Analysis on Bi2Te3 thermoelectric cooler with silica aerogel encapsulation

Energy Conversion and Management 103 (2015) 981–990

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Analysis on Bi2Te3 thermoelectric cooler with silica aerogel encapsulation H.M. Hu, T.S. Ge, Y.J. Dai ⇑, R.Z. Wang Institute of Refrigeration and Cryogenics, Research Center of Solar Power and Refrigeration, M.O.E, Shanghai Jiao Tong University, Shanghai, China

a r t i c l e

i n f o

Article history: Received 12 April 2015 Accepted 5 July 2015

Keywords: Thermoelectric cooler Three dimensional model Silica aerogel encapsulation Air gap

a b s t r a c t A Bi2Te3 TEC with silica aerogel encapsulation is developed. Silica aerogel with different thicknesses is filled in the void spaces around the TE legs and started from cold-side ceramic plate. A three dimensional mathematical model for the TEC is developed. This model considers the effect air gap and silica aerogel. (Bi0.2Sb0.8)2Te3 and Bi2(Te0.97Sb0.03)3, which have temperature-dependent TE properties, are selected to be p-type and n-type TE materials. Also, an experimental test bench is built to validate the three dimensional model. The performances of non-silica aerogel encapsulated TEC with and without consideration of air gap are investigated. Meanwhile, the effects of different thicknesses of silica aerogel encapsulation under different Tas and Vas are analysed. The results show that the cold side ceramic and interconnector, and cold part of TE legs can be insulated effectively while the hot part of TE legs can be effectively dissipated using part silica encapsulation when Th P Ta P Tc. The maximum Qc at Laer = 0.8 mm is nearly increased by 7% as compared with that at Laer = 0 mm when Ta = (Tc + Th)/2. Moreover, apart from the cold side interconnector, Laer should be about 2%, 15% and 25% of the Lleg corresponding to the maximum Qc condition when Ta = Tc, Ta = (Th + Tc)/2 and Ta = Th, respectively. The value of Laer can be (TaTc)/(Th Tc)Lleg corresponding to the optimum COP condition. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Thermoelectric (TE) effect can directly convert temperature difference into electricity and vice versa [1]. There are two kinds of applications based on TE effect. One is thermoelectric cooler (TEC) converting electricity into cooling and the other is thermoelectric generator (TEG) converting heat into electricity. TECs can provide high cooling capacity, without any moving parts as well as refrigerant fluids, and they are noise free during operation. Therefore, compared to conventional vapour compression cooling system, TECs are commonly used in the fields of cosmetic cooler, laser diodes, medical devices and microelectronic systems [2,3]. The performance of the TEC is related to the figure of merit of the thermoelectric mate  2 rial ZT ¼ qa k T , where a q k and T are Seebeck coefficient, electric resistivity, thermal conductivity and working temperature, respectively. High a, low q and k can increase the figure of merit of the thermoelectric material, which can further improve the performance of the TEC. Researchers [4] have developed different kinds of thermoelectric materials with high ZT for different temperature ranges. Nanostructured thermoelectric materials have a higher ZT ⇑ Corresponding author. Tel.: +86 21 34204358. E-mail address: [email protected] (Y.J. Dai). http://dx.doi.org/10.1016/j.enconman.2015.07.015 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

value compared to corresponding bulk thermoelectric materials, such as superlattices, quantum dots, nanowires and nanocomposition [5]. Nanostructured material can improve electronic properties and also decrease the lattice thermal conductivity. Venkatasubramanian et al. [6] developed p-type and n-type superlattices of Bi2Te3/Sb2Te3 with a ZT of 2.4 and 1.2 respectively at room temperature. However, it cannot be used as bulk material. Poudel et al. [7] from MIT and GMZ Company showed that a peak value for ZT = 1.4 at 100 °C, can be achieved in a p-type nanocrystalline BiSbTe bulk alloy. They also presented a general way for the usage of a new nanocomposite approach in developing highperformance low-cost bulk thermoelectric materials. Jimenez et al. [8] fabricated p-type Bi0.4Sb1.6Te3 material via mechanical alloying and they found that ZT is up to 1.2 at around 360 K. Review on thermoelectric material shows that the Bi2Te3 and its alloys currently have been commercialized successfully and achieved the highest ZT values around the room temperature [7]. Mathematical models are an effective method to evaluate performance of TEC systems. These models can be divided into three types. The first type uses equivalent circuits to develop the heat transfer model of TEC [9,10]. Their studies show three important parameters for TEC module including Seebeck coefficient, electric resistance and thermal conductance, can be extracted from manufacturer’s data for TEC products. The second utilizes thermal

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Nomenclature A cp COP E I J L p Qc Qcj Qloss T DT U V

area (m2) specific heat (J kg1 K1) coefficient of performance electrical potential (V) electrical current (A) current density (A m2) thickness (m) pressure (Pa) cooling load and cooling capacity (W) cooling capacity on cold junction (W) energy loss on cold side ceramic plate and interconnector (W) temperature (K) temperature difference between hot side and cold side (K) voltage (V) velocity (m s1)

q r b

l k

density (kg m3) electrical conductivity (X1 m1) Thomson coefficient (V K1) dynamic viscosity (Pa s) thermal conductivity (W m1 K1)

Subscripts a ambient aer aerogel c cold side ce ceramic plate h hot side inter interconnector n n-type TE leg p p-type TE leg max maximums/maximum Qc condition opt optimal COP condition

Greek symbols a seebeck coefficient (V K1)

network to build an energy equilibrium model [11,12], where the heat balance equations on the hot side and cold side of TEC are developed. The major advantage of these models is that it can predict TEC performance in a straightforward manner; however, their accuracies are very limited due to its simplifying assumptions. The last is one-dimensional or three-dimensional model using finite element method [13,14], in which Peltier effect, Joule effect, Fourier effect, Thomson effect and TE material properties could be considered more accurately. From previous research, it can be concluded that most of the theoretical models focus on TEC including TE legs, metal connected TE legs and boundary conditions on cold side and hot side. The air gap exists in the TEC because the p-type and n-type TE legs cannot touch each other. Most of the studies focus on the adiabatic boundary on the side surfaces of TE legs and interconnectors. Thus, the effect of air gap is neglected. Only few studies [15–18] focus on the convective boundary conditions on the side surfaces of the TE legs; however, equivalent h (convective heat-transfer coefficient) is employed to analyse the effects. The realistic heat transfers among air gap, the TE legs, interconnectors and ceramic plates due to air flow, are not discussed in their studies. At the same time, some thermal and electric insulated materials are generally employed to fill the void spaces between the TE legs in a TEG module [19]. It is because part of the thermal energy absorbed on hot side leaves through side surfaces of TE legs by convection between air gap and TE legs [20]. Moreover, the metal vapour produced by TE legs at high temperature leads to the electrical short circuits [19]. Silica aerogel with the extremely low thermal conductivity (0.02 W m1 K1) is popularly used as this thermal and electrical insulated material [21]. The price of silica aerogel is about 600 € m3, which is far less than that of Bi2Te3 (250  104 € m3) [22,23]. So the cost would be increased little for TE device encapsulated by silica aerogel. Recently, Sakamoto et al. [24] successfully developed TEG encapsulated by silica aerogel due to its mechanically and thermally robust. They showed that the silica aerogel encapsulation could improve long-term stability for TEG. However, thermal and electrical insulated materials are rarely used for TEC encapsulation. Furthermore, the performances of TEC with different thicknesses of silica aerogel encapsulation are not investigated. In this paper, a Bi2Te3 TEC with different thicknesses of silica aerogel encapsulation (Laers) is proposed. The silica aerogel is filled

in the void spaces around TE legs and is started from cold side ceramic plate. So the cold side ceramic and interconnector can be insulated while the hot part of TE legs can be cooled by air gap. In order to analyse the effect of air gap as well as silica aerogel encapsulation, a three dimensional model of the TEC is developed, which considers heat transfers among air gap, TE legs, ceramic plates, interconnector and silica aerogel. Firstly, the performances of non-silica aerogel encapsulated TEC, with and without consideration of air gap, are compared and analysed. Then, effects of Laers under different air velocities (Vas) on the performance of TEC are investigated. Lastly, the optimal Laers of silica aerogel are determined under different working conditions.

2. Description of TEC with silica aerogel encapsulation A TEC module consists of a number of TE element pairs which are connected electrically in series and thermally in parallel between two ceramic plates. The two ceramic plates are cold side and hot side ceramic plates. Due to periodic thermal characteristic of the pairs, a TEC with one TE element pair is considered in the study shown in Fig. 1. The specification of the TEC is shown in Table 1. The TE element pair is made of Bi2Te3 material due to its high ZT value around the room temperature. (Bi0.2Sb0.8)2Te3 and Bi2(Te0.97Sb0.03)3 are adopted as the p-type and n-type TE materials [25], which are strongly temperature-dependent. As shown in Eqs. (1)–(3), Seebeck coefficient is expressed as a cubical function of temperature, and thermal conductivity and electrical conductivity are expressed as a quadratic function of temperature. Current flows through a junction from n-type leg to p-type leg, and heat can be absorbed in this junction while current flows from p-type leg to n-type one, heat can be generated in this junction due to Peltier effect. The heat can be generated in the p- and n-type legs due to Joule effect and heat would be transferred from hot junction and cold junction due to Fourier effect. Under the effect of temperature gradient and electric current, the Thomson heat can be generated in the TE legs. As shown in Fig. 1(a), the air gap is between the hot side and cold side ceramic plate around the TE legs if the TEC is not encapsulated by thermal insulation material. Heat transfers occur between TE legs, ceramic plates, interconnector and air gap. Moreover, the air movement would also affect the performance of TEC. As shown in Fig. 1(b), TEC encapsulated by thermal

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Cold side Cold side Silica aerogel

Air gap Cold junction

Cold side ceramic plate

Cold side ceramic plate

Air gap

interconnetor

A

P

N Input

z

interconnetor

A

interconnetor

Laer

A Input

N

P

interconnetor

interconnetor

Hot side ceramic plate y x

Hot side ceramic plate

Ground

Hot junction Hot side

A

Ground Hot side

Inlet

Inlet

A

A

Ceramic plate

Air gap

A

Silica aerogel

Air gap

N

N

P Outlet

Outlet

interconnector

P Outlet

Outlet

y

x

A

Outlet

Outlet

(a)

(b)

Fig. 1. Description of TEC in this study: (a) non-silica aerogel encapsulation (Laer = 0 mm) and (b) silica aerogel encapsulation (Laer – 0 mm).

Table 1 The specification of the TEC. TE legs (mm)

Interconnectors (mm)

Ceramic plate (mm)

Silica aerogel (mm)

1.50  1.50  2.50

4.12  1.68  0.35 2.06  1.68  0.35

2.50  5.0  0.80

2.50  5.00  (0–3.20)

insulation material (silica aerogel) with different thicknesses is proposed. And the silica aerogel is filled from the cold side ceramic plate to prevent the heat transferring to the cold side ceramic plate. And the Laer is from 0 mm to 3.2 mm. The TEC is not silica encapsulated at Laer = 0 mm while the TEC is fully silica encapsulated at Laer = 3.2 mm. The thermal and electrical properties of materials adopted in the present study are shown in Table 2. The thermoelectric properties of TE materials can be expressed as [25]: ( ap ¼ ð9:582  106 T 3  0:0137T 2 þ 5:755T  520:7Þ  106 ð1Þ an ¼ ð2:683  106 T 3 þ 0:0048T 2  2:583T þ 276:5Þ  106

(

(

5

5 2

rp ¼ 10 =ð2:352  10 T þ 0:02132T  1:921Þ rn ¼ 105 =ð8:555  106 T 2 þ 0:009957T  1:335Þ kp ¼ 6:007  106 T 2  0:002513T þ 1:01 kn ¼ 1:194  105 T 2  0:007817T þ 2:277

ð2Þ

ð3Þ

3. Mathematical model As shown in Fig. 1, seven computational domains can be divided in the TEC including cold side and hot side ceramic plates, p-type TE

leg, n-type TE leg, interconnectors, air gap and silica aerogel. The radiation heat transfer is not considered in the present study due to the low working temperature and small temperature difference between the hot side and cold side of TEC. Thus, the governing equations, initial and boundary conditions can be expressed as follows. 3.1. Governing equations

r  ðkrTÞce ¼ 0

ð4Þ

r  ðkrTÞaer ¼ 0

ð5Þ

ðqcp Þa ½r  ðV a  TÞ ¼ r  ðkrTÞa

ð6Þ

Eqs. (4)–(6) represent energy conservation equations of ceramic plate, silica aerogel and air gap, respectively. The computational domains of air gap and silica aerogel are not considered by previous studies.

r  ðkrTÞp=n=inter þ

J2

rp=n=inter

!  bp=n=inter J rT ¼ 0

ð7Þ

Eq. (7) represents energy conservation equation of the p, n-type TE legs and interconnector, respectively. The three terms on the left side of the equation represent heat flux vector due to Fourier effect, Joule heat in the TE legs and Thomson heat [14], respectively. b is the Thomson coefficient and it can be expressed as:

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Table 2 Properties of the materials in this study. k (W m1 K1) Interconnector [16] Silica aerogel [21] Air [26] Ceramic plate [17]

bp=n=inter ¼ T

400 0.018 0.023 35

  dap=n=inter dT

rV a ¼ 0

q (kg m3) 8900 2700 1.2 3800

3900 900 1.005 775

ð8Þ ð9Þ

qa ½V a  rV a  ¼ rp þ la r2 V a

ð10Þ

Eqs. (9) and (10) represent the continuity and momentum equations of air gap, respectively. The la is the dynamic viscosity of air. 3.2. Boundary conditions On the surface of input, there is a constant current applied to the interconnector and the value equals the current density multiplied by cross area (A). On the surface of ground, the electrical potential is zero.

IjInput ¼ JAjInput ¼ constant

ð11Þ

EjGround ¼ 0

ð12Þ

On the surface of the hot junction and cold junction:

    @T @T k þ aTJ ¼ k þ aTJ @z @z p=n inter

Cp (J kg1 K1)

ð13Þ

The first terms in the left and right hand sides of Eq. (13) represent Fourier effect on cold and hot junctions. The second terms of them represent Peltier effect of TE legs and interconnector, respectively. On the surface of the hot side and cold side:

Tjhotside ¼ T h

ð14Þ

Tjcoldside ¼ T c

ð15Þ

The inlet and outlet of air gap can be shown in Fig. 1. The velocity and temperature of air on inlet surface is set to be Va and Ta. Meanwhile, on the side surfaces of the ceramic plates of hot side and cold side, the adiabatic boundary conditions are specified.

a (V K1) 6

6.5  10 – – –

r (X m1) 5.88  108 – – –

COMSOL Multiphysics [27] is utilized to solve the governing equations in association with the boundary conditions. 4. Experimental study Experimental test bench is built to validate the three dimensional model. The commercial TEC module (127 pairs of TE legs) without silica aerogel encapsulation is tested. And the sizes of the TE legs, interconnectors, and the ceramic plate for one pair are identical with that shown in Fig. 1. The experimental test bench is shown in Fig. 2. Four T-type thermalcouples are uniformly placed on the surface of the cold side to measure the average Tc. There is no cooling load on the cold side. The cold side is insulated using thermal insulated material (silica aerogel) to avoid the errors in measuring the magnitude of the cooling load and the heat losses of it. The hot side of TEC module is cooled using water block which is connected with water bath (TZL-1015D). One T-type thermalcouple is placed between the hot side and water block to measure Th. So Th can be controlled by changing the temperature of water bath and Th is fixed to be 303 K. The water block, TEC module and insulated material are fixed using clamp. One T-type thermalcouple is used to measure Ta. All of the temperatures measured by temperature sensors are transmitted to Agilent 34972A data logger and then to computer for analysis. The temperature accuracy is ±0.5 °C for T-type thermalcouple. The DC current is supplied by ITECH IT672 power supply. Fig. 3 shows the variation of simulated and experimental Tc with I. It can be noted that both the simulated and experimental Tc decrease with increasing of I and then increase with further increasing of I. It is because the Peltier cooling effect plays dominant role on the cold junction at a small current while the Joule heating effect along the TE legs increases dramatically with increasing of I due to its square of I. The largest temperature difference between simulation and experiment is less than 2.5 K. Thus, the simulated results closely agree with the experimental data. 5. Result and discussions

3.3. Performance index The cooling capacity (Qc) and coefficient of performance (COP) of the TEC are two important parameters to evaluate the performance of TEC when Tc and Th are fixed. The Qc can be expressed as:

Q c ¼ kce

Z Z

  dTðx; y; zÞ dxdy dz coldside

ð16Þ 5.1. Non-silica encapsulation TEC with and without consideration of air gap

The COP can be expressed as:

COP ¼

Qc Q ¼ c Power IDU

The performances of non-silica aerogel encapsulation TEC with and without air gap are investigated. The different Laers for TEC with air gap are investigated under different Vas. At last, the optimal Laer for TEC would be determined under different operating conditions. The TEC investigated in this section is identical with that described in Section 2.

ð17Þ

where DU refers to the voltage drop through TEC. 3.4. Numerical solution To investigate the performances of TEC with different thicknesses of silica aerogel encapsulation, the commercial software

Fig. 4 shows performances of TEC with and without consideration of air gap under different DTs. There is no silica aerogel encapsulation in the TEC. The Va is generally from 0.2 m s1 to 0.4 m s1 in indoor environment of buildings [28]. The Va and Ta are set to be 0.4 m s1 and 293 K, respectively. First of all, it can be noted that the both COP and Qc firstly increase with increasing of I and then decrease with further increasing of I. So there exist a maximum COP and Qc. It is because the Peltier cooling effect play dominant

H.M. Hu et al. / Energy Conversion and Management 103 (2015) 981–990

985

Fig. 2. The experimental test bench.

role on the cold junction at a small I while the Joule heating effect along the TE legs increases dramatically with increasing of I due to

280 simulation experiment

T/K

270

260

250

240

0

1

2

3

4

I/A Fig. 3. Simulated and experimental Tc variation with I.

5

its square of I. And then the large Joule heat leads to large Fourier heating effect on the cold junction. Moreover, the current (Iopt) leading to optimum COP is smaller than the current (Imax) leading to maximum Qc. Secondly, it can be noted that the Qc of TEC without air gap is smaller than that with air gap, especially at large I (I > 2 A). It is because TE legs can be cooled by air movement, which leads to small Fourier effect on the cold junction. Similarly, this difference is obvious at larger Th due to the larger temperature difference between air flow and TE legs. The Imaxs of TEC with air gap are larger than that without air gap. As shown in Fig. 4(a), the Imaxs are about 3.0 A and 2.5 A with and without air gap, respectively. It is because the Joule heat produced in the TE legs can be effective dissipated by air gap. Fig. 5 shows the temperature distributions on the middle cross-section at I = 3 A and DT = 40 K. Firstly, the temperature of p-type TE leg is larger than that of n-type TE leg due to larger rn which is shown in Eq. (2). Moreover, it can be noted that the Tmax on the TE leg of TEC with air gap is smaller than that of TEC without air gap. The Tmax is 353 K for air gap while that is 361 K for non-air gap. It is because the Joule heat produced in the TE leg can be effectively cooled by air gap, which is distinctly shown in the temperature of air gap between two TE legs. It agrees with the description shown in Fig. 4.

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0.16

5.2. Variation of performance under different Laers

T=20K non air gap T=40K non air gap T=60K non air gap T=20K air gap T=40K air gap T=60K air gap

0.12

Qc/W

Tc=293K 0.08

0.04

0.00

0

1

2

3

4

5

I/A

(a) 1.6 T =20 K non air gap T =40 K non air gap T =60 K non air gap T =20 K air gap T =40 K air gap T =60 K air gap

COP

1.2

Tc=293 K

0.8

0.4

0.0

0

1

2

3

4

5

I/A

(b) Fig. 4. Performances of TEC with and without consideration of air gap under different DTs: (a) Qc and (b) COP.

During TEC operation, the Ta is between Tc and Th in the air-cooling TEC module [29]. The Ta is specifically assumed to be (Tc + Th)/2. In order to simplify the discussion, the Th and Tc are set to be 313 K and 293 K, respectively. And the Va is assumed to be 0.4 m s1 and 1.6 m s1. The large Va (1.6 m s1) is adopted to investigate the effect of forced air flow [30]. The distance between the cold side and hot side is 3.2 mm, and the Laer is set to be 0 mm, 0.8 mm, 1.6 mm, 2.4 mm and 3.2 mm, respectively. Fig. 6 shows performance of the TEC with different Laers at Ta = (Tc + Th)/2. It can be seen that the Qc and COP at Laer = 1.6 mm are larger than that at other Laers around Iopt. It is because the temperature distributions along the TE legs are almost a line at smaller current, which would be shown in Fig. 7. It suggests that apart from interconnector, the value of Laer/Lleg should equal that of (Ta Tc)/(ThTc). Meanwhile, it is noted that the COP and corresponding Qc at Laer = 0 mm are smaller than that at other Laers around Iopt. It implies that the TEC should be encapsulated at this operation condition. However, the Qc and COP at Laer = 0.8 mm are larger than that at other Laers around Imax. It can be seen that maximum Qc at Laer = 0.8 mm is almost increased by 6% and 20% as compared with that at Laer = 0 mm and Laer = 3.2 mm at Va = 1.6 m s1. Moreover, Qc and COP increase with increasing of Va at I > 1.5 A. It can be noted that the maximum Qc increases from 0.132 W to 0.145 W when Va increases from 0.4 m s1 to 1.6 m s1 at Laer = 0.8 mm. At the same time, the Qcs are almost identical when Laer is 3.2 mm at different Vas and the maximum Qc is around 0.120 W. It indicates that the performance of TEC with part encapsulation can be improved using forced air flow when Ta is between Tc and Th. Fig. 7 shows the temperature distributions along the interconnector and TE legs. Fig. 8 shows the temperature distributions on the middle cross-section at I = 3 A. It can be noted that the temperature distributions along the interconnectors and TE legs at these three Laers at I = 1 A are nearly a line and almost identical. It is because the Joule heating effect could not play an obvious effect. Moreover, it can be seen that the temperature variations along the interconnectors are very small. It is because the rinter and kinter are extremely large due to copper-based interconnector, which leads to small Joule heating produced in interconnector and temperature uniformity along the interconnector. Meanwhile, the

Fig. 5. Temperature distributions on the middle cross-section (y = 0 mm) at I = 3 A and DT = 40 K: (a) non air gap and (b) air gap.

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0.15

0 mm 0.8 mm 1.6 mm 2.4 mm 3.2 mm

0.12

-1

Va = 0.4 ms

1.0

COP

Qc/W

0.09

1.5

0.06 0.5 0.03

0.00

0

1

2

3

4

5

0.0

I/A

(a) 0.15

1.5

5.3. Optimal Laer corresponding to maximum Qc condition at different Tas

0.12 1.0

COP

Qc/W

0.09

0.06

0.00

0

1

2

3

Fig. 11 shows the variation of maximum Qc with Laer and Ta under different DTs. So the applied current is Imax. Firstly, Qc decreases with increasing of DT due to increment of Fourier effect on cold junction. Secondly, there are the peak Qcs for Ta = Tc, Ta = (Th + Tc)/2 and Ta = Th. The optimal Laer is 0.4 mm, 0.7 mm and

0.5

0 mm 0.8 mm 1.6 mm 2.4 mm 3.2 mm V = 1.6 ms-1 a

0.03

Fig. 10 shows variation of maximum Qc with Ta at different Laers. Thus, the applied current is Imax. The Ta is increased from Tc to Th. It is noted that all of the Qcs decreases with increasing of Ta. It is due to the increment of Qloss and decreasing of Qcj. It can be seen that Qc at Laer = 0 mm is the largest one in the five Qcs when Ta = Tc, however, it is decreased to be the lowest one when Ta = Th. It indicates the gradient for Qc at Laer = 0 mm are larger than that at other Laers. It is because the cold side ceramic plate and interconnector are directly contacted with air flow. So that can be heated by air gap effectively when Ta > Tc, which leads to increasing of Qloss. At the same time, Qc at Laer = 3.2 mm is not the largest one even at Ta = Th. Though Qloss can be kept at a small value using full encapsulation, the hot part of TE legs, of which temperature is larger than Ta, could not be cooled by air gap. As a result, the Fourier effect at cold junction increases leading to low Qc. Thus, it is important to determine the optimal Laer corresponding to maximum Qc condition.

4

5

1A 0mm 3A 0mm 1A 0.8mm 3A 0.8mm 1A 3.2mm 3A 3.2mm

0.0

310

I/A

temperature of TE leg at Laer = 0 mm is smaller than that at Laer = 3.2 mm. It implies that the TE leg can be cooled by air gap leading to the smaller Fourier effect at cold junction for non-encapsulation than that for full encapsulation. Fig. 9 shows the variations of Qcj and Qloss with I. Qcj is the cooling capacity on the cold junction and Qloss is the heat loss on the surface of cold side interconnector and ceramic plate. So Qc of the TEC is Qcj subtracts Qloss. It is noted that Qcj firstly increases with increasing of I and then decreases with further increasing of I. The reason of this is similar as that shown in Fig. 4(a). As shown in Figs. 7 and 8, the temperatures of TE legs at Laer = 0.8 mm and Laer = 0 mm are smaller than temperatures at Laer = 3.2 mm, especially for large I. It is because that the Joule heat produced along the TE legs can be effectively cooled by air movement at Laer = 0.8 mm and Laer = 0 mm. Thus, it can lead to the small Fourier effect at cold junction. Thus, Qcj at Laer = 3.2 mm are distinctly smaller than that at Laer = 0.8 mm and Laer = 0 mm, especially at large I. Two conclusions can be drawn with regards to Qloss. One is that Qloss at Laer = 0 mm is far larger than that at other Laers at small I. It is because the heat can be directly transferred to cold side ceramic and interconnector from air gap without any encapsulations. Thus, Qc at Laer = 0 mm is smaller than that at other Laers, which have been discussed in Fig. 6. The other is that Qloss at Laer = 3.2 mm increases rapidly with increasing of I. It is because the temperature of silica aerogel near cold side is very large because large heat generation of TE legs could not be cooled by air movement. It can be seen in Fig. 8. Thus, there are a balance between enhancement on Qcj and Qloss.

Ta

300

n-type TE leg

290 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Z/mm

(a)

1A 0mm 3A 0mm 1A 0.8mm 3A 0.8mm 1A 3.2mm 3A 3.2mm

340 330

T/K

Fig. 6. Performance of the TEC with different Laers at Ta = (Tc + Th)/2: (a) Va = 0.4 m s1 and (b) Va = 1.6 m s1.

T/K

(b)

320 310 300 290 0.0

Ta 0.5

1.0

p-type TE leg 1.5

2.0

2.5

3.0

Z/mm

(b)

Fig. 7. Temperature distributions along the interconnector and TE legs.

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Fig. 8. Temperature distributions on the middle cross-section (y = 0 mm) at I = 3 A: (a) Laer = 0 mm, (b) Laer = 0.8 mm and (c) Laer = 3.2 mm.

0mm 0.8mm 3.2mm

0.016

Laer=0mm

0.16

0.15

Laer=0.8mm Laer=1.6mm Laer=2.4mm

0.05

0.008

0.00

Laer=3.2mm

0.14

Qc/W

Qloss/W

0.012

Qcj/W

0.10

0.12

0.004

0

1

2

3

4

5

I/A Fig. 9. Variations of Qcj and Qloss with I.

1.2 mm when Ta is Tc, (Tc + Th)/2 and Th at DT = 20 K. It indicates that the optimal Laer increases with increasing of Ta. Secondly, it is also noted that Qc is nearly constant when Laer 6 optimal Laer at Ta = Tc. It is because the temperature of cold junction (Tcj) is slightly smaller than Tc. Thirdly, the Qc increases significantly with increasing of Laer at Ta = (Th + Tc)/2 and Ta = Th, respectively. As shown in Fig. 11(c), Qc is smaller than 0.03 W when DT = 60 K and Tc = Th. It implies that the TEC has no cooling effect. It is because the Qloss significantly degrades the performance of TEC due to air movement. It indicates that the TEC should be encapsulated by

290

295

300

305

310

315

Ta/K Fig. 10. Variation of maximum Qc with Ta at different Laers.

thermal insulated material if Ta > Tc. Meanwhile, it is also noted that the Qc decreases with increasing of Laer if Laer P optimal Laer. It is mainly because the hot part of TE legs could not be effective cooled by air movement, which leads to large Fourier effect at cold junction to decrease the Qc. Lastly, the Laer increases slightly with increasing of DT. Thus, apart from the cold side interconnector, the Laer should be encapsulated around the 2%, 15% and 25% of Lleg when Ta = Tc, Ta = (Th + Tc)/2 and Ta = Th, respectively.

H.M. Hu et al. / Energy Conversion and Management 103 (2015) 981–990

Ta=Tc Ta=(Tc+Th)/2

0.16

Ta=Th

Q c/W

T=20K Tc=293K 0.14

0.12

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Laer /mm

(a) Ta=Tc

0.14

Ta=(Tc+Th)/2 Ta=Th T=40K Tc=293K

0.12

989

aerogel and ceramic plate are considered. And, the experimental test bench is built to validate the established mathematical model. The performance of non-silica aerogel encapsulated TEC with and without consideration of air gap is investigated. Different thicknesses of silica aerogel encapsulation of TEC are investigated under different Tas, Vas and Is. The conclusions made are as follows: (1) The cold side ceramic and interconnector and cold part of TE leg can be insulated effectively while the hot part of TE leg can be dissipated effectively using part silica encapsulation at Th P Ta P Tc. (2) Apart from the cold side ceramic plate and interconnector, the optimal value of Laer can be (TaTc)/(ThTc)Lleg at the optimum COP condition. (3) The maximum Qc at Laer = 0.8 mm is almost increased by 6% and 20% as compared with that at Laer = 0 mm and Laer = 3.2 mm at Va = 1.6 m s1. (4) Apart from the cold side interconnector, the Laer should be about 2%, 15% and 25% of the length of TE leg respectively, when Ta = Tc, Ta = (Tc + Th)/2 and Ta = Th corresponding to maximum Qc condition. (5) Partly encapsulated TEC cooled by forced air flow is another effective way to improve the performance of TEC at Ta 6 Th.

Q c /W

0.10

Acknowledgements 0.08

This work is supported by the National Key Development Program of Scientific Instrument of China (2011YQ030139). We would like to thank Per Kjellsen from Norwegian University of Science and Technology for feedbacks on English language and grammar improvements.

0.06 0.04 0.0

0.5

1.0

1.5

2.0

2.5

3.0

References

Laer/mm

(b) 0.12 0.09

Q c /W

0.06 0.03 Ta=Tc Ta=(Th+Tc)/2

0.00

Ta=Th T=60K

-0.03 0.0

Tc=293K 0.5

1.0

1.5

2.0

2.5

3.0

Laer/mm

(c) Fig. 11. Variation of maximum Qc with Laer and Ta under different DTs: (a) DT = 20 K, (b) DT = 40 K and (c) DT = 60 K.

6. Conclusion A Bi2Te3 TEC with silica aerogel encapsulation is proposed. A three dimensional model for this TEC is developed in this study. The heat transfers among air gap, TE leg, interconnector, silica

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