experimental results of thermoelectric generators (TEGs) designed by Jaworski et al. 23 for radiative heating and passive cooling of PCMs are presented here.The test was performed in open and closed circuits.The results obtained confirm the possibility of using PCM to release heat from the cold side of TEG.In addition, they tested the reverse operation of TEG and also confirmed the potential of PCMs as TEG cooling/heating media.Darkwa et al. 24 studied the concept of an integrated thermoelectric PCM system to improve the photovoltaic (PV) efficiency.Due to the small temperature difference under natural convection conditions, the power output of TEG is small.The simulation results highlight the importance of high PCM conductivity of a thick PCM layer to reduce its insulation effect on TEG and PV layers.The best thermal performance of the PV/TEG/PCM system is obtained by a 50-mm-thick PCM layer with a thermal conductivity of 5 W/(m 2 K) and a phase transition temperature of 40-45°C.Studies by Selvam et al. 25 have shown that by using PCM, the temperature on the cold side of the TEG is significantly reduced and persists.The researchers found that when the height of the PCM is 3 mm, the efficiency of TEG is increased by 36.7%, 33.8%, and 30% for the heat input of 0.1, 0.15, and 0.2 W, respectively.
Other researchers have shown great interest in PCMs for implementation in thermoelectric systems.Currently, the most commonly used PCMs for thermal management in TECs are classified as low-temperature PCMs.These include eutectic water-salt solutions, eutectic organic compounds, organic compounds, fatty acids, inorganic salt hydrates, and inorganic mixtures. 26These PCMs can be packaged in specialized containers such as tubes, shallow panels, or plastic bags. 27Additionally, PCM-based flexible heatsinks offer advantages of smaller size and lighter weight compared to conventional metal heatsinks. 28Chougule and colleagues 29 reported the benefits of thermal management using heat pipes and PCM integrated with a nanofluid (multiwall carbon nanotube/water) charged heat pipe for electronic cooling.In their design, the adiabatic section of the heat pipe was covered by PCMs (paraffin in their study) and placed inside a container filled with acrylic material.The PCM absorbs and releases thermal energy based on the fluctuations in the heating load, resulting in improved cooling performance and reduced fan power consumption compared to a cooling module utilizing only a heat pipe.Omer et al. 30 investigated the potential application of PCMs integrated with thermosyphons in a 150 W TEC system.They found that using an encapsulated PCM as the cold sink improved the thermal performance compared to a design with a conventional heat sink system.Furthermore, they explored the integration of a thermal diode with PCM to enhance the storage capability during off-power periods.The PCM-thermal diode system demonstrated significant enhancement in TECs' storage ability.The authors 31 suggested that this PCM-thermal diode system could be integrated with PV solar energy systems to generate electricity while serving as a cooling box for storing medicine.In summary, these studies highlight the potential of PCMs in TECs for improving thermal management, reducing power consumption, and enhancing storage capabilities.Further research and development are needed to explore the applications of PCM-TEC integration in various fields, such as solar energy and medicine storage.
It can be observed from the above literature that the current research direction of integrating PCMs with TECs primarily focuses on two aspects: PCM attachment to the TEC's hot end radiator and the use of circulating refrigerants.However, there is limited application of integrating PCM with miniature TECs for temperature control in precision microinstruments.As a result, there is a lack of comprehensive analysis regarding the thermal management dynamics of PCM-integrated miniature TECs.Furthermore, the existing research on the dynamic analysis of refrigeration performance of miniature TECs under high current and weak heat dissipation conditions is still insufficient.Advancing this research would be significant for the temperature control of precision instruments using miniature TECs.Therefore, it is necessary to optimize the refrigeration performance of miniature TECs under high current and weak heat dissipation conditions.
Fully considering all this, this research suggests a novel approach to improve heat dissipation at the high temperature side of an uneven micro two-step series TEC by incorporating a material that undergoes a change in state, eliminating the requirement for an additional heat dissipation mechanism.This research examines the correlation among various PCM substances, heat transfer coefficient at the hot end, excitation current, thickness of the heat storage block, temperature difference of TEC, and COP.The findings of this investigation demonstrate that the suggested approach of combining PCM with TEC can significantly improve the heat dissipation of the TEC's hot end, eliminating the requirement for an additional heat dissipation system.The TEC's performance has been greatly enhanced, resulting in a higher temperature difference and COP.The research additionally emphasizes the notable impact of PCM substance, hot end thermal conductivity, excitation current, and heat storage block width on the TEC efficiency.To sum up, the suggested approach of combining phase transition substances with TECs offers an efficient resolution for improving the heat dispersion of small-scale TECs utilized in precise microinstruments.Additional research can be conducted to enhance the design variables and explore the real application of this approach in various contexts.

| Structure of the TEC
The paper discusses an asymmetric TEC structure consisting of N c pairs of thermoelectric particles in the upper layer and N h pairs of thermoelectric particles in the lower layer.The cross-sectional area of each element is A, and the height of P-type and N-type thermoelectric particles is h P = h N = 1.4 mm.The ceramic plate thickness is 0.8 mm, and the conductive material is copper with a thickness of 0.4 mm.The TEC bottom is the hot end, while the top is the cold end.The cross-sectional area of each thermoelectric particle is A = l P × w P = l N × w N = 0.9 × 0.9 mm 2 .
When designing the thermoelectric particle pair, the Seebeck coefficient of the P-type and N-type thermoelectric particles is considered to be opposite to each other. 32The paper does not consider the case of hot and cold side switching, and the excitation current I is kept constant.To address the possibility of solid-liquid leakage from the PCM causing a short circuit in the circuit, this study uses aluminum nitride (AIN) as the encapsulation material for the PCM.The thickness of the AlN enclosure is t shell,x = t shell,y = t shell,z = 0.2 mm.The schematic diagram in Figure 1 shows only a single pair of thermoelectric particles to highlight the integration of PCM and TEC.The actual structure of the TEC can be determined based on the structural parameters provided in Table 1.

| Computational methodology
The governing equations for analyzing the thermoelectric cooling behavior using COMSOL Multiphysics 6.0 are provided as follows 25 : In the formula, ρ is the density of the thermoelectric material (kg m −3 ), C p is the specific heat capacity of the thermoelectric material (kJ kg −1 K −1 ), q is the heat flux F I G U R E 1 Schematic representation of a thermoelectric cooler (with two thermoelements) integrated with PCM.AIN, aluminum nitride; PCM, phase-change material.
T A B L E 1 TEC structure parameters.

Parameter Number
Thermoelectric arm thickness (h P = h N ) (mm) 1.4 Thermoelectric particle cross-sectional area through Fourier heat conduction and Peltier heat (W m −2 ), Q is the internal heat of the TEC (W m −3 ), σ is the electrical conductivity of the thermoelectric material (S m −1 ), S is the Seebeck coefficient (V K −1 ), J is the current density (A m −2 ), P is the Peltier coefficient (W A −1 ).The boundary conditions are set as follows: the cooling capacity Q c is set at the cold end, and the external heat transfer coefficient k h is set at the hot end.
Referring to the work of Manikandan and Selvam, 16 this paper considers the unsteady state including PCM heat transfer, using liquid phase ratio (α(T)) to evaluate the melting rate of PCM per unit time.The properties of the corresponding materials (thermal conductivity, density, specific heat capacity, viscosity, and latent heat) are defined for the liquid phase and the solid phase, respectively.The properties of the corresponding material in liquid and solid phases are combined with a phasechange function for phase change from one phase to another.The specific heat capacity of PCMs can be determined as Equation ( 4) The values of (α(T)) in the PCM liquid phase and solid phase are 1 and 0, respectively.Considering the latent heat absorbed or released by PCM per unit time, Equation ( 4) can be changed to where L is the fusion latent heat of PCM.The heat transfer in the solid phase without convective heat transfer can be determined as Equation ( 6) 25 ρC The PCM is arranged near the hot end of the TEC, which is divided into two layers.The lower layer is filled as the gap of the hot end conductive sheet, and the upper layer is arranged in the gap of the thermoelectric particles.For the simple model calculation, the following assumptions are made: 1. TEC side insulation, no heat exchange with the outside world.2. Electrical resistivity, thermal conductivity, and temperature difference of thermoelectric arm particles; the potential does not change with temperature.
3. Ignore the Thomson effect and other microscale effects.
Based on the conclusions in Kaushik et al., 33 the COP is as follows: where Z is the quality factor of the thermoelectric material calculated based on the thermoelectric properties of Bi 2 Te 3 , and T m is the average temperature between the hot side and the cold side of the TEC.

| Grid independence verification of the model
To ensure the accuracy and reliability of the numerical model developed, this section includes grid sensitivity analysis and comparison of results.First, five different meshes (labeled as 1, 2, 3, 4, and 5) are used to evaluate the mesh independence of the PCM-based thermoelectric device in this numerical study.The number and dimensions of the elements are presented in Table 2.
The model is divided into two domains: one for the thermoelectric device and the other for the PCM-based heat sink.The number of elements in each domain varies under different meshes, with counts of 30,457, 64,235, 120,745, 352,007, and 848,420 respectively.Setting the refrigeration capacity at the cold side (Q c ) to be 0.64 W, the heat transfer coefficient between the hot side and the surroundings (k h ) as 300 W/(m 2 K), and the initial ambient temperature at 293.15 K, we input currents of 2.5 A. These currents are used for calculations using the specified grids mentioned earlier to observe the effects of the grid quantity on the cold-side temperature (T c ) and hot-side temperature (T h ) of the thermoelectric refrigeration device.Figure 2 illustrates the relationship between the cold-side temperature of the integrated PCM thermoelectric refrigeration device and the liquid fraction of the PCM over time at different grid quantities.It can be observed that the output results of the model have very small errors for different grid quantities, which meets the validation requirements.

| Model accuracy verification
The purpose of this section is to validate the accuracy of TEC modeling.The TEC modeled in this paper refers to the 83521 model by Hangzhou Deyou Company in China.Therefore, the TEC used for the experimental testing is also the 83521 model by Hangzhou Deyou Company. Figure 3 illustrates the setup of the TEC validation experiment, which includes a vacuum Dewar flask to minimize heat consumption and ensure refrigeration capacity.The TEC testing is conducted inside the Dewar flask with a vacuum level below 0.1 Pa.The current source is used as the power supply and control device for the TEC, allowing for testing with different currents.The TEC's hot side is connected to a heat sink for air cooling, and the heat transfer coefficient to the outside is adjusted by controlling the airflow rate.A temperature sensing device is placed at the refrigeration side of the TEC, connected to a temperature recording device.The experimental procedure includes circuit connection, sealing of the Dewar flask, leak testing of the Dewar flask, electrical testing of the circuit, and recording of experimental data.Figure 4 illustrates the internal structure of the Dewar flask.The black square in the middle represents the actual placement of the TEC, and the circular hole at the bottom is the connection point between the Dewar flask and the vacuum pump.The blue and red wires represent the connection lines of the temperature measuring resistors.Figure 5 illustrates the external environment of the experiment, showing the vacuum pump, the shape of the Dewar flask, and the experimental components such as the testing computer.Figure 6 compares the TEC simulation results with the actual test results.It can be observed that the actual test TEC cold end temperature is approximately 5 K higher than the simulation results.This is primarily due to the fact that the boundary conditions set in the simulation assume complete insulation from the outside world, while the vacuum dewar and vacuum pumping measures taken in the experiment cannot fully achieve complete insulation of the TEC side.As a result, the TEC cold end has some cooling capacity and is not in the noload state.These factors lead to the TEC actual cooling temperature being higher than the simulation results.

| RESULTS AND DISCUSSION
The thermal management of the model in Figure 1 is calculated by COMSOL Multiphysics 6.0.The boundary conditions set as cold end cooling capacity (Q c ) is 0.64 W and hot end and external heat transfer coefficient (k h ) is 300 W/(m 2 K), assuming that the TEC side is insulated from the outside.The thickness of the contact thermoelectric arm of the heat storage block (Δh PCM ) is 0.8 mm, the excitation current (I) is 3 and 3.5 A, and the initial ambient temperature is 293.15K. Figure 6 shows the TEC temperature distribution without PCM integration under two current conditions.
Figure 7 shows the TEC temperature distribution without PCM integration under two current conditions.It can be observed that under the two large current conditions of 3 A and 3.5 A, a high temperature zone appears in the middle of the thermoelectric particles at the bottom, which reduces the TEC temperature gradient and ultimately affects the TEC refrigeration efficiency.When the current is 3.5 A, the calculated temperature in the middle of the underlying thermoelectric particles reaches 360 K. Therefore, it is important to optimize the heat dissipation of the hot end of the finless TEC under large current and working conditions.
In the next section, the paper will evaluate the integration of PCM and TEC under different factors, including different PCMs, different hot end and external heat transfer coefficients (k h ), different excitation currents (I), and the height of PCM (Δh PCM ).The goal is to strengthen the hot end heat dissipation effect of TEC under high current and no radiator auxiliary conditions.F I G U R E 6 Temperature and power simulation of thermoelectric cooler cold end compared with actual data.

| Effect of different PCMs
To investigate the impact of thermal properties of PCMs on the cooling performance of TECs, this section first selects three typical low-temperature PCMs for comparison.These three PCMs are Wood's alloy, paraffin, and nitrates, which correspond to liquid metal PCM, organic PCM, and inorganic salt PCM, respectively.This paper utilizes three distinct materials for thermal storage that undergo phase change, and their characteristic parameters can be found in Table 3. Wood's alloy possesses the greatest thermal conductivity among the three materials, paraffin exhibits the lowest melting point and the highest latent heat, while sodium nitrate demonstrates the highest specific heat capacity.The objective is to investigate the parameters of the PCM and the integration method of PCM and TEC that have a significant influence on enhancing heat dissipation at the TEC's hot end.For simplicity, the following three PCMs are used: PCM1, PCM2, and PCM3.
The experiment's boundary conditions include a cooling capacity (Q c ) of 0.64 W, a hot end heat transfer coefficient (k h ) of 300 W/(m 2 K), the height of PCM of 0.8 mm (Δh PCM ), an excitation current (I) of 3.5 A, and an initial ambient temperature of 293.15 K.
The section conducts a transient stimulation of the TEC system with the integration of three PCMs with a time length of 100 s and a step length of 1 s.At 100 s, Figure 8 displays the temperature distribution of the TEC system with the integration of three PCMs.In comparison to Figure 7, the TEC system without PCM integration exhibits a cold end temperature of 266 K and a hot end temperature of 317 K. Conversely, the TEC system integrated with three PCMs showcase cold end temperatures of 246.7, 250.76, and 246.82K, along with hot end temperatures of 316.23, 316.57, and 316.25 K, respectively.On average, the cold end temperature typically decreases by approximately 20 K, whereas the hot end temperature remains nearly constant.
Figure 9 illustrates the variations in temperature at the cold and hot ends, the Seebeck coefficient of the thermoelectric component, and the COP of the TEC system with or without PCM integration as time progresses.As time passes, it is noticeable that the cold end temperature of the TEC system integrated with and without PCM decreases, whereas the hot end temperature remains relatively constant.Consequently, this results in an expansion of the temperature disparity.Nonetheless, the TEC system with PCM integration diminishes the Seebeck coefficient of the thermoelectric arm, resulting in a higher COP compared to the TEC system without PCM integration in the initial 10 s, but a lower COP within the 10-100 s timeframe.The decrease in the Seebeck coefficient is depicted in Figure 10A.As   the temperature rises, the Seebeck coefficient of the thermoelectric material also increases.However, when the TEC is integrated with PCM, it reduces the temperature at both the cold and hot ends of the TEC.This leads to a decrease in the Seebeck coefficient of the thermoelectric element compared to a TEC without PCM integration.In Figure 10B, the COP comparison is shown between the TEC integrated with PCM and PCM in liquid form.The COP of the TEC integrated with PCM is noticeably greater than that of the TEC without PCM when observing the melting process of PCM.Nevertheless, after the PCM is fully liquefied, the rate at which the temperature rises at the hot end of the TEC system with PCM increases, while the temperature at the cold end is lower compared to the TEC system without PCM.As a consequence, the TEC system with PCM exhibits a reduced COP once the PCM has melted.Furthermore, a comprehensive comparison of the temperature and COP results for PCM1, PCM2, and PCM3 in Figure 9A,B shows that, in the initial stage, the cold terminal temperature of PCM1 and PCM3 is similar and lower than that of PCM2.The hot terminal temperature is higher for PCM2, followed by PCM1 and then PCM3.In terms of COP, PCM3 has a higher value than PCM1 and PCM2.After 20 s, the cold terminal temperature of PCM1 and PCM3 becomes similar and lower than that of PCM2.Similarly, the hot terminal temperature of PCM1 and PCM3 also becomes similar and lower than that of PCM2.The COP values for all three PCMs become quite Based on these observations, we can conclude that before complete melting of the PCM, PCM3 benefits from its higher latent heat, allowing it to absorb heat from both the TEC's cold and hot terminals more effectively.Although it does not result in lower cold terminal temperature, it leads to lower hot terminal temperature and higher COP.However, once the PCM is completely melted, the latent heat no longer plays a role, and the TEC performance for PCM1 and PCM3 becomes almost identical.
The primary aim of the new method of the TEC with PCM integration is to alleviate the heat accumulation in the middle section of the TEC hot end thermoelectric arm under large current conditions, as observed in Figure 7, through the heat absorption of PCM.This method aims to strengthen the heat dissipation of the hot end.Figure 11 illustrates the relationship between PCM liquid phase, PCM average temperature of the middle section of the TEC hot end thermoelectric arm with or without PCM integration for TEC systems integrated with different PCMs.
The TEC hot end thermoelectric arm without PCM integration reaches a temperature of 360 K at 10 s, whereas the TEC hot end thermoelectric arm with PCM integration experiences a gradual increase in temperature as the PCM melts.The thermoelectric arm of the Wood's alloy-and sodium nitrate-integrated PCM system reaches a middle temperature of 330 K at 10 s, whereas the paraffin-integrated system achieves a middle temperature of 340 K. Despite having the highest latent heat, paraffin exhibits the fastest melting rate and reaches the highest final temperature due to its exceptionally low melting point.Conversely, Wood's alloy and sodium nitrate exhibit elevated melting temperatures, leading to reduced melting speeds, and Wood's alloy possesses the greatest thermal conductivity, whereas sodium nitrate boasts the highest heat of fusion.The hot end strengthening effect is influenced by these factors, with paraffin having the least impact in comparison to Wood's alloy and sodium nitrate.

| Effect of hot end heat transfer coefficient (k h )
To verify that the new TEC with PCM integration mode can enhance the heat dissipation of the TEC hot end under more severe heat transfer conditions, this section evaluates the effect of strong and weak heat transfer coefficients on the PCM system by varying the heat transfer coefficient of the hot end surface.The boundary conditions are set as follows: the cooling capacity (Q c ) of the cold end is 0.64 W, the heat transfer coefficient (k h ) of the hot end is varied from 200 to 500 W/ (m 2 K), the height of the PCM block (Δh PCM ) is 0.8 mm, and the current condition is set to 3.5 A. The initial ambient temperature is 293.15K, and PCM1 is used.
The aim of this analysis is to evaluate whether the new TEC with PCM integration mode is effective under more severe heat transfer conditions.By varying the heat transfer coefficient of the hot end surface, the impact of different heat transfer conditions on the performance of the TEC system can be evaluated.The results of this analysis will help to identify the most effective approach to optimize TEC performance under practical operating conditions.
Figure 12A illustrates the cold-and hot end temperatures of TEC with or without PCM integration under different hot end heat transfer coefficients.It can be observed that the use of TEC integrated with PCM under different heat transfer coefficient conditions results in a maximum temperature drop of 5 K compared to the TEC system without PCM integration, while the cold end temperature drops by about 20 K.The cold end temperature of the integrated PCM system is lower than that of the TEC without PCM integration at k h = 200 W/ (m 2 K), demonstrating the optimization of temperature difference at the cold end.At k h = 500 W/(m 2 K), the cold end temperature of the TEC without PCM integration is the same as that of TEC with PCM integration, demonstrating the effectiveness of PCM integration in reducing the cold end temperature.Figure 12B shows the relationship between the heat transfer coefficient and the PCM liquid under different heat transfer coefficients.It can be observed that at k h = 200 W/(m 2 K) and k h = 300 W/(m 2 K), the PCM melts completely within 10 s.However, at k h = 400 W/(m 2 K) and k h = 500 W/(m 2 K), the PCM does not completely melt, and after reaching the highest melting point, it falls back to a solid state.This is because under high heat transfer coefficients, the TEC hot end temperature exceeds the PCM melting point, and the melting of PCM absorbs a lot of heat, leading to a stable TEC hot end temperature at the PCM melting point, causing some of the PCM to solidify again.Figure 12C shows the COP optimization diagram, which demonstrates that the COP of TEC integrated with PCM is better than that of TEC integrated without PCM when PCM is melted.However, the COP of TEC with integrated PCM is lower than that of TEC without integrated PCM when PCM is melted, and the time is about 0-20 s. Figure 12D shows the Seebeck coefficient of the thermoelectric element and the instantaneous temperature of the PCM of the TEC integrated with PCM and the TEC integrated without PCM.It can be observed that under different heat transfer coefficient conditions, the TEC integrated with PCM reduces the temperature of the cold and hot ends of the TEC simultaneously, leading to a decrease in the Seebeck coefficient of the thermoelectric element.The PCM temperature follows the law of the PCM liquid phase ratio and reaches the highest value at 20 s under the four heat transfer coefficient conditions, after which it stabilizes.
Figure 13 illustrates the temperature of the middle section of the TEC hot end thermoelectric arm with or without PCM integration under different hot end heat transfer coefficients compared with PCM temperature and PCM liquid.It can be observed that the middle temperature of the hot end thermoelectric arm of the TEC system without PCM integration reaches over 360 K.In contrast, the temperature of the middle section of the TEC hot end thermoelectric arm with PCM integration is 343 K at the worst heat transfer coefficient (k h = 200 W/ (m 2 K)), 320 K at the best heat transfer coefficient (k h = 500 W/(m 2 K)), and the difference between the four heat transfer coefficient conditions is about 40 K.Under the two heat transfer coefficient conditions of k h = 200 W/(m 2 K) and 300 W/(m 2 K), the PCM is completely melted within 10 s, and the PCM temperature tends to stabilize after 10 s.Under the two heat transfer coefficient conditions of k h = 400 W/(m 2 K) and 500 W/ F I G U R E 13 PCM liquid fraction at different heat transfer coefficients.Intermediate temperature of the TEC hot end thermoelectric arm with or without PCM integration.(A) (m 2 K), the PCM reaches the maximum melting amount at about 20 s, and the temperature of the PCM also reaches the highest at about 20 s, after which it decreases as the melting rate of the PCM decreases.These results demonstrate the effectiveness of the PCM integration approach in reducing the temperature of the middle section of the TEC hot end thermoelectric arm under severe heat transfer conditions.The results also highlight the importance of selecting an appropriate heat transfer coefficient for the hot end to optimize the performance of the TEC system.

| Effect of current (I)
The objective of this section is to investigate how the integration of PCM in TEC mode enhances the heat dissipation of the TEC hot end at varying current conditions.The specified boundary conditions include a cold end cooling capacity (Q c ) of 0.64 W, a hot end heat transfer coefficient (k h ) of 300 W/(m 2 K), and the height of the PCM block (Δh PCM ) of 0.8 mm.The current conditions are divided into 2.5, 3, and 3.5 A. The initial ambient temperature is 293.15K, and PCM1 is used.The aim of this analysis is to evaluate whether the TEC with PCM integration mode is effective under different current conditions.The evaluation of the TEC system's performance can be done by altering the current conditions and observing the effects of different operating conditions.Analyzing the data will assist in determining the most efficient method to enhance TEC performance in real-world operating conditions.
At various current conditions, Figure 14A illustrates the temperature and temperature variation between the hot and cold ends of the TEC integrated with PCM.The temperature variation between the cold end of TEC integrated with PCM and TEC integrated without PCM is less than 5 K when the current is 2.5 A, and the hot end temperature decreases by approximately 1 K.When the current is 3 A, the integrated PCM experiences a decrease of 9 K in temperature at the cold end, while the temperature at the hot end decreases by less than 1 K.By adjusting the current condition to 3.5 A, the cold end temperature can be enhanced by up to 20 K.At a current of 2.5 A, the TEC equipped with integrated PCM achieves a maximum temperature difference of 74 K, while at 3 A, it achieves a maximum temperature difference of 73 K. TEC can achieve a reduced cooling temperature when operating with two smaller current conditions.
At various current conditions, Figure 14B depicts the correlation between COP and PCM liquid fraction over time for TEC integrated with or without PCM.Figure 14C represents the amplification at a local level of Figure 14B within a time span of 0-20 s.Under the current condition of 2.5 A, there is minimal evidence of PCM melting.In the current state of 3 A, the proportion of liquid phase in PCM ultimately amounts to 56%, with a maximum melting speed of 70% and a duration of 20 s.PCM is fully melted within 10 s under a current condition of less than 3.5 A. During the melting of PCM, the TEC integrated with PCM exhibits a higher COP under various current conditions compared to the TEC without PCM.The TEC's refrigeration efficiency decreases when integrated with PCM compared to the TEC without PCM, at a current of 2.5 A. After the PCM solidifies, the COP of the TEC integrated without PCM surpasses that of the integrated PCM, gradually decreasing.The relationship between the temperature of PCM and the Seebeck coefficient of the thermoelectric element is depicted in Figure 14D over time.The PCM temperature and liquid fraction exhibit a comparable temporal pattern, resembling the previous discourse.However, the Seebeck coefficient of the TEC thermoelectric component combined with PCM is inferior to that of the TEC lacking integrated PCM.It is important to mention that in the present state of 2.5 A, despite the PCM's melting rate consistently nearing 0, the TEC's cold and hot ends experience a decrease in temperature as the PCM temperature gradually rises.This decrease also to a reduction in the Seebeck coefficient of the thermoelectric component.The findings illustrate how the integration of PCM in TEC mode enhances heat dissipation at the TEC hot end across various current conditions.
Figure 15 illustrates the PCM liquid fraction at different currents, the temperature of the middle section of the hot end thermoelectric particles with or without PCM, and the relationship between PCM temperature and time.It can be observed that at a current of 2.5 A, the PCM melting rate between 5 and 22 s is within 1%, and the rest of the time is 0, which makes the PCM temperature close to the temperature of the middle section of the thermoelectric particles at the hot end of the TEC, and the difference between the two is within 2 K.This is due to the fact that the TEC will not have a serious heat accumulation in the middle section of the thermoelectric particles at the hot end under the high current condition of 3.5 A. Under this condition, the temperature of the middle section of the thermoelectric particles at the hot end of the TEC system without PCM integration is 330 K.When the current is 3 A, the middle temperature of the thermoelectric particles at the hot end of the TEC system without PCM integration is 340 K, and the melting rate of the integrated PCM cannot reach 100% at this temperature.The final PCM melting rate is 56%, which makes the temperature of the middle section of the hot end thermoelectric arm drop to about 320 K, and the average temperature of PCM is stable at about 314 K.When the current is 3.5 A, the temperature of the middle section of the thermoelectric particles at the hot end of TEC system integrated without PCM is 360 K, and PCM is completely melted in about 10 s, so that the temperature of the middle section of the thermoelectric particles at the hot end of TEC is finally stabilized at about 330 K, and the average temperature of PCM is 320 K.
These results demonstrate the effectiveness of the TEC with PCM integration mode in reducing the temperature of the middle section of thermoelectric particles at the hot end under different current conditions.By using PCM, the TEC system can achieve better thermal management and improve its performance.

| Effect of contact height of PCM with thermoelectric particles (Δh PCM )
The purpose of this section is to examine how the distance of contact between the regenerator and the thermoelectric particles at the hot end of the TEC affects the improved heat dissipation at the hot end of the TEC.
The following are the specified boundary conditions: the cold end's cooling capacity (Q c ) is 0.64 W, the hot end's heat transfer coefficient (k h ) is 300 W/(m 2 K), and the current condition is set at 3.5 A. PCM1 is utilized while adjusting the thickness of the thermoelectric particles at the contact hot end of the heat storage block, ranging from 0 to 1.2 mm with 0.2 mm intervals.The aim of this analysis is to assess the impact of the proximity between the regenerator and the thermoelectric particles at the hot end of the TEC on heat dissipation.The evaluation of the TEC system's performance can be done by altering the thickness of the thermoelectric particles and observing the effect on various contact distances.The findings from this analysis will assist in determining the ideal proximity for achieving optimal heat dissipation performance of the TEC system in real-world operating conditions.The temperatures of the hot and cold ends and the temperature differences of the TEC integrated with PCM at various Δh PCM lengths are depicted in Figure 16A.The gradual decrease of the cold end temperature and hot end temperature of the TEC integrated with PCM can be noted as Δh PCM increases.At Δh PCM = 1 mm, the coldest temperature at the cold end is 246 K when t = 100 s, which is the lowest.At Δh PCM = 0.8 mm, the minimum hot end temperature is reached, measuring 309.8K at t = 100 s.Initially, the temperature disparity between the warm and cool extremities of the TEC rises but subsequently diminishes as Δh PCM increases.At a time of 100 s, the highest disparity in temperature is 68.92 K, occurring when the length of the path is 1 mm.The findings suggest that there exists an ideal length for the Δh PCM that can maximize the heat dissipation efficiency of the TEC system.
Under various Δh PCM lengths, Figure 16B depicts the variation in temperature of PCM and the Seebeck coefficient of the thermoelectric element in the TEC integrated with PCM.The temperature of PCM exhibits an initial increase followed by a subsequent decrease across all Δh PCM lengths.In the initial 50 s, the PCM's temperature rises as Δh PCM increases, while in the final 50 s, the PCM's temperature decreases as Δh PCM increases.As Δh PCM increases, the time taken to reach the maximum temperature of PCM decreases.When Δh PCM = 1.2 mm, PCM reaches the highest temperature in 20 s.As the PCM liquefies and takes in the heat gathered at the TEC's hot end, the temperature of the thermoelectric component decreases in comparison to the TEC integrated without PCM.Likewise, the Seebeck coefficient of the thermoelectric component initially decreases and subsequently rises as Δh PCM increases.
Figure 17A shows the COP and PCM liquid fraction of TEC integrated with PCM at different l p . Figure 17B,C  absorption of PCM, the temperature rise rate of the hot end is lower than that of the TEC without PCM integration.At this time, the COP of the integrated PCM has an optimization amount more than that of the TEC without PCM, and the optimization amount increases first and then decreases with the increase of Δh PCM .When the optimization amount is the largest, Δh PCM is 0.8 mm.After 20 s, due to the large decrease in cold end temperature, the change of hot end temperature is much smaller than that of TEC without PCM, which makes the COP of TEC with PCM lower than that of TEC without PCM, and the COP decreases first and then increases with the increase of Δh PCM .The minimum COP of Δh PCM is 1 mm. Figure 17D illustrates the relationship between the temperature of the middle section of the thermoelectric particles at the hot end of the TEC and the PCM liquid fraction.It can be seen that the heat absorbed during the PCM melting process relieves the accumulated heat in the middle of the thermoelectric particles at the hot end of the TEC.With the increase of Δh PCM , the temperature of the middle section of the thermoelectric particles in the hot end of TEC decreases first and then increases, and the lowest Δh PCM is 1 mm.The findings indicate that the ideal length of the Δh PCM can also impact the thermal characteristics of the TEC system integrated with PCM.Therefore, it is crucial to determine the optimal Δh PCM length to attain optimal heat dissipation performance for the TEC system.

| CONCLUSIONS
The present research suggests a novel approach to combine PCMs with hot spot coolers to improve the heat dissipation of the hot section in an imbalanced twostep TEC during situations of elevated current.The study has yielded the following findings: Integrating various PCMs in TEC leads to a decrease in the TEC's cold end temperature.The temperature drops from 266.11 K (without PCM) to 246.7 K for Wood's alloy, 250 K for paraffin (possessing the greatest latent heat), and 246.82K for sodium nitrate.The temperature difference increases from 51.67 K to a maximum of 67.53 K.
When PCM is integrated with TEC, the cold end temperature decreases by 20 K under various hot end heat transfer coefficients.Additionally, the temperature difference increases by an average of 15 K compared to TEC without PCM integration.
When the current is small, the TEC's hot end temperature does not reach the phase transition temperature of the PCM, causing the cold end temperature to decrease from 20 to 5 K in comparison to high current situations.
The optimal enhancement is attained by ensuring that the contact length between the regenerator and the hot end thermoelectric particles is equal to half the height of the hot end thermoelectric particles.
During the melting phase of the PCM, the COP of integrated PCM surpasses that of integrated TEC without PCM, but at other times, the COP is inferior to that of integrated TEC without PCM.
The thermoelectric particles with PCM TEC exhibit a lower Seebeck coefficient compared to those without PCM TEC.
In general, incorporating phase-change substances with hot spot coolers can greatly decrease the temperature at the cold end and enhance the temperature difference of TEC.It is important to mention that the enhancement in the COP of TEC is significant solely during the melting stage of the phase-change substance.Additional investigation is required to examine the thermal aversion of PCM, which has the potential to prolong the melting duration of PCM and enhance the COP even more.The research offers a fresh approach to improving the efficiency of thermoelectric devices.

F I G U R E 2
Thermoelectric refrigeration device and phase-change material (PCM) grid independence test.(A) T c and (B) liquid fraction of PCM.F I G U R E 3 Verification of TEC modeling accuracy experiment.TEC, thermoelectric cooler.CHEN and ZHANG | 57

F I G U R E 4
The actual test diagram of thermoelectric cooler in vacuum dewar.F I G U R E 5 Experimental overall physical picture.

F I G U R E 7
Thermoelectric cooler temperature field distribution under 3 A and 3.5 A current conditions.(A) I = 3 A and (B) I = 3.5 A. T A B L E 3 Characteristic parameters of three PCMs.Parameter Wood's alloy (PCM1) Paraffin (PCM2) Sodium nitrate (PCM3) Thermal conductivity [W/(m

F I G U R E 8 F
Integrated thermoelectric cooler temperature distribution of different phase-change materials.PCMs are: (A) Wood's alloy, (B) paraffin, and (C) sodium nitrate.(A)F I G U R E 9 (A) Thermoelectric cooler (TEC) real-time cold and hot end temperature.(B) TEC real-time temperature difference and COP.COP, coefficient of performance; PCM, phase-change material.I G U R E 10 (A) Relationship between the Seebeck coefficient of Bi 2 Ti 3 and temperature.(B) Relationship between COP and liquid fraction of PCM.COP, coefficient of performance; PCM, phase-change material.

11
Phase-change material (PCM) liquid fraction and average temperature in the thermoelectric cooler integrated with PCM.PCMs are: (A) Wood's alloy, (B) paraffin, and (C) sodium nitrate.CHEN and ZHANG | 61

F
I G U R E 12 Thermoelectric cooler (TEC) transient calculation results under different heat transfer coefficients.(A) Hot and cold end temperatures of TEC.(B) Relationship between Refrigeration coefficient and phase-change material (PCM) liquid fraction (t = 0-100 s).(C) Relationship between refrigeration coefficient and PCM liquid fraction (t = 0-20 s).(D) Relationship between PCM temperature and Seebeck coefficient.

FF
I G U R E 14 (A) Temperature and temperature difference between hot and cold ends.(B) Relationship between coefficient of performance (COP) and phase-change material (PCM) liquid fraction (t = 0-100 s).(C) Relationship between COP and PCM liquid fraction (t = 0-20 s).(D) PCM temperature and thermoelectric particle Seebeck coefficient.I G U R E 15 PCM liquid fraction PCM temperature under different currents.Intermediate temperature of the TEC hot end thermoelectric arm with or without PCM integration.(A) I = 2.5 A, (B) I = 3 A, and (C) I = 3.5 A.
is partially enlarged from Figure 17A by 20 s.It can be seen that the PCM under all conditions is completely melted at 10 s, and the complete melting time increases with the increase of Δh PCM .In the first 20 s, due to the heat (A) (B) F I G U R E 16 (A) The temperature and temperature difference between the hot and cold ends of thermoelectric cooler (TEC) with phasechange material (PCM) under different Δh PCM .(B) PCM temperature and Seebeck coefficient of thermoelectric elements of TEC integrated with PCM at different Δh PCM .

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I G U R E 17 (A) Coefficient of performance (COP) of thermoelectric cooler (TEC) with phase-change material (PCM) and liquid fraction of PCM under different Δh PCM (t = 0-100 s).(B) COP of TEC with PCM and liquid fraction of PCM under different Δh PCM (t = 0-20 s).(C) COP of TEC with PCM and liquid fraction of PCM under different Δh PCM (t = 20-100 s).(D) COP of TEC with PCM and liquid fraction of PCM under different Δh PCM (t = 0-20 s).