Design and performance analysis of hot side heat sink of thermoelectric cooler device based on simulation and experiment

As for improving the heat diversion capacity of the hot side heat sink of the thermoelectric cooler (TEC), thereby improving the operational performance of the TEC, this study designed a type of double‐embedded flat heat pipe (EFHP) finned heat sink and compared with a standard aluminum (Al) heat sink. In experimental studies, TEC under two heat sinks were placed under different operating currents for heat transfer analysis and performance comparison. The experimental results demonstrated that the EFHP heat sink had better heat diversion ability, effectively improving the operational performance of TEC. When the TEC was input with a current of 6A, the thermal resistance of the double EFHP finned heat sink decreased by 19% compared to the Al heat sink; cooling capacity and coefficient of performance increased by 8.3% and 9.46%, respectively. Further, TEC's cold and hot surface temperatures decreased by 10.83% and 10.2%, respectively, and the heat uniformity of the heat sink improved. In addition, the CFD software Icepak was used to analyze the effects of double flat heat pipe spacing and length on the heat sink and TEC and the performance of two heat sinks and TEC under different heat dissipation conditions and obtained good agreement. This study can provide further guidance and assistance in designing the TEC cooling system.


| INTRODUCTION
Thermoelectric cooler is an innovative and environmental approach to cooling technology.Thermoelectric cooler (TEC) works mainly based on the Peltier principle, which causes TEC to absorb heat on one side and heat release on the other when direct current passes through the TEC, 1 so the TEC can be used as a cooling or heating device.Compared with traditional compression coolers, it has many irreplaceable advantages, for example, small size, long life, no noise, accurate temperature control, no working fluid, reliability, and no need for refrigerant.
These advantages make thermoelectric cooler devices have extraordinary application prospects in the fields of medical treatment, 2 LED lamp coolers, 3 electronic equipment coolers, 4,5 and portable small thermoelectric refrigerators.However, the thermoelectric cooler devices exhibit a coefficient of performance (COP) that is inferior to that of compression coolers.So, enhancing the performance of thermoelectric coolers remains a pressing concern. 6enerally, two ways exist to enhance the cooling performance of a thermoelectric cooler device. 7(1) Change the internal inherent parameters of the thermoelectric device.For example, developing new thermoelectric materials, 8 changing the shape or size of thermoelectric arms, [9][10][11] segmented P-and N-type crystal grains 12 and multistage TEC. 13,14(2) Improving the heat dissipation capacity of thermoelectric cooler devices.The heat heatsinking effectiveness of the hot side restricts the cooling capability of thermoelectric cooling devices.He et al. 15 pointed out that during the actual operation of thermoelectric devices, the chip should maintain optimal working voltage and give precedence to improving the thermal side cooling performance of the devices to maximize the cooling performance.In addition, the layout and equipment size of TEC can also affect the performance of TEC, and Faraz et al. 16 studied the performance and layout size of the air-to-water binary TEC system.Extensive study has been done to increase cooling efficiency and heat dissipation situations on the hot side of TEC.To cool down the hot sides of thermoelectric devices, there are natural convection heat dissipation, 17,18 forced air cooling, heat pipe, water cooling, 19 thermosyphon, 20,21 microchannel heat sink, 22 recently about sky-based radiant TEG cooling technology has been successfully developed, [23][24][25] and so on.Among these cooling methods, heat pipe cooling technology is worthy of attention.Heat pipes rely on the liquid and gas in the tube to undergo a phase change to transfer heat.It is a highly efficient, reliable heat transfer device with low thermal resistance.It expands the heat transfer area, reduces temperature difference in the heat transfer process, and then ensures temperature uniformity during the heat transfer process.Sun et al. 26 advised the installation of gravity-assisted heat pipes on the hot sides of TEC devices to enhance thermal performance and conducted an experimental comparison with an aircooled heat sink.Their consequences show that gravityassisted heat pipes can increase the cooling capacity of the TEC device by 64.8%.Lv et al. 27 designed three different hot-side cooling modes for thermoelectric generators (TEG) to produce a large temperature difference when studying TEG, and verified through experiments that heat pipe cooling heat exchanger is the most effective.Liu et al. 28 established five different forms of heat dissipation methods to study the effectiveness of the thermoelectric module frosting system.The comparison results show that the thermoelectric device with fanenhanced heat pipe heat dissipation has the highest frost COP, which is better than water-cooled heat dissipation.Li et al. 29 combined a flat heat pipe with a finned heat sink and tested the heat dissipation capacity of this type of heat sink under natural convection.Their results showed that heat load effectively eliminated is 80 W and minimum thermal resistance is 0.025 KW −1 .Wu et al. 30 designed the gravity-type flat heat pipe as a heat sink, which diffused the heat from the local heat source, and compared it with the aluminum finned heat sink, proving that effectiveness of thermoelectric generator can be improved by increasing temperature uniformity.
In summary, it can be seen that heat pipes are widely used in thermoelectric devices because of their superior thermal conductivity, and TEC can be better performed by using heat pipes.However, previous studies have mainly used gravity-assisted heat pipes in large equipment to enhance heat exchange, which often requires additional space and is unacceptable when space constraints cannot provide extra space.Moreover, there is not much research on the application of heat pipes in commonly used small aluminum flat-fin heat sinks and how heat pipes affect the performance of TEC.From previous literature and experience, we can guess that a heat pipe quickly transfers concentrated heat to the far end of the heat sink to make the heat distribution uniform, so in this paper, an embedded flat heat pipe (EFHP) finned heat sink is proposed to explore the influence of temperature uniformity on TEC performance.The design in this article has the advantage of not requiring additional space and being economical.Additionally, numerical research has also become an important part of literature research, and some scholars have combined numerical research and experiments to study heat transfer systems to obtain better research results. 16,31,32This study uses a combination of experimental and numerical research to verify the model's accuracy and feasibility under different conditions.

| Heat transfer processes and mathematical model of TEC
Figure 1 presents a thermal analogy network and schematic diagram of the TEC.The thermoelectric cooling system comprises a cold plate, insulation cotton, a thermoelectric module, a hot-side heat sink, and a hot-side fan.The experimental study used two commercially available TECs from Henan Guanjing Technology Company (Product No.: SP4040079L1) and subsequent numerical simulations.The primary geometric parameters of the TEC are listed in Table 1, and their commercial performance parameters are presented in Table 2.
The main evaluation criteria for the heat sink thermoelectric cooler module include its gross cooling capacity under various operating conditions, entire thermal resistance, and overall COP. 33For TEC, when DC passes through the TEC, the Peltier effect causes heat absorption on one side of the TEC and heat release on the other, resulting in a temperature difference between the two sides of the TEC.Generally, the cooler side absorbs heat, while the hotter side releases heat.So, TEC can realize the ability to bring heat from the cold side to the hot side.
The internal thermal equilibrium equation of the TEC is 34 : where Q c and Q h are the TEC's gross cooling capacity and heating generation, respectively.The experiment allows for the measurement of all T C and T h variables.I is the amount of current traversing the TEC.The terms S m , R m , and K m in the equation, stand for the Seebeck coefficient, electrical resistance, and thermal conductivity of the TEC, respectively.Based on the TEC operating parameter table (Table 2) provided by the vendor, the values of S m , R , m and K m can be calculated using the below formula proposed by Zhang et al. 35

S
The entire thermal resistance of the thermoelectric cooling device is the ratio of its heat dissipation to the ambient temperature difference.We can calculate it by the below formula.
COP is an important index for evaluating the cooling performance of thermoelectric cooler devices.COP is defined as the ratio of the overall cooling capacity of the equipment to the overall energy input.| 4465 where P represents the electrical power input to the TEC model and is calculated as the difference between heat dissipation and heat absorption of the TEC.
2.2 | Double embedded flat heat pipe finned heat sink model The heat pipe is a highly efficient heat dissipation device that uses the principle of evaporation and condensation heat transfer.A schematic diagram of the flat heat pipe working principles is shown in Figure 2A, and its position and size in the heat sink are shown in the red part in Figure 2B, Figure 2B is the structure and principle diagram of the EFHP heat sink.
During the working process, the heat source heats the local wall of the flat heat pipe, and the liquid working fluid inside the liquid suction core near the heat source is heated, and phase change evaporation occurs.Due to the evaporation of the working fluid near the heat source in the steam zone, the mass flow rate and temperature are higher, resulting in higher pressure, pushing the steam flow to other areas with lower pressure, and condensing and releasing heat in the low-temperature region.The working fluid condensed into a liquid state flows back along the capillary core to the area near the heat source under the action of capillary force and re-evaporates, thus forming a cycle over and over again.
The finned heat sink is made of aluminum alloy, and heat pipes are embedded in the substrate, the purpose of which is to transfer the concentrated heat on the substrate to other areas to utilize the heat dissipation capacity of the heat sink fully.Figure 2B presents the working principle and structural dimensions of the double EFHP heat sink used in the experiment.Among them, the length of the EFHP (L hp ) is 120 mm, the width (W hp ) is 10 mm, the thickness is 4 mm, and the spacing between the double heat pipes (S hp ) is 5 mm.

| Experiment procedures
A finned heat sink with an aluminum bottom was created to compare with an EFHP heat sink for investigating the heat dissipation performance of this type of heat sink.Physical diagrams of these two heat sinks are presented in Figure 3.Among them, the top view of the two heat sinks is consistent.The number of fins and overall geometry size of the two heat sinks should be consistent to facilitate experimental comparison.Thermal grease was uniformly applied between the TEC device and heat sink to decrease the thermal resistance of the heat transfer process.Additionally, a layer of insulation cotton was added around the TEC to reduce heat loss.Cooling devices were assembled and fixed with bolts and nuts, and it is worth noting that a torque wrench was used during installation to ensure that the torque was set to 0.8 to prevent the TEC unit from cracking due to uneven force distribution.
The experimental device diagram is illustrated in Figure 4. T-type thermocouples are utilized for temperature detection in the data acquisition system; a paperless recorder records temperature and the computer is responsible for data processing.Figure 5 displays the specific locations of the thermocouple used in this experiment, with eight recorded locations.Within Figure 5, temperature points 1-4 depict the four measurement points on the underside of the heat sink, which were utilized to assess the uniformity of heat distribution across the heat sink.Temperature measuring points 5-6 are the common temperature between the hot side of TEC and the bottom of the heat sink.Underneath TEC is a cold plate wrapped in insulated cotton.Additionally, a temperature measuring point was implemented on the cold surface, which corresponds to the hot surface of TEC.To ensure a stable power supply, current source one was used to control incoming current to the TEC, and current source two was used for a steady power supply of the fan.In addition, the size of the fan used in the experiment is 120 × 120 × 25 mm, the voltage is 24 V, the speed is 2000 PRM, the wind pressure is 2.97 mmH 2 O, and the air volume is 69.71CFM.The accuracy of the instruments employed is presented in Table 3.

| NUMERICAL SIMULATION MODELS 3.1 | Physical model
The interior of the thermal conduit constitutes a multiphase flow thermal exchange process, and the process cannot be directly simulated.To facilitate  | 4467 numerical simulations, the heat pipe in the model is equivalent to a high thermal conductivity component.In this way, the high heat conductivity of local modules can be simulated without affecting the heat transfer of other component components.According to the data provided by the manufacturer and referring to previous related studies, [36][37][38] the equivalent thermal conductivity of the flat heat pipe is set to 2000 W/(m•K).
In this study, the numerical simulation of the air-cooled thermoelectric device is carried out, and its physical model is shown in Figure 6.The surface at both ends of the heat sink serves as an outlet for airflow.Two TECs are arranged between the heat sink and cold plate, and a fan model is set in a central area above the heat sink.The fan diameter is 120 mm, the initial rotation speed is 2000 RPM, the air volume is 69.71CFM, and the wind pressure is 2.91 mmH 2 O, which is consistent with the experimental parameters.The position and dimensions of the heat sink and TEC are consistent with the above experiment.The material of the heat sink is aluminum alloy, and the fluid working fluid is air.Table 4 shows the physical properties of the materials used for the simulation.Where ρ is the density, C p is the heat capacity, λ is the thermal conductivity, and η is the dynamic viscosity coefficient of air.

| Boundary conditions and basic assumptions
The numerical simulation analysis adopts ANSYS Icepak software based on the coupling numerical simulation of three-dimensional thermal fluid structure.The set computing domain is larger than the physical model.Both ends of the computing domain are openings connected with the outside world, and the other faces are non-thermal conductive interfaces.The fan is a boundary fan.Air is blown into the calculation area from the outside through the fan and flows out from the opening at both ends through the heat sink.The followings are basic assumptions of numerical simulation 39,40 : 1. Thermal conduction, convective thermal transfer, and gravity are considered, but heat radiation is not considered.2. No relative position, thermal contact resistance is not considered.3. The fluid is incompressible air, and the initial ambient temperature is 21°C.The solution process is a steadystate solution.4. The TEC model is set at the bottom of the substrate, and its internal physical materials and geometric parameters are consistent with the experimental TEC parameters.

| Governing equation
Based on the above assumptions and conditions.Continuity equation for the steady, incompressible laminar flow 41 : Momentum equation:   Energy equation: where u v w , , are the velocities in x y z , , directions; ρ 0 is the density of the air corresponding to the ambient temperature; C p is constant heat capacity; T is temperature.

| Grid independence test
Mesher-HD mesh (hexahedral dominant mesh) was used for numerical simulation in this simulation.To facilitate meshing and solving, a 2D fan model provided by Icepak was used for calculation.When studying the influence of meshes on simulation results, not only is the mesh encrypted to ensure mesh quality and skewness values, but also different mesh accuracy and quantity are tested and compared, and the overall mesh and local mesh details are shown in Figure 7.The number of grids and results of specific tests are shown in Table 5.As seen from the results in Table 5, different grids have little effect on the calculation results.For careful consideration, grid 2 is used for calculation in the following simulation.

| Simulation and experimental validation
To verify the accuracy of the model, the TEC created in Icepak was first numerically simulated, and the manufacturer's experimental data and simulation results are shown in Figure 8.The overall data of the two are relatively close, specifically reflected in the large error at ΔT (temperature difference between the two sides of the TEC) = 0°C, the maximum relative error is 6.9%, and the error is getting smaller and smaller as ΔT increases.The results of Figure 8 show that the TEC model has good accuracy.
The experiment and simulation keep the same trend, and the error is within a reasonable range.This conclusion can be found in Figure 9 and Table 6.Error value of experimental and simulation results of (T h -T c ).Through comparing simulation results to experimental results, it is observed that the error between the experiment and simulation is not obvious when the current is small.As the current rises, the error becomes more severe.First of all, this is because the simulation model and conditions are carried out under ideal conditions.Second, although the inclusion of heat conductivity grease with the aim of decreasing heat resistance in the experiment, its impact cannot be entirely eradicated, and the thermal resistance at the contact interface between heat pipe and heat sink as well as heat resistance at the contact interface between vapor chambers base and fins are existing.The influence of these factors increases as heat production increases.

| Experimental results
In this study, the heat dissipation capacity of the heat sink under different working conditions was studied by different currents input to the TEC, and the heat dissipation capacity of the two heat sinks was compared F I G U R E 7 Detailed mesh of thermoelectric cooling components.by recording the analysis data, and the specific experimental results are shown below.

| Basic performance comparison of heat sink
Figure 10 shows the transient changes in cold and hot surface temperatures of TEC when the current was set at 7A, as well as the heat uniformity of the heat sink.Figure 10A displays the results of changes in cold surface temperature of TEC over time.These results indicate that the temperature dropped sharply at the beginning of the TEC current input, and the double EFHP finned heat sink had lower temperatures than the aluminum-based heat sink when reaching a steady state.Figure 10B displays changes on the hot surface of TEC and temperature measurement point 1 over time.The results indicate that the temperature slowly rose and reached a steady state.The aluminum heat sink had a higher temperature on the hot side and at point 1 than the heat pipe heat sink.This indicates that the newly designed heat sinks have better heat dissipation performance and thermal uniformity than aluminum-based heat sink.

| Effect of electric current
The temperature of TEC's hot and cold sides are shown in Figure 11 for different currents.Figure 11 shows that as the current increases, the hot surface temperature F I G U R E 9 Comparison between experiment and simulation of thermoelectric cooler hot and cold surface temperature.
T A B L E 6 Error value of experimental and simulation results of (T h -T c ).

I(A)
Avg error (%) Error (%) Al heat sink 3.8 1.2 6.9 8.3 7.2 5.4 Embedded flat heat pipe heat sink 0.9 2 7.9 10.1 10.3 6.2 continues to climb.The temperature of the TEC hot surface under these two heat dissipation conditions has a small difference when the input current of TEC is minimal.The temperature rise of the TEC hot surface beneath the aluminum heat sink is substantially greater when the current is increased than that of the EFHP heat sink.This is because when the current is small, the heat dissipation of the TEC is relatively small, and both heat sinks can dissipate heat into the air in time.When the current is large, the heat dissipation of TEC increases and the TEC temperature of the EFHP heat sink is lower, indicating that EFHP has a better heat dissipation effect.According to Figure 11, the temperature of the cold surface of TEC first decreases and then increases with the current.This is because when the current is too large, the temperature difference between the hot and cold surfaces is too large because of the high temperature of the hot surface so that the heat transferred from the hot surface to the cold surface increases and the temperature of the cold surface rises.
The hot surface temperatures of TEC beneath Al and EFHP heat sinks are 46.2°C and 41.49°C, respectively, when the input current of TEC is 6A.Compared to Al heat sinks, the hot surface temperatures of TEC under the EFHP heat sinks are 10.2% lower, respectively.The cold side temperatures of TEC beneath the two heat sinks were −19.76°C and −21.9°C, respectively, when the input current of TEC was set at 6 A. Compared to the Al heat sinks, the cold surface temperature of TEC was reduced by 10.83% under the EFHP heat sink, respectively.
Figure 12 depicts the (T T − ) h under various currents, where T h is the hot side of TEC and T is the average temperature of temperature measurement points 1-4 in Figure 5. (T T − ) h can reflect the thermal uniformity of the heat sink to a certain extent.According to the results in Figure 12, the EFHP heat sink has better thermal uniformity, which is beneficial for the heat transfer of heat sinks.With current increasing, maximum (T T − ) h under the aluminum heat sink can reach roughly 7°C.Heat pipe heat sinks have a difference just 0-1°C.
The performance of TEC under different currents is shown in Figure 13. Figure 13A shows the cooling capacity, and COP of TEC, and Figure 13B shows the thermal resistance of TEC hot surface to the environment.The cooling capacity of TEC increases, and the cooling efficiency drops as the TEC current increases.This is because electric currents tend to have a positive effect on the Peltier effect, while Joule heating is counterproductive.When the current is small, the Peltier effect plays a dominant role, Joule heat is small, and the cooling coefficient is high.As the current increases, Joule heating increases, and the cooling coefficient decreases.
Because of the inability of the heat sink to dissipate heat effectively, the thermal resistance from the hot surface of TEC to the environment also increases as the heat produced by TEC increases.The thermal resistance of the EFHP heat sink is smaller than that of the aluminum heat sink with various currents, as shown in Figure 13B, indicating that EFHP heat sinks have greater heat dissipation efficiency than the Al heat sink.In this experiment, when the current of TEC is 6A, the cooling capacity of the heat pipe heat sink increases by 8.3%, COP increases by 9.46%, and thermal resistance decreases by 19%.

| Air flow contour and temperature distributions of heat sink
The profile and temperature distribution of the air flow are important parameters for evaluating the performance of the heat sink, and the contour and flow structure of the airflow and the temperature distribution of the heat sink can be more conveniently displayed in the numerical model simulation.Since the two heat sinks' finned structure and heat dissipation method are the same, the air flow structure is consistent.Figure 14 shows the velocity pressure streamline diagram and cloud diagram of the air flow profile, from which it can be seen that there is a large pressure difference inside the heatsink, a low speed and strong pressure in the center area of the heatsink, a small pressure near the outlet of the heatsink, and a large pressure difference from the center of the heatsink to the outlet, so the maximum flow velocity is generated near the outlet, and the flow velocity and  pressure distribution near the outside of the heatsink are relatively uniform.
In the numerical simulation, the heat transfer characteristics of the heat sinks are first studied according to the experimental conditions.Figure 15 depicts the cloud diagram of temperature for the two heat sinks in consideration of an incoming current of 6A in TEC.The figures provide an insight into the distinct temperature distributions of these heat sinks.The temperature distribution cloud diagram of the heat sink bottom surface can be found in Figure 15A-1,B-1.Furthermore, Figure 15A-2,B-2 showcase the overall temperature cloud map of the heat sink.
Comparing Figure 15A,B, distinct temperature distributions can be observed among the two heat sinks.The high-temperature area of the bottom surface of the aluminum heat sink is concentrated in the contact position with the TEC hot surface, and the temperature is higher along the fin direction and lower on both sides.Overall temperature distribution demonstrates that the temperature of the middle fins is high, while the fins on both sides remain at a lower temperature.Also, the overall temperature uniformity of the heat sink is inadequate.While temperature distribution on the bottom of the heat pipe heat sink is high along the direction of the heat pipe, and farther away from the heat pipe, the lower the temperature, which also shows the excellent heat diversion of the heat pipe.The overall temperature distribution shows the phenomenon of high temperature at the bottom and center and low temperature at the top and edge.Also, the overall temperature uniformity of the heat sink is greatly improved.
Figure 16 shows the temperature uniformity of the substrate surface of the two heat sinks under different current conditions, in which ∆t represents the difference between the maximum temperature and the lowest temperature on the substrate surface; σ t represents the stdev of the surface temperature; t indicates the average surface temperature.The temperature uniformity of heat transfer in heat sinks can be described in terms of ∆t and σ t .It can be seen from the figure that the average temperature of the two is the same at different currents, but the ∆t and σ t of the EFHP heat sink are much lower than the Al heat sink.For ordinary aluminum plates, the temperature in the center area is very high, and the temperature in other areas is low, which makes the surface of the Al heat sinks not fully utilized.The heat concentration area of EFHP heat sinks is very small, and EFHP can diffuse the heat to increase the utilization rate of the surface.As the current increases, the t and t of the Al heat sink increase significantly, while the ∆t and σ t of the EFHP heat sink increase is small, which shows that the EFHP heat sink has better temperature uniformity.

| Influence of EFHP geometry
The effects of S hp and L hp on the temperature uniformity and TEC performance of the heat sinks were studied when the T in (inlet air temperature) = 21°C, Q (inlet air volume) = 69.71CFM, and I = 6 A. Figure 17 shows the TEC performance and temperature uniformity of the heat sink as a function of S hp (L hp = 120 mm).From Figure 17A-C, it can be seen that the relationship between temperature, Q c , COP, R h,total of the TEC and S hp .S hp performs relatively better when it is greater than 5 mm and less than 17.5 mm.S hp was optimal at 12.5 mm; compared to the worst-case scenario, Q c and COP further improved relative by 5.5% and 6.4%, and R h, total decreased by 14.4%.The ∆t and σ t of the heat sink show the same trend, achieving the optimal value at S hp = 12.5 mm, while t has little to do with S hp , and has remained around 34.6°C.This shows that when the two EFHPs are too far or too close, it will have a certain negative impact on the performance of the TEC and the thermal uniformity of the heat sink substrate, and reasonable spacing will help further improve the performance of the EFHP heat sink.
Figure 18 shows the relationship of L hp to TEC performance and heat sink temperature uniformity (S hp = 5 mm).The results shown in Figure 18 show that the performance of the TEC and the temperature uniformity of the bottom surface of the heat sink will further improve with the increase of L hp , but the effect of the increase will slowly decrease, and the relative change after L hp reaches 100 mm (2.5 times the length of TEC) is small, and the performance after reaching 110 mm is almost the same.This shows that the effect of increasing the local high thermal conductivity module after reaching a certain length will be weakened, which is due to the thermal conductivity and thermal conductivity area; with the increase of L hp , the temperature of the remote end will become lower and lower, resulting in the increased length cannot play a well thermal conductivity effect.

| influence of external conditions
To study the influence of external factors on the performance of heat sinks and TEC, the performance of the two heat sinks under different inlet air temperatures and heat dissipation conditions was compared and analyzed.Figure 19 shows the relationship of T in to TEC performance and heat sink temperature uniformity (Q = 67.91CFM).It can be seen from Figure 19A,C that the difference between T h , T c , and R h,total of TEC under the two heat sinks is basically not large at different T in , which indicates that the improvement numeric value of EFHP heat sink relative to Al heat sink on TEC performance is less affected by T in , so the relative performance improvement percentage of TEC under different T in is different, for example, when T in = 15°C and 45°C, the lifting amount of Q c is 2.02 W, 14.03% and 2.36 W, 17.4%;The increase in COP was 0.035, 16.36% and 0.039, 20.3%.However, as T in increases, the overall performance of both TECs with different heatsinks degrades.In addition, it can be found from Figure 19D that the ∆t and σ t of the EFHPP heat sink are less affected by Tin, while the ∆t and σ t of the Al heat sink increase significantly with the increase of T in , and the t of the two heat sinks under different T in is basically the same.
Figure 20 shows the relationship of different heat dissipation conditions to TEC performance and heat sink temperature uniformity.Different heat dissipation conditions are simulated by varying the air volume (T in = 21°C).From the results in Figure 20, it can be seen that the performance curves of TEC under the two heat sinks seem to be parallel, which shows the same characteristics as T in , indicating that the improvement value of EFHP heat dissipation effect has little to do with the heat dissipation conditions.Therefore, the relative improvement effect is more obvious when the heat dissipation conditions are poor.In addition, the performance of the TEC improves as the air volume increases, but the boost effect decreases as the air volume increases, which can be seen in the curves of the hot and cold surface temperature of the TEC, Q c , COP, and R h,total .This is because, with the increase of air volume, convective heat transfer is enhanced, but the wind speed will become faster and faster, resulting in too short heat exchange time between air and fin, and when the flow rate is too large, frictional heat will also occur between the gas and the fin, affecting the heat dissipation effect.Therefore, it is necessary to choose the appropriate air volume in the actual application process.

| CONCLUSIONS
In this present study, a new form of double EFHP finned heat sink designed for TEC heat dissipation is proposed and validated through both experimentation and simulation.Through experiment comparative analysis of the aluminum heat sink, the heat transport efficiency of the TEC was investigated and analyzed under varying current conditions.
The experimental results show that the double EFHP finned heat sink has better cooling capacity than the aluminum heat sink, which is reflected in the lower thermal resistance and better thermal uniformity than the aluminum heat sink.In this experimental study, when the current of TEC is 6A, the thermal resistance of the TEC hot side decreases by 19% compared with that of aluminum heat sinks.(T T − ) h can reflect the thermal uniformity of the heat sink to some extent.In this experiment, when the incoming current of TEC is 6 A, the values of the aluminum heat sink and the heat pipe heat sink are 5.49°C and 0.66°C, respectively.When the input current is stable, better heat dissipation conditions can make TEC play a better performance, which is mainly reflected in lower cold surface temperature and hot surface temperature, higher cooling capacity, and COP under the same current.In this experimental study, when the current is 6A, the cold surface temperature of TEC decreases by 10.83%, the hot surface temperature decreases by 10.19%, and COP increases by 9.46% under the EFHP finned heat sink.
In addition, the spacing and length of the double EFHP will further affect the performance of TEC and the thermal uniformity of the heat sink, which is manifested as the relative effect is slightly worse when S hp is too small (less than 0.5 times TEC width) or too large (greater than 1.5 times TEC width), and the optimal value is obtained when S hp = 12.5 mm in this study, and the Qc and COP of TEC are further increased by 5.5% and 6.4%, and the thermal resistance is reduced by 14.4%.The improvement effect of TEC performance and thermal uniformity of the heat sink will decrease with the increase of L hp , and the effect will be significantly weakened when L hp reaches 2.5 times the length of TEC, and the improvement effect will not be obvious when L hp exceeds 2.5 times the length of TEC.
The improvement value of EFHP heat sink to TEC performance is less affected by the heat dissipation conditions.Compared with Al heat sinks, the performance improvement value of TEC is almost the same under different inlet air temperatures and air volumes, so the relative percentage increase is higher under poor heat dissipation conditions, and the improvement effect is more obvious.
Working principle (A) and geometric structure (B) of double embedded flat heat pipe finned heat sink.F I G U R E 3 Physical diagrams of the two heat sinks.
Experimental device schematic (A) and physical (B) diagram.

F
I G U R E 5 Position of thermocouples on heat sink substrate (the red dotted lines indicate the position of the thermoelectric cooler).T A B L E 3 Precision of the experimental instruments.

6
Simulation physical model of thermoelectric device.T A B L E 4 Physical property parameters of the material.Material • ρ [kg m ]

T A B L E 5
Comparison of the three kinds of grids.

F I G U R E 8
Comparison of thermoelectric cooler's Q c (A) and COP (B) simulation data and manufacturer data.

F
I G U R E 10 Variation of temperature on cold (A), hot (B) sides of thermoelectric cooler and point 1 (B) with time under two heat sinks.F I G U R E 11 Comparison of temperature between cold and hot sides of thermoelectric cooler under different input currents.

F
U R E 13 Qc, coefficient of performance of thermoelectric cooler (TEC) (A), and thermal resistance of TEC hot surface (B) under different input currents.

F
I G U R E 14 Air flow contour, velocity (A), pressure (B), streamline, and velocity (C), pressure (D), nephogram.F I G U R E 15 Bottom (A1), overall (A2) temperature distribution of Al heat sink and bottom (B1), overall (B2) temperature distribution of EFHP heat sink.

F
I G U R E 16 Temperature uniformity of the heat sink substrate at different currents.

F
I G U R E 17 Performance of thermoelectric cooler's Qc and COP (A), hot and cold sides temperature (B), heat sink's thermal resistance (C) and bottom thermal uniformity (D) with different S hp .

F
I G U R E 18 Performance of thermoelectric cooler's Qc and COP (A), hot and cold sides temperature (B), and heat sink's thermal resistance (C) and bottom thermal uniformity (D) with different L hp .

F
I G U R E 19 Performance of thermoelectric cooler's Qc and COP (A), hot and cold sides temperature (B), and heat sink's thermal resistance (C) and bottom thermal uniformity (D) with different T in .
Geometric parameters of the thermoelectric cooler.
1 Schematic diagram and thermal analogy network of thermoelectric cooler.① Hot-side fan; ② hot-side heatsink; ③ insulation; ④ thermoelectric module; ⑤ cold plate.T A B L E 1