Performance enhancement investigation of thermoelectric cooler with segmented configuration

Applied Thermal Engineering 168 (2020) 114852

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Performance enhancement investigation of thermoelectric cooler with segmented configuration

T ⁎

Limei Shena, Wenshuai Zhanga, Guanyu Liua, Zhilong Tua, Qingqing Lua, Huanxin Chena, , Qingjun Huangb a

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China State Key Laboratory of Disaster Prevention & Reduction for Power Grid Transmission and Distribution Equipment, State Grid Hunan Electric Power Corporation Disaster Prevention & Reduction Center, Changsha, China b

H I GH L IG H T S

efficient way to utilize state-of-the-art thermoelectric materials is provided. • An interactive effects of influence factors are discussed. • The segment number is more sensitive to the thermal conductivity of material. • The optimum segment number of segmented thermoelectric element is two. • The • Standard thermoelectric energy balance equation is modified.

A R T I C LE I N FO

A B S T R A C T

Keywords: Segmented thermoelectric cooler Interactive effect Dimension Performance enhancement Heat redistribution

In analogy to segmented thermoelectric generator, the segmented thermoelectric cooler is proposed to enhance the cooling performance without increasing overall figure of merit. The physical model and governing equations of the segmented thermoelectric element are established according to internal heat distribution and transport. The performance enhancement of segmented thermoelectric cooler is investigated by comparing with the traditional thermoelectric coolers. The interactive effects between segment number and thermal physical properties, working conditions and dimension on the cooling performance are discussed. The results show that the segment number is more sensitive to the thermal conductivity of thermoelectric material, and the maximum cooling capacity and temperature difference of segmented thermoelectric element are larger than that of traditional thermoelectric element. The optimum two-segmented thermoelectric element is studied to further optimize the performance of thermoelectric cooling. It is found that the maximum cooling capacity, temperature difference and coefficient of performance of two-segmented thermoelectric element could be remarkably improved by 118.1%, 118.1% and 2.1% when the overall figure of merit remains unchanged. Thereinto, the proposed optimal two-segmented structure modifies the standard thermoelectric energy balance equation with 0.35 of Joule heating traveling back to the cold side instead of 1/2 for the internal heat redistribution.

1. Introduction Thermoelectric (TE) technology has drawn great attention for its compact size, silence in operation, high reliability, environmental friendliness and the lack of mechanically moving components [1]. While the widespread applications of TE technology are still limited by the relatively low ZT of the commercial TE materials where Z is figure of merit of TE materials and T is absolute temperature [2]. Although, significant ZT improvement has been reported in nanostructured

⁎

materials. However, practical thermoelectric coolers have not been made from these materials due to the enormous difficulties in integrating nanoscale materials into microscale TE devices. Hence, how to fulfill the application of these high ZT materials into devices is getting more attention [3]. Inspired by the segmented thermoelectric generator [4], which segmentally connects two or more thermoelectric (TE) materials in series to optimize the conversion efficiency, segmented thermoelectric cooler is proposed to enhance the efficiency of thermoelectric cooling (TEC) by adopting current high ZT TE materials.

Corresponding author. E-mail address: [email protected] (H. Chen).

https://doi.org/10.1016/j.applthermaleng.2019.114852 Received 17 August 2019; Received in revised form 2 December 2019; Accepted 25 December 2019 Available online 26 December 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A COP h I K L Lc Lh N Qc R S Sc Sh T ΔT x Z ZT ZTc

ZTh ZTtotal

the cross-section area of thermoelectric legs [m2] coefficient of performance the convective heat transfer coefficient between the cold side and the ambient [W∙m−2∙K−1] electrical current [A] the overall thermal conductance [W∙K−1] length of thermoelectric element [m] length of segment next to the cold side [m] length of segment next to the hot side [m] segment number cooling capacity [W] the overall electric resistance [Ω] seebeck coefficient [V∙K−1] seebeck coefficient of the segment next to the cold side [V∙K−1] seebeck coefficient of the segment next to the hot side [V∙K−1] absolute temperature [K] the temperature difference between hot-side and cold side [K] the ratio of Joule heating traveling back to the cold side figure of merit of thermoelectric material [K−1] dimensionless figure of merit figure of merit of the first segment thermoelectric material

figure of merit of the last segment thermoelectric material ZT of overall thermoelectric element

Greek letters ρ ρc ρh λ λc λh α

electric resistivity of thermoelectric material [Ω∙m] electric resistivity of the segment next to the cold side [Ω∙m] electric resistivity of the segment next to the hot side [Ω∙m] thermal conductivity of thermoelectric material [W∙m−1∙K−1] thermal conductivity of the segment next to the cold side [W∙m−1∙K−1] thermal conductivity of the segment next to the hot side [W∙m−1∙K−1] The overall Seebeck coefficient [V∙K−1]

Subscripts c h i max n p

cold side of the thermoelectric element hot side of the thermoelectric element the No. of the ith segment maximum value N-type thermoelectric leg P-type thermoelectric leg

20%. Drabkin [15] firstly generalized one-dimensional heat balance model of segmented TE leg to simplify the calculation procedure, the model could take into account the effect of contact resistances which were previously neglected. Badillo-Ruiz et al. [16] studied the influences of the Thomson effect and leg geometry (i.e. rectangular prism, trapezoidal prism) on the performance of two-segmented TE microcooler, the results found that the efficiency of rectangular prism leg is best and the maximum cooling capacity could improve by 5.10% after considering the Thomson effect. But note that this study was performed under two fixed conditions: specific thermoelectric materials Bi2Te3 and (Bi0.5Sb0.5)2Te3 and a fixed temperature gradient of ΔT = 30 K. Lundgaard and Sigmund [4] utilized a density-based topology optimization method to optimize the cooling power and efficiency of segmented thermoelectric coolers. They found that the topology optimization method can respectively improve the cooling power and efficiency of thermoelectric coolers by 48.7% and 11.4% comparing with the classical segmentation method. Four observations can be made according to the above review of previous research on the segmented TE coolers. Firstly, previous studies separately investigated the influence of segment number and thermal physical properties, geometry on cooling performance. While the influences of these factors are mutual dependent. Thus, it’s necessary to analyze the interactive effects of the factors. Secondly, boundary conditions used in the previous studies was proceeded under a fixed temperature difference. Actually, the boundary condition is determined by the application scenarios. Thirdly, the length of TE leg had a significant impact on the cooling performance of TE cooler [17]. However, the previous studies were seldom discussed it. In addition, the length used in previous studies were almost longer than 5 mm which was not practical in real TE element, and the length of each segment is uniform. Thus, further studies are necessary to investigate the interactive impacts of segments number versus thermal physical properties, working condition and dimension on the cooling performance of segmented TE cooler. Finally and most importantly, previous studies investigate the segmented TE cooler using the standard thermoelectric energy balance equation. Actually the segmented structure will lead to the internal heat redistribution and modifying standard thermoelectric energy balance

Basically, the working principle of proposed segmented thermoelectric cooler is similar to that of the thermoelectric cooler with inhomogeneous material. So the studies of segmented thermoelectric cooler can be traced back to the year of 1953, the thermoelectric effects in the inhomogeneous medium were firstly theoretically demonstrated, and experimentally confirmed in 1958 by Baransky using the inhomogeneous samples made of n-Ge [5]. In 1959, Ioffe et al. [6] did a research of changing the material parameters along thermoelectric element leg to increase the efficiency of thermoelectric elements. Mahan [7] found the coefficient of performance (COP) could be enhanced by inhomogeneous doping thermoelectric material with the high conductivity at the cold side of TE refrigerator. And in 1967 the Borg-Warner Corporation firstly proposed the segmented thermoelectric element in a patent which realized its application [8]. But the segmented thermoelectric cooler didn’t draw much attention as segmented thermoelectric generator for its small temperature gradient. In recent years, only few investigators started to conduct the relevant study. Müller et al. [9–11] theoretically studied the influence of properties gradient with N = 10 and segment number (N) with Sc/ Sh = 0.5 on cooling performance of TE element, respectively. Sc/Sh is the ratio of Seebeck coefficient at the cold side to Seebeck coefficient at the hot side. The results showed that the cooling capacity improved by 10% when N = 10, the maximum temperature difference and COP respectively improved by 2.4% and 6% when N = 2, the maximum temperature difference increased by 15% when the ratio of Seebeck coefficient at the cold side to Seebeck coefficient at the hot side (Sc/Sh) equals to 0.1. Bian et al. [12] found that the cooling temperature difference of TE element could be increased by using TE material with staircase Seebeck coefficient. Vikhor et al. [13] theoretically studied the influence of thermoelectric leg length and contact thermal resistance of each section on the maximum temperature difference (ΔTmax), an improvement of 3–4 K of ΔTmax in two- and three-segmented coolers was demonstrated by comparing with traditional TE coolers. Anatychuk and Cherkez [14] proposed a novel permeable segmented TE element to cool liquid or gas fluxes by passing through the segmented TE legs with penetrated channels. It showed that the coefficient of performance is increased by 10% to 30% and the specific cooling capacity by 10% to 2

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2.1. Governing equations

equation. Thus, it′s important to build a novel standard equation for segmented cooler. Hence, the objective of this work is to build a novel standard thermoelectric energy balance equation to fully investigate the performance enhancement of segmented TE cooler and systematically explore how sensitivity of each parameter impacts on the optimal design. To achieve this objective, a segmented TE element model is developed to investigate the interactive impacts between the physical properties, working condition, dimension and segment numbers of TE element. A more sensitive relation between Seebeck coefficient, thermal conductivity and electrical resistivity is analyzed. As for parameters with heavy impact, the influence of working condition and TE element length is conducted. Finally, the optimal design scheme and modifying standard thermoelectric energy balance equation of segmented TE cooler are obtained.

At the steady-state, the thermal and electrical transports coupled thermoelectricity effect in each segment of P-type or N-type leg are described by the following equations [19,20].

∇ ·(Si TJ ) − ∇ ·(λi ∇T ) = q ̇

(1)

∇ ·(σi Si ∇T ) + ∇ ·(σi ∇φi ) = 0

(2)

where T is the absolute temperature, q̇ is the heat generation rate per unit volume, J is the electric current density vector. φ is the electric scalar potential. S is the Seebeck coefficient, λ is the thermal conductivity, σ is the electrical conductivity. The subscript i represents the ith segment of TE element. The equations described above are performed using the finite volume method. With regard to the thermal physical parameters of each segment, the value of Seebeck coefficient, thermal conductivity and electrical resistivity are assigned in the form of arithmetic progression, as given by

2. Simulation model The basic working unit of TE cooler is the thermoelectric element, which consists of a pair of N-type and P-type semiconductors, as shown in Fig. 1(a). In this study, the so-called traditional TE element refers to this structure. Temperature gradient is built at the two sides of a thermoelectric element, when a direct current passes from the N-type semiconductor to the conductor (copper) and then from the conductor to the P-type semiconductor. The heat is absorbed from the environment and the temperature at one junction (cold side) decreases. Meanwhile, the heat is rejected to the environment and the temperature at the other junction (hot side) increases. Reversing the hot and cold sides can be easily achieved by reversing the direction of the current. A number of thermoelectric elements are assembled to form a thermoelectric cooler. The thermal characteristics in each pair are identical. Therefore, only one pair TE element is considered here. With regard to the segmented TE element, the physical structure schematic is shown in Fig. 1(b). The P- and N-type legs are respectively consisted by N discrete segments (N≥2). For each segment, one kind of TE material is assigned. For each TE leg, N kinds of TE materials are segmentally connects in series. The simulation model of traditional and segmented TE elements is built in ANSYS basing on the following assumptions [18]:

Sp, i = −Sn, i =

N−i i−1 Sc + Sh N−1 N−1

(N ⩾ 2, i = 1, 2, …N )

λ p, i = λ n, i =

N−i i−1 λc + λh N−1 N−1

(N ⩾ 2, i = 1, 2, …N ) ρp, i = ρn, i =

(3)

(4)

N−i i−1 ρ + ρ N−1 c N−1 h

(N ⩾ 2, i = 1, 2, …N )

(5)

where ρ is the electrical resistivity which is the reciprocal of electrical conductivity (σ). N is the segment number. The subscript c and h respectively represent the first segment adjacent to the cold side (i = 1) and the last segment adjacent to the hot side (i = N) of segmented TE element. The subscript p and n represent the P-type and N-type TE material, respectively. To analyze and compare the impact sensitivity of Seebeck coefficient, thermal conductivity and electrical resistivity in a wide range, the ratio of Sh/Sc, λh/λc, ρh/ρc are introduced. The thermal physical properties and geometric parameters are assigned based on a commercial TE cooler [21,22], as listed in Table 1.

(1) The contact resistances at all interfaces are ignored to figure out the performance enhancement limit of segmented TE cooler. (2) The heat only flows through the element along the length direction of TE leg. (3) Heat loss by radiation and convection is neglected. (4) The thermal physical properties of TE material for each segment are isotropic and independent of temperature.

2.2. Evaluation criteria The performance of a TE cooler is usually evaluated with three parameters the maximum cooling capacity (Qc,max), the maximum temperature difference (ΔTmax) and the maximum coefficient of performance (COPmax). The cooling capacity (Qc), temperature difference

Fig. 1. The schematics of traditional and segmented thermoelectric element. 3

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Table 1 The thermal physical properties and geometric parameters of traditional thermoelectric element. Thermal physical properties

Value(unit) −1

Seebeck coefficient of p-type TE leg (Sp) Seebeck coefficient of n-type TE leg (Sn) Thermal conductivity (λp, λn) Electric resistivity (ρp, ρn)

0.22 (mV∙K ) −0.22 (mV∙K−1) 1.8 (W∙m−1∙K−1) 1e-5(Ω∙m)

(6)

ΔT = Th − Tc

(7)

α1 ITc − xI 2R − K ΔT αN ITh − α1 ITc + I 2R

COP =

x=

(9)

here, x is the ratio of Joule heating traveling back to the cold side instead of 1/2 in the standard thermoelectric energy balance equation for the non-uniform Joule heating, it is introduced to present the modifying standard thermoelectric energy balance equation. I is the electrical current, IΔTmax is the electrical current when TEC reaches its maximum temperature difference, Tc and Th are respectively the cold side temperature and hot side temperature of segmented TE element. ΔT is the temperature difference between cold side temperature and hot side temperature of segmented TE element. α1 = Sp,1-Sn,1 is the total Seebeck coefficient of the 1st segment, αN = Sp,N-Sn,N is the total Seebeck coefficient of the Nth segment. R and K are respectively the overall electric resistance and thermal conductance. The overall Seebeck coefficient (α), R and K are respectively calculated according to the principle of Seebeck effect, Fourier law and Ohm law, as given by N

i=1

N

R=

L p, i

∑ ρp,i A 1 N

∑ i=1

N

+

p,i

i=1

K=

(10)

ΔT

Lp, i λp, i Ap, i

L

∑ ρn,i An,i

+

(11)

n, i

i=1

1 N

∑ i=1

Ln, i λn, i An, i

(12) th

where Ap,i and An,i are the cross-section area of the i segment P-type and N-type TE legs. Lp,i and Ln,i are the length of the ith segment P-type and N-type TE legs. ΔTp,i and ΔTn,i are the temperature difference of the ith segment P-type and N-type TE legs. Note that N

N

N

N

ΔT = ∑ ΔTp, i = ∑ ΔTn, i , Lp = Ln = ∑ Lp, i = ∑ Ln, i . Thus, the overall i=1

i=1

i=1

(13)

Experiments were conducted to validate the simulation model. The experimental testing rig is shown in Fig. 2. The thermostat is used to supply 20 °C water for cooling the hot side of the TE module. The thermal insulation material is used to implement the experiment carrying out under Qc = 0 W. In the simulation, the ambient temperature was set as 20 °C, and the heat exchange coefficient between ambient and hot side of TE module were set as 8695.73 W∙m−2∙K−1 which had been obtained by combining the experiment and trial methods. The electrical current is supplied by KXN-6020D, the electric current was monitored by a digital multimeter with 1% accuracy. The hot and cold side temperatures measured by T type thermocouples (TT-T-24-SLE1000, accuracy ± 0.5 °C) are transmitted to the recorder and then to the computer for analysis. It should note that only a commercial thermoelectric cooler with traditional TE element was used to conduct the validation study [22]. Because there is no commercial thermoelectric cooler with segmented TE element. To ensure the consistency of experiment and simulation working condition, the validation is conducted in following two steps. First, the experiment studies was conducted when applied electrical current changes between 0A and 4A at the interval of 0.5 A. Second, the working condition of experiment was tested and then simplified to apply in the simulation studies. The simulation and experiment results are shown in Fig. 3. It could see that the temperature profiles of numerical simulation agree well with that of experiments. The maximum error for the cold side temperature is 1.82%, and 1.32% for the hot side temperature. The deviations are within 2%, thereby confirming the validity of the model. Furthermore, the experiment error, the negligence of contact thermal and electrical resistances are mainly responsible for the differences between the experiment and simulation. The cold and hot side

N

i=1

1.4 × 1.4 (mm) 1.5 (mm) 0.4 (mm)

2.3. Model validation

∑ Sp, i ΔTp, i − ∑ Sn, i ΔTn, i α=

Section area of TE leg Length of TE leg (Lp, Ln) Thickness of copper

where h is the convective heat transfer coefficient between the cold side and the ambient, A is the cold side area of TE cooler, Ta is ambient temperature. To simplify the calculation, the hot side temperature (Th) is assumed to be a constant. The Qc,max, ΔTmax and COPmax could be similarly obtained as above. The simulation model is solved with the input electrical current changing between 1 A and 22 A at the interval of 0.1 A, then the responding Qc, ΔT and COP could be respectively calculated using Eqs. (6)–(13), then maximum Qc, ΔT and COP are finally selected.

(8)

αTc 2I△Tmax R

Value (unit)

α1 ITc − xI 2R − K ΔT = hA (Ta − Tc )

(ΔT) and coefficient of performance (COP) of thermoelectric element are expressed by

Qc = α1 ITc − xI 2R − K ΔT

Geometric parameters

i=1

figure of merit of segmented TE element equals to α 2 (RK ) . When the TE element directly attaches to the cooled objective, it usually works by controlling input electrical current to cool down the objective to a constant temperature (Tc). To simplify the calculation, it assumes the TE cooler works under the first boundary condition. Thus, the hot side and cold side temperature of TE cooler is constant. The Qc,max and ΔTmax could be obtained as follow. The simulation model is solved with the input electrical current, the input electric current changes between 1 A and 22 A at the interval of 0.1 A, then the corresponding Qc, ΔT and COP could be respectively calculated using Eqs. (6)–(12), the maximum Qc, ΔT and COP are finally selected. When the TE element indirectly attaches to the cooled objective through heat exchanger, i.e. thermoelectric refrigerator/air-conditioner, the heat balance of the cold side of segmented TE element is given by

Fig. 2. The experimental test rig. 4

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temperature of experiments are larger than that of simulations. This is because it’s difficult to achieve absolutely adiabatic condition and maintain the water temperature at 20 °C in the experiment. 3. The interactive effect 3.1. The physical properties Firstly, the interactive effect between Seebeck coefficient, thermal conductivity, electrical resistivity and segment number on the maximum cooling capacity, maximum temperature difference and maximum COP are discussed respectively. The model was conducted under the practical condition of Th = 300 K, Ta = 300 K and h = 1500 Wm−2K−1. Note that the hot side temperature could be maintained by using thermostatic water bath. The TE element was equidistantly divided into N segments, N changed from 2 to 5 at the interval of 1. The length of each segment was L/N, the total length L equaled to 1.5 mm. The value of Sc, λc and ρc were as the benchmark, which were assigned according to reference [21], i.e., Sc = Sp, λc = λp, ρc = ρp. The Seebeck coefficient, thermal conductivity and electrical resistivity of other segments were respectively calculated using Eqs. (3)–(5) at given ratio of Sh/Sc, λh/λc, ρh/ρc. To illustrate the performance enhancement of

Fig. 3. Comparison between simulation and experiment results.

(a) Qc,max ~ Sh/Sc

(d) Qc,max ~ λh/λc

(g) Qc,max ~ ȡh/ȡc

(b) ΔTmax ~ Sh/Sc

(e) ΔTmax ~ λh/λc

(h) ΔTmax ~ ȡh/ȡc

(c) COPmax ~ Sh/Sc

(f) COPmax ~ λh/λc

(i) COPmax ~ ȡh/ȡc

Fig. 4. The interactive effects between segment number and thermal physical properties on cooling performance of segmented TE element. 5

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cooling capacity and COP of two-segment TE element are both larger than the others segmented TE element for the higher overall figure of merit. It illustrates that the optimal segment number is 2 at any working conditions. It should be noted that the segmented structure could obviously enhance the cooling capacity. In addition, the maximum COP of traditional TE element is always larger than that of segmented TE element as the higher overall figure of merit of traditional TE element [23].

segmented TE cooler, the performances of traditional TE element were also studied. Here, N = 1 represents the traditional TE element, and the Seebeck coefficient, thermal conductivity and electrical resistivity are equals to Sc, λc and ρc. Fig. 4 shows the interactive influence between Seebeck coefficient, thermal conductivity, electrical resistivity and segment number on the maximum cooling capacity, maximum temperature difference and maximum coefficient of performance. There is hardly no interaction effect between Seebeck coefficient, electrical resistivity and segment number on cooling performance of segmented TE element for the overlap curves, especially when Sh/Sc and ρh/ρc are in the range of 0.5–1.5. The reason is that the Peliter heat is a surface effect, which means the Peltier cooling at the cold side has no relationship with the segment number. However, the interaction effect between thermal conductivity and segment number is remarkable. The segment number is much sensitive to the thermal conductivity. Fig. 4(d)–(f) shows that when λh/λc greater than 1, the maximum cooling capacity, temperature difference and COP of segmented TE element decrease with the increase of segment number, and the maximum cooling capacity and temperature difference of segmented TE element are larger than that of traditional TE element unless N ≥ 5. Note that the optimal segment number is 2. This is because the total thermal conductance of two-segment TE element is the smallest. In addition, the cooling performance of segmented TE element is better than that of traditional TE element when Sh/Sc > 1, λh/λc < 1 or ρh/ρc < 1. This is because the overall figure of merit of segmented TE element is larger. Thus, that′s why it couldn′t compare the cooling performance of traditional and segmented TE element here. It will be discussed in the following section.

3.3. The dimension of TE element The TEC performance dependent on TE element dimension, and it’s well known that the decrease of a TE leg length will increase its cooling power density due to lower electrical resistance. With respect to the commercial TE modules, the length of one-stage TE element is in the range of 0.2 mm–2 mm[23]. Thus, we discussed the interactive influence between TE element length and segment number on cooling performance of segmented TE element. The thermal physical properties of the simulation model were also assigned the value of Sh/Sc = 1, λh/ λc = 2 and ρh/ρc = 1. Fig. 6 shows the interactive influence of length and segment number on the maximum cooling capacity, maximum temperature difference and maximum coefficient of performance. It observes that the maximum cooling capacity, maximum temperature difference and maximum coefficient of performance all decrease with the increase of the length. The cooling performance of two-segment TE element has the most significant enhancement than that of elements divided into other numbers, and the maximum cooling capacity and maximum temperature difference of two-segment TE element are better than that of traditional TE element when the length is in the range of 0.7 mm–2 mm. It also finds that the maximum cooling capacity and maximum temperature difference of segmented TE element are larger than that of traditional TE element when the length is larger than 1.52 mm. But the higher maximum COP of traditional TE element is attributed to the higher overall figure of merit. In addition, the segmented structure is better for the TE element with thick leg length when the overall figure of merit of segmented TE element is smaller than that of merit of traditional TE element, or the segmented structure is better for the TE element with thin leg length.

3.2. The working condition Then, the influence of the segment number on the cooling performance of segmented TE cooler is studied under different working condition. Considering that the TE cooler direct or indirect cooling the objective can finally attribute to controlling the temperature difference between hot-side and cold-side of TE cooler, the use of temperature difference as the working condition could reflect the interaction effect. According to the above section analysis, we know that the segment number is sensitive to the thermal conductivity rather than Seebeck coefficient and electrical resistivity. Thus, the model of segmented element was built with Sh/Sc = 1, λh/λc = 2 and ρh/ρc = 1. The influence of the segment number on the cooling performance of segmented TE cooler under different working conditions are shown in Fig. 5. The maximum cooling performance of segmented and traditional TE element both decrease with the increase of temperature difference. The maximum cooling capacity of segmented TE element is larger than that of traditional when ΔT is smaller than 46.6 °C. And the maximum

4. Two-segmented TE element The above study shows that the optimal segment number for the segmented TE element is two. Thus, a further study was conducted to optimize cooling performance of two-segmented TE element, as shown in Fig. 7. First, the cooling performance of two-segmented TE element with Lc/L = 0.5 were investigated under two scenarios. Scenario A: the overall Seebeck coefficient, electric resistance and thermal conductance

(a) Qc,max ~ ΔT

(b) COPmax ~ ΔT

Fig. 5. The interactive effect between segment number and working condition on cooling performance of segmented TE element. 6

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(a) Qc,max~L

Fig. 7. The schematic of two-segmented thermoelectric element.

uniform length of segments had been discussed under two scenarios. Because the length of segment affects the overall thermal physical parameters of TE element. Note that the optimized length of TE leg was 1 mm, so a series of asymmetric element model containing two segments were established with the total length of 1 mm. Thereinto, the Seebeck coefficient, thermal conductivity and electrical resistivity of each segment were respectively calculated using Eqs. (3)–(5). 4.1. Performance analysis Fig. 8 shows the influence of thermal physical properties on cooling performance of two-segmented TE element under two scenarios. With regard to scenario A and scenario B, the identical definitions of (Sh + Sc) and (ρh + ρc) respectively result in the identical performance variations changing with Sh/Sc and ρh/ρc, as shown in Fig. 8(a) and (b). It can be found that the Qc,max, ΔTmax and COPmax increase with the increasing Sh/Sc at first and reach its maximum value. After that Qc,max, ΔTmax and COPmax decrease with the increase of Sh/Sc. The critical ratios of Sh/Sc in this case are respectively 1.5, 1.5 and 1, and the responding Qc,max, ΔTmax and COPmax are respectively 0.325 W, 44.09 ⁰C and 4.454. The two-segmented structure respectively improves the Qc,max and ΔTmax of TEC by 2.9% and 2.9%. Furthermore, the Qc,max and ΔTmax are both obtained when the ZTh = 1.16 and ZTc = 0.516, which is easy to implement by selecting corresponding materials from state-ofthe-art(SOAT) TE materials. The performance of two-segmented TE element is better than that of traditional TE element when the ratio of Sh/Sc is in the range of 1–2.5, which shows that it’s no need to do much more effort to increase the Seebeck coefficient of TE material for the segmented TE cooler. Fig. 8(b) shows that the Qc,max, ΔTmax and COPmax increase with the increase of ρh/ρc, and the increment is remarkable when ρh/ρc is smaller than 6. Because the generating Joule heating of the first segment is small for the low electrical resistivity, thus the Joule heating flowing to the cold side is small. And the Joule heating flowing to the cold side decreases with the increasing ρh/ρc. The two-segmented structure significantly improves the Qc,max, ΔTmax and COPmax of TEC by 36.2%, 36.2% and 1.0% when ρh/ρc = 6. The Qc,max, ΔTmax and COPmax variation with λh/λc under scenario A are shown in Fig. 8(c). It could see Qc,max, ΔTmax and COPmax increase with the increase of λh/λc and these phenomena are remarkable when λh/λc is smaller than 6. The cooling performance of two-segmented TE element is better than that of traditional TE element when the ratio λh/ λc is larger than 1, and the two-segmented structure significantly improves the Qc,max, ΔTmax and COPmax of TEC by 36.2%, 36.2% and 1.0% when λh/λc = 6. The enhanced cooling performance can be concluded that the Joule heating and Peltier heating are redistributed through the TE leg for the high thermal resistance of the first segment, the Joule

(b) ΔTmax~L

(c) COPmax~L Fig. 6. The interactive effect between segment number and dimension of TE element on cooling performance.

of two-segmented TE element respectively equaled to that of traditional TE element. Namely, the value of (Sh + Sc), (1 λ c + 1 λh ) and (ρh + ρc) were respectively equal to 2Sp, 2 λp and 2ρp. Here the overall figure of merit (ZTtotal) of two-segmented TE element could be equal to that of traditional TE element. Scenario B: the sum of Seebeck coefficient, electric resistance and thermal conductance between cold side and hot side of two-segmented TE element respectively equaled to that of traditional TE element. Namely, the sum of (Sh + Sc), (λh + λc) and (ρh + ρc) were respectively equal to 2Sp, 2λp and 2ρp. Here the overall figure of merit (ZTtotal) of two-segmented TE element would be equal or greater than that of traditional TE element. Secondly, the effect of non7

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(a) Sh/Sc effects under scenario A and B

(b) ȡh/ȡc effects under scenario A and B

(c) Ȝh/Ȝc effects under scenario A

(d) Ȝh/Ȝc effects under scenario B

Fig. 8. The influence of thermal physical properties on cooling performance of two-segmented TE element under two scenarios (Sh/Sc = 1, ρh/ρc = 1 or λh/λc = 1 identify with traditional TE element).

Fig. 8(d) exhibits the effects of λh/λc on Qc,max, ΔTmax and COPmax under scenario B. In this situation, the Qc,max, ΔTmax and COPmax decrease with the increase of λh/λc at first and then increase sharply with the increasing λh/λc. The increment is remarkable when ρh/ρc is smaller than 8. It shows the two-segmented structure significantly improves the Qc,max, ΔTmax and COPmax of TEC by 76.2%, 76.2% and 28.0% when λh/ λc = 8. The enhancement can be contributed by two reasons: one is the internal heat redistribution, the other one is the increased overall figure of merit. Furthermore, it observes that the Qc,max ΔTmax and COPmax of

heating and Peltier heating flows to the cold side difficultly, and the Peltier cooling flows to the hot side also difficultly. Furthermore, the larger of λh/λc is, the better of the performance of two-segmented TE element is. Comparing with Fig. 8(b) and (c), there exists one interesting phenomena, the responding valules of Qc,max(λh/λc) and Qc,max(ρh/ρc), ΔTmax(λh/λc) and ΔTmax(ρh/ρc), COPmax(λh/λc) and COPmax(ρh/ρc) are respectively equivalent when λh/λc = ρh/ρc. It illustrates that the influence of the ratio of λh/λc and ρh/ρc on cooling performance of two segmented TE cooler are identical in scenario A.

(a)Scenarios A: Sh/Sc=1, ȡh/ȡc=6, Ȝh/Ȝc=6

(b)Scenarios B: Sh/Sc=1, ȡh/ȡc=6, Ȝh/Ȝc=8

Fig. 9. The influence of non-uniform length of segment on cooling performance. 8

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than that of traditional TE element when Lc/L ≥ 0.175 (scenario A) or 0.048(scenario B), and the COPmax is larger when Lc/ L ≥ 0.455(scenario A) or 0.181(scenario B). Note that when Lc/L is in the range of 0.455–0.5 in scenario A, the overall ZT value of two-segmented TE element is smaller than that of traditional TE element, but the performance of two-segmented TE element is still larger than that of traditional TE element for the asymmetric structure. In scenario B, when Lc/L is in the range of 0.181–0.213, the ZT value of two-segmented TE element is smaller, but the performance of two-segmented TE element is better. According to above analysis, it can conclude that two-segmented cooler could obtain higher performance by using asymmetric structure with Lc/L ≥ 0.5. Meanwhile, when Lc/L is larger than 0.455 in scenario A or 0.181 in scenario B, the performance of two-segmented TE cooler is better than that of traditional TE cooler for the segmented structure. 4.3. Optimal performance evaluation

Fig. 10. The influence of TEC current on cooling performance under optimal condition (Sh/Sc = 1, ρh/ρc = 6 and λh/λc = 6) when Lc/L = 0.5.

According to the above analysis, the optimal design of two-segmented TE element is proposed under scenario A without changing overall ZT value. Thereinto, the Sh/Sc, ρh/ρc, λh/λc and Lc/L are respectively assigned the value of 1, 6, 6, 0.5 (scenario A) on the basis of achieving the optimal performance. To further investigate the performance enhancement, the performances of two-segmented TE element and traditional TE element were evaluated under different input electrical current, as shown in Fig. 10. The curve with solid symbols represents the results of two-segmented TE element, and the curve with hollow symbols represents the results of traditional TE element. With regard to traditional and two-segmented TE elements, the Qc, ΔT and COP curve trend are respectively similar. The Qc and ΔT increases at first and then decreases with the increase of the input electrical current, while the COP rapidly decreases and then slowly decreases. It can be found that Qc, ΔT and COP are very sensitive to the current, and there is a critical input electrical current, which enables the TE element to achieve the maximum Qc or ΔT. Therefore, the performance of TE element can be rapidly changed according to the application requirement by adjusting the input current. Comparing with the traditional structure, the optimum two-segmented structure remarkably improves the Qc,max, ΔTmax and COPmax of TEC by 118.1%, 118.1% and 2.1%, respectively. In addition, it finds the input current for achieving maximum Qc and ΔT of two-segmented TE element is much larger than that of traditional TE element. This is because the lower thermal conductivity and electrical resistivity at cold side and higher thermal conductivity and electrical resistivity at hot side lead to the non-uniform Joule heating modifying the standard thermoelectric energy balance equation. Instead of 1/2 of the Joule heating traveling back to the cold side for traditional TE element, here only 0.35 of the Joule heating reduces the total cooling for two-segmented TE element. According to these conclusions, it could conclude that the twosegmented TE element using different TE materials with the almost same value of Seebeck coefficient, but a great difference of ZT, could obtain the better cooling performance without increasing the overall ZT of TE cooler. Thus, we design a selection criteria for SOAT materials of segmented TE cooler to enhance the cooling performance of TEC by utilizing high ZT nanostructure TE materials, as shown in Fig. 11. It should be mentioned that in this study, the optimum parameters of segmented TE element, i.e. segment number, length of each segment, should be redesigned according to the TE materials and operating condition.

two-segmented TE element are smaller than that of traditional TE element when the ratio λh/λc is in the range of (0.16–1), (0.16–1) and (0.73–1), respectively. The ratio of λh/λc for achieving the minimum Qc,max, ΔTmax and COPmax is respectively 0.5, 0.5 and 0.9. It demonstrates the higher ZT could not always achieve the better cooling performance. As regards scenario A, the overall figure of merit maintains at constant, but the performance of two-segmented TE cooler is much better than that of traditional TE cooler when ρh/ρc and λh/λc are both larger than 1. As regards scenario B, the overall figure of merit of twosegmented TE cooler is larger than that of traditional TE cooler when λh/λc ≠ 1, but the performance of two-segmented TE cooler performed better only when λh/λc is in the range of (0–0.16) or (1~+∞). Comparing scenario A and B, it finds the COP of TE cooler is mainly affected by ZT regardless of the tradtional or segmented structure. It′s also concluded that the cooling performance of two-segmented TE cooler could be significantly improved by using two different TE materials with a large ratio of ZTc to ZTh and identical Seebeck coefficient. 4.2. Non-uniform length The effect of non-uniform length of segments on cooling performance of two-segment TE element is studied under two scenarios. The ratio of Lc/L is introduced to describe the asymmetric length of segmented TE element. Lc represents the length of segment near the cold side, which varies from 0 mm to 1 mm. When Lc equals to 0 mm or 1 mm, the element becomes traditional TE element. Lh represents the length of segment near the hot side. Here the ratio of Sh/Sc, ρh/ρc and λh/λc are assigned value of 1, 6, 6 (scenario A) and 1, 6, 8 (scenario B). The performance of asymmetric segmented TE element in scenario A and B is shown in Fig. 9. For the asymmetric segmented TE element, the Qc,max and ΔTmax first rapidly increases and then slowly decreases with the increase of the Lc/L, while the COPmax just increases with the increase of the Lc/L. It’s obvious that the uniform segment length (Lc/ L = 0.5) is not the optimized geometry for two-segment TE element, the optimal ratio of Lc/L is 0.8 in scenario A and 0.7 in scenario B. It should be noted that the asymmetric structure achieving the highest ZT value is responsible for this phenomena. In addition, when Lc/L equals to 0 or 1, the element represents the traditional TE element only with the second segment TE material (Sh, λh, ρh) or the first segment TE material (Sc, λc, ρc), respectively. With no doubt, the performance of TE element with the second segment TE material is much smaller than that of TE element with the first segment TE material for the lower figure of merit. Comparing with traditional TE element using the TE material (Sp, λp and ρp), the Qc,max and ΔTmax of two-segmented TE element are larger

5. Conclusion In summary, this study develops a comprehensive governing equation to fully investigate the performance enhancement of the segmented TE element, and an efficient way to utilize the SOAT TE materials enhancing the cooling performance of TEC is obtained. The interactive 9

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for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is jointly supported by the National Natural Science Foundation of China (Grant No. 51506060) and the Natural Science Foundation of Hunan Province (2018JJ3005). The supports are gratefully acknowledged. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114852. References [1] Y. Cai, Y. Wang, D. Liu, F. Zhao, Thermoelectric cooling technology applied in the field of electronic devices: updated review on the parametric investigations and model developments, Appl. Therm. Eng. 148 (2019) 238–255. [2] D. Zhao, G. Tan, A review of thermoelectric cooling: materials, modeling and applications, Appl. Therm. Eng. 66 (2014) 15–24. [3] X. Zhou, Y. Yan, X. Lu, H. Zhu, X. Han, G. Chen, Z. Ren, Routes for high-performance thermoelectric materials, Mater. Today (2018). [4] C. Lundgaard, O. Sigmund, Design of segmented thermoelectric peltier coolers by topology optimization, Appl. Energy 239 (2019) 1003–1013. [5] L.M. Vikhor, Functionally graded thermoelectric materials and thermoelements on their basis (review), J. Thermoelect. (2005) 7–21. [6] A.F. Ioffe, L.S. Stil'Bans, E.K. Iordanishvili, T.S. Stavitskaya, A. Gelbtuch, G. Vineyard, Semiconductor thermoelements and thermoelectric cooling, Phys. Today 12 (1959) 42. [7] G.D. Mahan, Inhomogeneous thermoelectrics, J. Appl. Phys. 70 (1991) 4551–4554. [8] I. Borg-Warner, Improvements in or relating to peltier thermoelectric couples (1967). [9] E. Müller, S. Walczak, W. Seifert, Optimization strategies for segmented peltier coolers, Physica Status Solidi (a) 203 (2006) 2128–2141. [10] E. Muller, G. Karpinski, L.M. Wu, S. Walczak, W. Seifert, Separated effect of 1d thermoelectric material gradients, The 25th International Conference on Thermoelectrics: 2006, 2006, pp. 204–209. [11] E. Muller, S. Walczak, W. Seifert, C. Stiewe, G. Karpinski, Numerical performance estimation of segmented thermoelectric elements, The 24th International Conference on Thermoelectrics: 2005, 2005, pp. 364–369. [12] Z. Bian, A. Shakouri, Beating the maximum cooling limit with graded thermoelectric materials, Appl. Phys. Lett. 89 (2006) 212101. [13] L.N. Vikhor, L.I. Anatychuk, Theoretical evaluation of maximum temperature difference in segmented thermoelectric coolers, Appl. Therm. Eng. 26 (2006) 1692–1696. [14] L.I. Anatychuk, R.G. Cherkez, Energy potential of permeable segmented thermoelements in cooling mode, J. Electron. Mater. 41 (2012) 1115–1119. [15] I.A. Drabkin, Optimization of segmented cooling leg, Semiconductors 51 (2017) 913–915. [16] C.A. Badillo-Ruiz, M.A. Olivares-Robles, P.E. Ruiz-Ortega, Performance of segmented thermoelectric cooler micro-elements with different geometric shapes and temperature-dependent properties, Entropy 20 (2018) 118. [17] L. Shen, H. Chen, F. Xiao, S. Wang, The practical performance forecast and analysis of thermoelectric module from macro to micro, Energy Convers. Manage. 100 (2015) 23–29. [18] D. Sun, L. Shen, Y. Yao, H. Chen, S. Jin, H. He, The real-time study of solar thermoelectric generator, Appl. Therm. Eng. 119 (2017) 347–359. [19] X. Meng, R.O. Suzuki, Helical configuration for thermoelectric generation, Appl. Therm. Eng. 99 (2016) 352–357. [20] T. Ming, Y. Wu, C. Peng, Y. Tao, Thermal analysis on a segmented thermoelectric generator, Energy 80 (2015) 388–399. [21] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M.S. Dresselhaus, G. Chen, Z. Ren, High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys, Science 320 (2008) 634. [22] Marlow industries. The datasheet of pl054-6-40. https://cdn2.hubspot.net /hubfs/ 547732/data_sheets/pl054-6-40.pdf. 2018.06.10. [23] D.M. Rowe, Thermoelectrics handbook macro to nano, CRC Press, Boca Raton, FL, 2005.

Fig. 11. The selection criteria of SOAT materials for segmented TE cooler.

impacts between segments number and thermal physical properties of TE material, working condition, dimension on the cooling performance of segmented TE cooler are analyzed. The analysis shows that the segment number is more sensitive to the thermal conductivity of TE material, and the optimum segment number is 2 at any condition. The maximum cooling capacity and maximum temperature difference of two-segmented TE element are better when the length is in the range of 0.7 mm–2 mm. Thereinto, the Qc,max, ΔTmax and COPmax of two-segmented TE element could be remarkably improved by 118.1%,118.1% and 2.1% in scenario A without changing overall ZT value. This significant performance enhancement is because the two-segmented structure modifies the standard thermoelectric energy balance equation with 0.35 of Joule heating traveling back to the cold side. 6. Author statement L. Shen completed the writing of the whole manuscript; and W. Zhang completed the data analyses of simulation and experiment; and G. Liu revised the governing equation of segmented thermoelectric element; and Z. Tu compared the results of simulation and experiment; and Q. Lu finished the experiment; and H. Chen provided the conception of segmented thermoelectric structure; and Q. Huang provided technical support for the construction of test rig. All authors have approved the final version to be published, and agree to be accountable 10