Entropy generation minimization of thermoelectric systems applied for electronic cooling: Parametric investigations and operation optimization

Energy Conversion and Management 186 (2019) 401–414

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Entropy generation minimization of thermoelectric systems applied for electronic cooling: Parametric investigations and operation optimization

T

Yang Caia,b,c, Wei-Wei Wanga,b,c, Wen-Tao Dinga,b,c, Guo-Biao Yanga,b,c, Di Liud, ⁎ Fu-Yun Zhaoa,b,c, a

Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education, Wuhan, Hubei Province, China Shenzhen Research Institute, Wuhan University, Shenzhen, Guangdong Province, China c School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei Province, China d College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao, Shandong Province, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Thermoelectric system Thermodynamic model Entropy generation minimization Irreversibility Energy efficiency

Two categories of thermoelectric systems, i.e. thermoelectric active cooling (TAC) and thermoelectric selfcooling (TSC), were broadly applied for electronic cooling. Energy efficiency maximization and entropy generation minimization will be simultaneously achieved for both thermoelectric systems. Thermodynamic models of TAC and TSC systems are established to clarify the effects of main influencing parameters (i.e., applied current, thermal conductance in hot and cold ends) on the energy and entropy performances. Subsequently, under the situation of electronic cooling with constant material properties, a comprehensive performance comparison between TAC and TSC has been conducted, including decision targets, irreversible characteristics and environmental impacts. Furthermore, in order to improve the heat dissipation potential, the effects of material properties on the system performance are also sensitively identified for both TAC and TSC systems. For both systems, internal irreversibility is more pronounced than external one. Numerical results demonstrated that system efficiency of TAC could be higher than that of TSC; the operating mode for TAC could be completely switched to that for TSC when the input power was turned into zero. Present investigation could give suitable guidelines for thermoelectric systems applied for electronic cooling.

1. Introduction With the rapid development of microelectronic technology and manufacturing technique, a variety of electronic devices such like PC processors, LED and electric battery etc. are being developed toward compact, miniaturization and high encapsulation [1]. This results in difficulties in thermal management of high-power electronic chips with high heat flux within a limited heat dissipation surface. Investigations show that a rise of 2 °C in temperature of a silicon chip leads to a decrease by about 10% in its thermal reliability, which results in an increase in challenges of thermal management [2]. Moreover, traditional cooling technologies by natural convection and forced convection are not sufficient to remove the heat fluxes at a sufficient high rate [3–5]. Avalanche researches have showcased the limitations of traditional cooling methodologies and technologies applied in the field of electronic cooling. As a result, developing high-performance thermal management solutions to cool high-flux electronic devices are urgently required [6,7].

⁎

In recent years, thermoelectric cooling technology, which exhibits its advantages of free noise, friendly environment and faster reaction in comparison to conventional cooling, has been used in combination with other cooling ways to cool electronic devices [8]. In fact, the electronic cooling by means of the thermoelectric technologies can be classified into two categories-thermoelectric active cooling (TAC) system making use of thermoelectric cooler to take away energy directly, while thermoelectric self cooling (TSC) system utilizing thermoelectric generator to generate electricity from a temperature gradient for power supply of fan or water pump. Their studies indicate that thermoelectric technologies are thought to be one of alternative technologies to traditional electronic cooling solutions. 1.1. Description of thermoelectric technology Thermoelectric technology is regarded as an alternative and environmentally friendly technology due to the fact that it can achieve the heat and electricity energy conversion without using moving parts or

Corresponding author at: School of Power and Mechanical Engineering, Wuhan University, 430072 Wuhan, Hubei Province, China. E-mail address: [email protected] (F.-Y. Zhao).

https://doi.org/10.1016/j.enconman.2019.02.064 Received 17 October 2018; Accepted 16 February 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A Aleg C COP E G I K L N P Q R S Sgen T Tj

Greek symbols ε ρ φ σ

area (m2) the area of p-n legs (m2) fluid specific heat (W/K) coefficient of performance exergy (W) geometric factor (mm) current (A) thermal conductance (W/K) length of P-N legs (m) number of thermoelectric couples electric power (W) capacity (W) thermal resistance (Ω) Seebeck coefficient (V/K) Entropy generation rate (W/K) temperature (K) chip temperature (K)

heat coefficient electrical resistivity (kg/m3) equivalent efficiency entropy generation rate (W/K·m3)

Subscripts c d e h in o out T

cold side destroy emit hot side inlet atmosphere environment outlet thermoelectric module

for performance analysis of electronic cooling and have been utilized to reduce the surface temperature or increase the cooling load of electronic devices by TAC system integrated various active cooling methods [25–29]. The research also indicated that the thermoelectric air-cooling module performs worse than the heat sink without of TEC when the total resistance of heat sink is higher than 0.385 K/W [28]. In order to decrease the thermal resistance of heat sink in hot side, some novel cooling methods (e.g. micro-channel cooled [30,31], PCM cooled [32,33], heat pipe cooled [12,34], water jet [35], nanofluid [36]) have been fully studied from the viewpoint of energy analysis and the low thermal resistance of 0.02 °C/W can be achieved. Apparently, the TAC system with the lower thermal resistance of heat sink would enhance heat transfer in the hot side of thermoelectric cooler and the maximum COP would be obtained due to heat being released. Recently, except from energy analysis of the TAC system, a wide variety research works have been proposed by combing the energy and entropy generation analysis, aiming at distinguishing the irreversibility in the TAC system [37]. Presented work by Bejan [38] introduced the theory of entropy generation minimization (EGM) and further taken the entropy generation minimization as the optimization objective for designing realistic thermodynamic processes. In recent years, EGM analysis has become powerful evaluation index to optimize the system performance of the TAC system including single-stage thermoelectric cooler [16] and two-stage thermoelectric cooler [39]. It is noted that entropy generation minimization, in fact, represents not only the minimum irreversibility in the system [40] but also the maximum exergy contribution when the environment temperature keeps constant [41]. Applications of EGM analysis to the TAC system have also been carried out through modeling analysis and parametric optimization [16,42]. One can observe from the literature review that these is a considerable increase in the research work during the recent years on the TAC system. However, it is also observed that only a few of these papers discuss parametric investigations of the TAC system in more elaborate detail according to an integrated model from the viewpoint of energy and entropy generation analysis. Also, the internal irreversibility associated with the TAC system should be identified and analyzed numerically.

avoiding the production of environmentally deleterious wastes [9]. Specifically, the thermoelectric devices are semiconductor devices that have the ability to either generate a voltage when exposed to a temperature gradient, exploiting the Seebeck effect, or produce a temperature gradient when supplied by electricity, exploiting the Peltier effect [10]. Until now, thermoelectric systems have been applied in military, aerospace, instrument, and industrial or commercial products, etc., as cooling devices, heat pump systems and power generation system for specific applications [11]. Although these are a series of advantages of thermoelectric systems, low efficiency and high cost have still been a barrier to their developments for more common applications. Great efforts have been made in the past decades to optimize thermoelectric models [12] and further develop high-performance thermoelectric systems [13]. The optimal performance of thermoelectric systems essentially depends on several factors such like crucial variable parameters of the overall system (i.e. thermal conductance, applied current and fluid parameters) and material properties of thermoelectric module [14–16]. Research and development of high-performance thermoelectric systems have been investigated for various applications such as electronic cooling [17], building ventilation [18], space heating and cooling [19], and waste heat recovery [20]. A dominating solution to improve the performance of thermoelectric systems is to develop advanced thermoelectric materials and processing technology in order to achieve a higher value of dimensionless figure of merit (ZT) [21]. The higher the thermal value coefficient ZT is, the better the thermoelectric material is. Relevant studies showed that 30% of Carnot efficiency (comparable to home refrigeration) could be reached by a device with a ZT value of 4 [22]. Simultaneously, the operating cost of the thermoelectric system could be compared against the operating cost of absorption refrigeration and air conditioning with an increase of ZT value [23]. Therefore, the main decision parameters and material properties of the thermoelectric system should be comprehensively considered on the system analysis and optimization. 1.2. Thermoelectric active cooling system A TAC system has been widely applied in the field of electronic cooling due to its advantages of miniature, feasibility and flexibility. As mentioned before, a TAC system comprises of a thermoelectric cooler (TEC), a heat sink, and a fan, which typically uses an energy conversion process (Peltier effect) to absorb the thermal energy from the surface of heat source and then to pump this energy into the environment through heat sink [24]. A number of investigations are reported in the literature

1.3. Thermoelectric self cooling system The thermoelectric self cooling technology which integrates a thermoelectric generator (TEG) and a generalized heat sink (e.g. radiator fan or water pump) has garnered considerable attention in recent years as a promising solution to thermal management of electronic 402

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thermodynamic models of these typical thermoelectric systems are established to clarify the effects of main decision parameters (i.e., applied current, thermal conductance in hot and cold ends) on the energy and entropy performance. Subsequently, a comprehensive comparison between thermoelectric active cooling and thermoelectric self cooling system performances for electronic cooling has been outlined in different aspects, such as decision targets, irreversible characteristics and environmental impact under the conditions of constant material properties. Finally, the effects of material properties on the system performance are further identified for both TAC system and TSC system in order to significantly improve the heat dissipation potential. Current thermodynamic analyses of two representative thermoelectric systems are also conducted to determine the ones that are most suitable for use based on various operating conditions.

devices [43–45]. This is due to the fact that a thermoelectric generator attached to an electronic device can utilize the heat to generate electricity for the heat sink and then take away heat. As a result, the electronic device would be properly cooled without external power consumption for heat sinks. Recent research studies were carried out to examine thermal performance of the TSC system on electronic cooling. Martínez et al. [45] experimentally and analytically studied the thermodynamic model of thermoelectric self cooling with air cooling and the thermal performance was statistically assessed. Their results showed the thermal resistance between the heat source and the environment would be reduced significantly by 25–30% when the TSC system works properly. Kiflemariam et al. [46] explored in detail an arrangement with primary and secondary heat paths to guide heat flow to the thermoelectric generator and heat sink. The experimental results showed that for the highest heat input studied, the temperature of the device can be reduced by 20–40% as compared to natural convection case. In fact, the thermal resistance of the entire cooling system (e.g. TSC system, TAC system) between electronic device and environment is one of key factors for reliable electronic cooling [47]. Their research works demonstrate the applicability of thermoelectric self-cooling to power electronics, such as CPU, LED, and LD. So far, thermoelectric generators have been investigated in detail from the viewpoint of energy and entropy generation analysis to indentify thermodynamic irreversibility and performance characteristics [48–52]. Their results revealed that the internal and external irreversibility should be considered in optimizing the thermoelectric generator for various finite conditions. In order to develop the full modeling of the TSC system, the analytical methods by simultaneously considering the energy and entropy generation analysis need to be developed and further indentify the effects of variable parameters on the TSC system applied in electronic cooling. Observing from the literature review, not only there is a lack of comprehensive comparison on system analysis between TAC system and TSC system, but also thermoelectric systems have not been fully evaluated under various operating conditions from the viewpoint of energy conservation and entropy generation analysis. Therefore, this paper is going to fill this research gap. In the present study, energy and entropy generation minimization analysis are carried out for two typical thermoelectric systems including thermoelectric active cooling system and thermoelectric self cooling system, which can be used for electronic cooling implementation. Depending on the thermoelectric effect and the effectiveness-number of transfer units (ε-NTU),

2. Thermodynamic modeling As mentioned above, two typical thermoelectric systems including thermoelectric active cooling system and thermoelectric self cooling system could be favorable for electronic cooling implementation. A complete combination of energy and entropy generation analysis principles would give more information about thermodynamic performance and irreversibility characteristics which is not obtainable by energy or entropy generation analysis alone. In this section, the energy and entropy generation analysis for two typical thermoelectric systems applied in electronic cooling are first conducted and a comprehensive comparison of parametric investigations is further discussed, aiming to critically evaluate the performance of thermoelectric system. The schematic diagram of a typical thermoelectric cooling system for electronic device is shown in Fig. 1, which consists of a TEC or TEG, an electronic device, a heat spreader, and a cast-aluminum heat sink. As shown in Fig. 1, each thermoelectric cooler or generator could be simplified as a thermoelectric module (TEM) and it comprises many pairs of P-N type semiconductor columns, metal connectors, and two electrically insulating ceramic plates. Many pairs of P-N type semiconductor columns are compactly connected electrically in series and thermally in parallel. The heat spreader is used as a buffer plate to avert decreasing the cooling capacity and COP. Also, one side of the TEM is in contact with a electronic device, while the other side of the module is linked to a heat sink for heat dissipation. The TEM directly absorbs heat from the heat source, and then the heat is transferred to the heat sink through the semiconductor materials, which leads to a temperature

Fig. 1. Two representative thermoelectric cooling systems for electronic cooling. 403

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drop of electronic device. It should be noted that for using a thermoelectric cooler the interface between the thermoelectric cooler and the heat spreader is the cold side of thermoelectric cooler and the interface contacted with heat sink is the hot side of thermoelectric cooler. However, the hot and cold sides of thermoelectric device are opposite when the thermoelectric generator is adopt as a cooling module in comparison to the use of thermoelectric cooler. Before the thermodynamic analysis, the following assumptions have been considered in this study to simplify the modeling complexity for two typical thermoelectric systems:

T (x ) = Tc + (Th − Tc )·

x 1 ρI 2 + · ·x (L − x ) 2 L 2 kAleg

(2)

The local heat flow includes the heat conduction (Fourier) flux and the Peltier heat flux, and it can be expressed as follows:

Q (x )leg = sIT (x ) − kA·

Th − Tc 1 ρI 2 + · ·(2x − L) L 2 Aleg

(3)

It is known that bismuth telluride is commonly used as commercial thermoelectric material and the material properties are dependent on temperature condition. In order to obtain the cooling load and power input of TEC, the total Seebeck coefficient S, electrical resistance R and thermal conductance K of a multi-couple thermoelectric cooler should be confirmed. According to Ref. [12], these physical parameters could be given in following formulas.

(1) Thomson effect is negligible. (2) The electrical and thermal resistance of the junction contacts, ceramic plates and joining coppers are assumed to be negligible. (3) One dimensional steady state heat transfer along the thermoelectric legs has been considered. (4) Only the Fourier’s heat conduction phenomena is the model of heat transfer from hot junction to the cold junction of TEC which is due to the inherent thermal conductivity of thermoelectric materials. (5) The fluid velocity is constant and the fluid pressure loss is not considered in the flow process of channel. (6) Heat loss for TEM and heat exchangers in both sides is negligible.

S = 2Ns

(4)

K = 2NkG

(5)

R = 2N

ρ G

(6)

Based on the above assumptions, the performance analysis and comparison of two typical thermoelectric systems coupling energy and entropy analysis have been carried out to confirm the effects of the main decision parameters on system performance in the later section.

2.1. Model of thermoelectric active cooling system Fig. 2(a) illustrates the model diagram of the TAC system, which includes all the relevant components and the neighboring region affected by discharging the spent hot stream. According to the Peltier effect, heat from the electronic heat source would be absorbed in the cold side of TEC and then dissipated in the hot side of TEC when a direct current passes through thermoelectric materials. Specifically speaking, the absorbed heat Qc (cooling capacity) is transferred from the electronic chip to the cold junction of TEC at temperature Tc, and the rejected heat Qh (heat dissipating capacity) is transferred from the hot junction of TEC at temperature Th to the heat sink. The air at temperature Tin is pumped into the hot side air duct to take away the heat through heat transfer process of forced convection. In this way, the chip temperature (Tj) would be maintained within a safety range. It is noted that the heat transfer processes through the hot and cold side thermal conductance (UhAh, UcAc) are involved in the external irreversibility due to the finite temperature differences while the internal irreversibility occurs in the TEC because of the internal thermal conductance and thermal resistance. Thus, the maximizing cooling capacity or minimizing chip temperature and minimizing entropy generation are simultaneously considered for evaluating the whole TAC system.

2.1.1. Energy analysis Our analysis starts with one-dimensional thermal balance of thermoelectric leg, which is available in previous literature [19]. The steady state energy equation for p and n legs is expressed as follows:

k

ρI 2 d 2T + 2 =0 2 dx Aleg

(1)

where I is the intensity of current, Aleg is cross area of p or n type semiconductor. k is thermal conductivity and ρ is electrical resistivity. By using the first kind boundary conditions (Tx=0 = Tc, Tx=L = Th), one dimensional temperature distribution of the thermoelectric leg could be obtained as follows:

Fig. 2. Thermodynamic model of the thermoelectric system: (a) thermoelectric active cooling system; (b) thermoelectric self cooling system. 404

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1

where N and G represent the number of thermoelectric couples and the geometric factor of thermoelectric leg, respectively. According to Eqs. (4)–(6), the module parameters (S, K, R) could be determined if the variables s, k, ρ, N, and G are given. According to the first kind boundary conditions and the physical properties of a multi-couple thermoelectric cooler, the energy equations for total cooling capacity Qc, heat dissipating capacity Qh, and power input P can be presented respectively as,

Qc = STc I −

1 2 I R − K (Th − Tc ) 2

(7)

Qh = STh I +

1 2 I R − K (Th − Tc ) 2

(8)

P = Qh − Qc = SI (Th − Tc ) + I 2R

(φUh Ah − SI + K ) Tj + 2 I 2R (φUh Ah − SI + 2K )/ Uc Ac Tc =

1 2 I R (φUh Ah 2

Tj =

− SI + 2K ) + KφUh Ah Tin

(K + SI ) φUh Ah − S 2I 2

(18)

Let UhAh, UcAc = +∞, Eq. (16) reduces to Th = Tout, Eqs. (17) and (18) reduce to Tc = Tj, which agrees with the physical intuition. Besides, one could observe that the analytical expressions for Th, Tc and Tj are obtained depending on those known parameters, such as thermoelectric physical parameters (S, K, R), input current (I), air parameters (Tin, C) and overall thermal conductance variables (UhAh, UcAc). Specifically speaking, the cooling capacity and surface temperature could be calculated within a broad range of certain parameters.

(9)

2.1.2. Entropy production analysis In a steady state operating condition, there is internal and external irreversibility for TAC system mainly due to the internal resistance and conductance of thermoelectric materials and external finite heat transfer rate, which result in an increase of entropy generation. Since entropy generation accounts the true value of irreversible process, it is expressive to use entropy as a basis index for evaluating the thermodynamic system. As mentioned above, the EGM analysis is a powerful method and plays an significant role in analysis and assessment of thermoelectric system. Application of EGM method for TAC system in electronic cooling is described in detail in the following section. The local entropy generation rate in one dimensional homogeneous phase is given as follows [51]:

(10)

In the above given relations, Tin and Tout represent the inlet and outlet temperatures of the cooling fluid in the hot side heat exchanger, respectively. C is heat capacity rate of the cooling fluid. The parameter ε is defined as the ratio of the actual heat transfer rate for a heat exchanger to the maximum possible heat transfer rate. Based on the εNTU relationships, the variable ε is a function of the overall thermal conductance UhAh and it can be expressed as follows:

U A ε = 1 − exp ⎛− h h ⎞ C ⎠ ⎝

(17)

{K − SI + φUh Ah + [(K + SI ) φUh Ah − S 2I 2]/ Uc Ac } Qc+

The hot side of TEC is cooled by a plate-fin heat exchanger. The method of ε-NTU is employed to establish the heat transfer module of the heat sink. Thus the Qh can be written as:

Qh = εC (Th − Tin ) = C (Tout − Tin )

+ KφUh Ah Tin/ Uc Ac K − SI + φUh Ah + [(K + SI ) φUh Ah − S 2I 2]/ Uc Ac

(11)

1 dQ 1 dT − 2Q T dx T dx

Combining Eqs. (10) and (11), heat dissipating capacity could be given as,

σ=

Qh = φUh Ah (Th − Tin )

Using Eqs. (2) and (3) into Eq. (19), the local entropy generation rate can be expressed as,

(12)

where φ is an equivalent thermal efficiency for hot side heat exchanger, it can be defined as:

φ=

σ = kAleg

[2kA2 (Tc L + x ΔT ) + I 2ρLx (L − x )]2 (20)

1

In 1 − ε

(13)

where ΔT = Th − Tc is referred to as the temperature difference of hot end to cold end of TEC. The entropy generation for a single thermoelectric leg is derived by integrating Eq. (20) from × = 0 to × = L. By combining Eqs. (2)–(6), the total entropy generation rate for TEC can be expressed as follows:

The cold side of TEC is compactly connected with the electronic chip by heat spreader. Therefore, the chip temperature is related to the cold end temperature of TEC by below equation:

Qc Uc Ac

(14)

Sgen - T =

where Tj represents the surface temperature of electronic chip and it should be within a permitted operating temperature range (< 70 °C). UcAc is the cold end thermal conductance from the cold junction of TEC to the cooled device. In this paper, the heat spreader would be taken as cold side heat exchanger. The system COP is always adopted to evaluate thermoelectric cooling system, which is defined as the ratio between cooling load from electronic chip and all power input for the thermoelectric cooler. Thus, the COP can be expressed as follows:

STc I − 2 I 2R − K (Th − Tc ) Qc = P SI (Th − Tc ) + I 2R

(15)

According to the above analysis, the analytical expressions for Th, Tc, and Tj are derived by using Eqs. (7)–(14):

KTj +

1 φUh Ah Tin [(K + SI )/Uc A c + 1] + 2 I 2R [(2K + SI )/ Uc Ac K − SI + φUh Ah + [(K + SI ) φUh Ah − S 2I 2]/ Uc Ac

Qh Q − c Th Tc

(21)

The entropy generation rates in cold side and heat side heat exchangers are different obviously due to the diversity in the heat transfer process. As shown in Fig. 2(a), for the cold side heat exchanger, only one-dimensional heat transfer leads to the entropy generation to the system as a result of the irreversible process. On the contrary, the entropy generation in hot heat exchanger could be separated into two terms, one associated with the stream-to-stream temperature difference, and the neighboring region affected by discharging the spent hot stream if the pressure drops of air fluid are assumed to be negligible. The fluid pressure loss is relative small in comparison to atmospheric pressure due to the smaller radiator for electronic cooling [44,46]. Then the entropy generation rates in hot side heat exchanger and cold side heat exchanger can be respectively written as [52]:

1

COP =

Th =

2 4LkAleg ρI 2 (Th L − ΔTx ) + 4k 2A4 ΔT 2 + I 4ρ2 L2 (L2 − 2Lx + 2x 2)

ε

Tj = Tc +

(19)

Sgen - h = C·In + 1]

Sgen - c =

(16) 405

To Q Q − h + o Tin Th To

Qc Qc Tc Tj

(22)

(23)

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The cooling rate experienced by the spent hot stream is Qo = C(Tout − To). The inlet air temperature Tin is practically at environment temperature To in most cases. In the end, the system entropy generation rate can be calculated as follows,

Sgen = Sgen - T + Sgen - h + Sgen - c =

Qh Q − c To Tj

P = Qh − Qc = SI (Th − Tc ) −

(24)

UA ε = 1 − exp ⎛− c c ⎞ C ⎠ ⎝

Qc = φUc Ac (Tc − Tin )

Tj = Th +

Qh Uh Ah

(33)

The system COP for the TSC system is defined as the ratio of the power output to the absorbed load from electronic chip. Thus, the COP can be expressed as follows:

COP =

P SI (Th − Tc ) − I 2R = 1 Qh STh I − 2 I 2R + K (Th − Tc )

(34)

Using Eqs. (27)–(34), the analytical expressions for Th, Tc, and Tj are numerically derived as: 1

Th =

Fig. 2(b) indicates the model diagram of a representative TSC system, which can be used for both electronic cooling and power output implement simultaneously. It is worth noting that the heat from the device is expressed by Qin, which represents Qh when a TEG is adopt as a TEM for electronic cooling. In a TSC system, the input load Qh passes from the device to the TEG module via a heat spreader after crossing the hot side thermal conductance (UhAh). After the heat enters the spreader, it could produce the temperature difference between hot and cold junctions of TEG, resulting in the energy conversion of heat into electricity by Seebeck effect. Finally, the external heat passes through the heat sink until it is rejected to the ambient air at the temperature of To. The coupled analysis for the entire system can also be divided into two parts:

1

(Qh + 2 I 2R )(φUc Ac − SI + K ) + K ( 2 I 2R + φUc Ac Tin ) (SI + K )(φUc Ac − SI + K ) − K 2

(

1

) (

K Qh + 2 I 2R +

1 2 I R 2

(35)

)

+ φUc Ac Tin (SI + K )

(SI + K )(φUc Ac − SI + K ) − K 2

(36)

(Uh Ah + SI )(φUc Ac − SI + K ) + K (φUc Ac − SI )] Qh+ 1

Tj =

1

Uh Ah [ 2 I 2R (φUc Ac − SI + K ) + K ( 2 I 2R + φUc Ac Tin )] Uh Ah [(SI + K )(φUc Ac − SI + K ) − K 2]

(37)

Finally, these dependent variables Th, Tc and Tj can be calculated through Eqs. (35)–(37). Also, those known parameters, such as thermoelectric physical parameters (S, K, R), input current (I), air parameters (Tin, C) and overall thermal conductance parameters (UhAh, UcAc) are considered as inputs of the computational model. 2.2.2. Entropy production analysis As mentioned before, the local entropy generation rate in one dimensional homogeneous phase is given as shown in Eq. (19). Likewise the local entropy generation rate can be expressed as:

2.2.1. Energy analysis In order to establish the analytical model for the TSC system, a onedimensional steady-state assumption applied to the thermoelectric legs is considered. Likewise by combining the first kind boundary conditions (Tx=0 = Th, Tx=L = Tc), the one-dimensional temperature distribution could be obtained as follows:

σ = kAleg 4 2 4k 2Aleg ρI 2 [Th L + (x − L)ΔT ] + I 4ρ2 L2 (L2 − 2Lx + 2x 2) + 4kAleg

[2kA2 (Th L − x ΔT ) + I 2ρLx (L − x )]2

ρI 2

(38) (26)

where ΔT = Th − Tc is referred to as the temperature difference of hot to cold end of TEG. The entropy generation for a single thermoelectric leg is derived by integrating Eq. (38) from × = 0 to × = L. By combining Eqs. (4)–(6), the entropy generation rate for TEG can be given as follows:

According to the same derived principle as the Eqs. (1)–(9), the energy equations for the total input load Qh, the rejected heat Qc, and the power output P could be therefore expressed respectively in following formulas.

1 2 I R + K (Th − Tc ) 2

(32)

The hot side of TEG is compactly connected with the electronic chip by heat spreader. The chip temperature can be calculated by the following equation:

Tc =

Qh = STh I −

(31)

Combining Eqs. (30) and (31), the absorbed load could be given as:

2.2. Model of thermoelectric self cooling system

x 1 − · ·x (x − L) 2 L 2 kAleg

(30)

where the variable ε is given in following equations,

(25)

T (x ) = Th − (Th − Tc )·

(29)

Qc = εC (Th − Tin ) = C (Tout − Tin )

Sgen − T Sgen

(28)

I 2R

The method of the ε-NTU is employed to simplify the heat transfer module of cold side heat exchanger. Similarly, the rejected load can be written as follows:

Eq. (24) shows the total entropy generation rate by using the method of ε-NTU, which agrees with that of the method of thermal resistance network. Obviously, the Eq. (24) represents the total entropy generation rate of TAC system due to the internal and external irreversibilities which occur with heat transfer from the heat source, heat transfer to the surroundings, heat and current transport between hot and cold sides of thermoelectric device. According to Eqs. (10), (11), (14) and (24), the thermal conductance in heat and cold side heat exchangers would greatly influence the system performance and the external irreversibility, especially for electronic cooling with a consideration of fixed constraints. Actually, the external irreversibility is caused due to the finite thermal conductance coupling with hot side thermal conductance UhAh and cold side thermal conductance UcAc, which are also thought to be one of the key factors in determining system performance. In order to meet demands of maximizing the cooling capacity or minimizing chip temperature, it makes sense to consider the thermal conductance as a decision variable to analyze and indentify its effect. In addition, the internal entropy production mainly plays an important role for the overall TAC system, thus a proper dimensionless entropy generation ratio of internal entropy generation rate to total entropy generation rate is further introduced (Ns), which is given as follows:

Ns =

1 2 I R + K (Th − Tc ) 2

Qc = STc I +

Sgen - T = −

(27) 406

Qh Q + c Th Tc

(39)

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In fact, the total entropy generation rate for TSC system includes the entropy generation of TEG, hot side heat exchanger and cold side heat exchanger. Furthermore, the entropy generation affected by discharging the spent hot stream is considered in the present work as an external entropy generation released into the environment which generates environmental impact [53,54]. Similar principle as the TAC system is applied to the TSC system as shown in Eqs. (40) and (41). The entropy generation rate in hot side heat exchanger and cold side heat exchanger can be written as:

Sgen - c = C·In

Sgen - h =

To Q Q − c + o Tin Tc To

(40)

Qh Qh Th Tj

(41)

Finally, the system entropy rate can be calculated as:

Sgen = Sgen - T + Sgen - h + Sgen - c =

Qc Q − h To Tj

(42)

Fig. 3. Effect of thermoelectric operating current on the chip temperature with various cooling loads for the TAC system and TSC system respectively.

The Eq. (42) shows that the total entropy generation rate by using the method of ε-NTU also agrees with that of the method of thermal resistance network. Likewise the entropy generation ratio for TSC system is given as the same as Eq. (25).

characteristics of two thermoelectric systems. Fig. 3 presents the effect of thermoelectric operating current on the chip temperature with various absorbed load Qin (40 W, 60 W, 80 W), which represents Qc for TAC system and Qh for TSC system respectively. It can be seen that the curves have the same trends, in which the chip temperature gradually decreases with an increase of continuous current from 0 to 3.6 A. This can be attributed to the fact that the temperature difference between hot and cold sides of thermoelectric device would increase for the TAC system and decrease for the TSC system with the increase of current respectively. It can also be found that the operating modes for TAC system and TSC system can be completely switched when the input power (P) is absolutely zero at different cooling load. The results indicate that during the operating mode for TSC system, when the electrical power is positive a small value, the voltage generated by internal resistance is insufficient to overcome the Seebeck effect that is occurring because of the existing thermoelectric temperature differential. Also, the corresponding chip temperatures are 54.56 °C, 70.32 °C and 86.15 °C for I = 0.66 A, 0.98 A and 1.28 A, respectively. When the electric current remains constant, the higher the absorbed load is, the lower the chip temperature is. The system entropy generation rate (Sgen) and entropy generation rate ratio (Ns) for the TAC system and TSC system are respectively depicted in the Fig. 4. As seen in Fig. 4, the Sgen and Ns simultaneously reduce for the TSC system while increase for the TAC system with rise in current. Accordingly, there clearly exists minimum values of Sgen and Ns when the electric currents leading to the P = 0 are 0.66 A, 0.98 A and 1.28 A for various Qin. It should be noted that the Ns values are over 0.88 in the range of 0–3.6 A, significantly indicating that the contribution of interior irreversibility to the total irreversibility is much larger as compared to that of external irreversibility. Fig. 5 depicts the effect of thermoelectric operating current on the system efficiency with various cooling load for the TAC system and TSC system respectively. With a rise in the operating current, the COP of TSC system is first increased and then decreased. There exist peak values of COP at 0.018, 0.026 and 0.034 when the electric currents are

3. Parametric investigations and discussions To have a good evaluation and comprehensive comparison of two typical thermoelectric systems, the physical properties of TEC and TEG are considered as identical along the following section. Analytical expressions of the thermoelectric material (bismuth telluride) used in the simulation are written as second-order polynomial forms and are listed in Table 1. In this study, all material properties are considered to be isotropic. By referring to the mean temperature of 310 K, the thermoelectric physical parameters for a TEM (S, K, R) are 0.08597 V/K, 0.7647 W/K, 3.893 Ω respectively. The air temperature and heat capacity remain constants at approximately 22 °C and 40 W/K, respectively. The input capacity from electric device to thermoelectric module is unified as the variable Qin which represents Qc in Eq. (7) for thermoelectric cooler and Qh in Eq. (27) for thermoelectric generator respectively. The numerical solution of the former equations through the thermodynamic model is obtained with the solver MATLAB. Parametric investigations and result discussions are performed for the present analysis of typical thermoelectric systems applied in electronic cooling in the following subsections. 3.1. Effect of thermoelectric operating current The thermoelectric operating current has a direct effect on the heat conduction of TEC and TEG. For a TEC model, the electric current is directly supplied to a TEC when it is operated in the cooling mode, resulting in the temperature difference between the hot and cold sides of TEC. Inversely, the electric current would be generated due to the temperature difference between the hot and cold sides of TEG when the thermoelectric device is adopted as a TEG module. Therefore, the thermoelectric operating current should be considered as a decision variable to exhibit the thermal performance and irreversible

Table 1 Simplified expressions of thermoelectric physical parameters for thermoelectric module. Property

Material parameters −1

Seebeck coefficient (Vk ) Thermal conductivity (Wm-1K−1) electrical resistivity (Ω m) Geometric factor Number of p-n junction

s = (22224 + 930.6 * Tm − 0.9905 * Tm ) * 10 k = (62605–277.7 * Tm + 0.4131 * Tm2) * 10-4 ρ = (5112 + 163.4 * Tm + 0.6279 * Tm2) * 10-10 – – 2

407

-9

conversion formula

TEM parameters value

S = 2·N·s K = 2·N·k G R = 2·N·ρ/G G = Aleg/L N

0.08597 V/K 0.7647 W/K 3.893 Ω 1.186 mm 199

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demonstrate that the lower cooling load fixed, the lower chip temperature could be for either TAC system or TSC system if the operating current is the same. Furthermore, the effect of thermal conductance in hot dissipater end on the entropy generation rate and entropy generation rate ratio with various cooling load for the TAC system and TSC system are further proposed as shown in Fig. 7. It can be found that increasing the value of UA results in a decrease of Sgen and simultaneously an increase of Ns at first and then the values of Sgen and Ns tend to be stable. This indicates that a relatively lower value of UA could be more sensitive to Sgen and Ns. In the meantime, the stable values of Sgen are 0.035 W/K, 0.041 W/K, 0.054 W/K for TAC system, and 0.014 W/K, 0.033 W/K, 0.057 W/K for TSC system when the absorbed loads are set to be 40 W, 60 W, and 80 W respectively. A remarkable finding is that the steady values of Ns are nearly over 0.9 for all working conditions, which suggests that increased hot dissipater end thermal conductance could significantly reduces external irreversibility. Fig. 8 shows the effect of thermal conductance in hot dissipater end on the system efficiency with various cooling load for the TAC system and TSC system respectively. Two distinct features can also be found through the simulation results as depicted in Fig. 8. The first aspect is that the values of COP would rapidly augment at first, and it would approach a parallel line when UA > 20 W/K. This is because, increasing thermal conductance in hot dissipater end would decrease the input power of TAC system and increase the output power of TSC system, further boosting the system efficiency. The second aspect is that the increment of COP at the range from 60 W to 80 W is greater than that from 40 W to 60 W at a fixed UA for the TAC system. For the TSC system, the COP decreases significantly with increase of Qin at a fixed UA. The current results reveal that the promotion of thermal conductance in hot dissipater end properly would enhance heat transfer potential; however, a larger UA value is unnecessary for improving the performance of thermoelectric system and inversely would raise the cost of heat exchanger.

Fig. 4. Effect of thermoelectric operating current on the entropy generation rate and entropy generation rate ratio with various cooling loads for the TAC system and TSC system respectively.

3.3. Effect of thermal conductance in hot absorbed end Fig. 5. Effect of thermoelectric operating current on the system efficiency with various cooling loads for the TAC system and TSC system respectively.

The thermal conductance in hot absorbed end could put great effects on the heat transfer between the electric device and thermoelectric module, further influencing the performance of the thermoelectric systems. Furthermore, the external irreversibility of thermoelectric system is dependent on absorbed side thermal conductance, which should be considered to reduce entropy generation. Therefore, the impact of this factor for TAC system and TSC system is numerically simulated using the energy and entropy analysis for a range of absorbed

0.32 A, 0.48 A and 0.62 A respectively. It is different from TSC system that the COP of TAC system is always reduced with increase of current and several orders higher than that of TSC system. The reason behind this variation is that, on the one hand, the output power for TSC system is prominently lower than the input power for TAC system along the overall current range; on the other hand, the system performance of TSC system is highly dependent on the temperature difference between hot and cold sides of thermoelectric generator.

3.2. Effect of thermal conductance in hot dissipater end As mentioned in the aforementioned section, in order to show the external irreversibility when finite heat transfer rate between hot side of TEC or cold side of TEG and environment source exists for the real thermodynamic system, the thermal conductance in hot dissipater end should be analyzed to reveal the performance of thermoelectric systems. Here, the currents for the TAC system and TSC system are set to be 1.6 A and 0.4 A, respectively. Fig. 6 illustrates the variation of thermal conductance in hot dissipater end on the chip temperature with various cooling load for the TAC system and TSC system. As shown in Fig. 6, the chip temperature (Tj) decreases quickly before UA < 20 W/K and after UA > 20 W/K maintains almost constant. This occurs due to the fact that when hot end thermal conductance increases at the beginning, the heat transfer would enhance, resulting in decreased chip temperature and then the dissipated heat potential would get weak. The simulation results also

Fig. 6. Effect of thermal conductance in hot dissipater end on the chip temperature with various cooling loads for the TAC system and TSC system respectively. 408

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change of absorbed side thermal conductance are depicted in Fig. 11 (cooling loads are set to 40 W, 60 W, and 80 W). It could be noted that if the operating current and cooling loads are simultaneously fixed, the system efficiencies would be determined no matter what the absorbed side thermal conductance is. This is due to the fact that the temperature difference between the chip temperature and the cold side temperature of TEC or hot side temperature of TEG decreases proportionally with increase in UA. Constant values of COP are thus obtained with 4.28, 9.48, 24.26 being achieved for TAC system and 0.017, 0.026, 0.03 being achieved for TSC system respectively.

3.4. Effect of chip temperature It is worthy to explore the effect of chip temperature on the present thermoelectric systems, because the chip temperature often needs to be maintained within a temperature range, and the drop of the chip temperature could be beneficial to ensure the reliability of modern electronic equipment. Two sets of analytical solutions for thermoelectric system applied in electronic cooling have been proposed based on a fixed cooling power or a fixed chip temperature [24,27]. To obtain the relationships between the cooling load and the chip temperature, the quantitatively simulation results about the dependent variables Qin, Sgen, Ns, and COP are presented for TAC system and TSC system respectively. Figs. 12–14 display the effect of chip temperature on evaluation indexes (Qin, Sgen, Ns, and COP) with various heat sink for the TAC system and TSC system respectively. As mentioned previously, the heat transfer potential in hot dissipater side could be represented by the UA value, which is a fundamental index for heat exchanger. In this subsection, the various cooling ways including air cooling, water cooling and heat pipe cooling are depicted through operating parameters of UA. As shown, the cooling load and entropy generation rate are increased continuously with rise in chip temperature for both TAC system and TSC system respectively. However, the entropy generation rate ratio shows a decreasing trend with an increase of Tj for TAC system, which is opposite as compared to that of TSC system. It can be inferred from the graph that the lower chip temperature maintained by the TAC system is more beneficial than that by the TSC system, which is due to a higher Qin being achieved at a fixed Tj. Apparently, the lower temperature difference between hot and cold sides of thermoelectric generator would cause the lower output power. Furthermore, the results from the Fig. 13 demonstrate that the higher chip temperature could result in the relatively lower internal irreversibility for TAC system and higher internal irreversibility for TSC system respectively. For the TAC system,

Fig. 7. Effect of thermal conductance in hot dissipater end on the entropy generation rate and entropy generation rate ratio with various cooling loads for the TAC system and TSC system respectively.

Fig. 8. Effect of thermal conductance in hot dissipater end on the system efficiency with various cooling loads for the TAC system and TSC system respectively.

side thermal conductance in this subsection. Fig. 9 presents the change of chip temperature according to the absorbed side thermal conductance for both TAC system and TSC system. Here, a general observable trend is that the lower values of the absorbed side thermal conductance yield very high values of the Tj, which are disadvantageous for electronics. Also, the simulation results from Fig. 9 demonstrate that a higher absorbed side thermal conductance has very little effect on the Tj and the stable values of Tj are 29.7 °C, 52.9 °C, 76.1 °C for TAC system and 62.3 °C, 88.6 °C, 114.9 °C for TSC system when the absorbed loads are set to be 40 W, 60 W, and 80 W respectively. Fig. 10 shows the effect of thermal conductance in hot absorbed end on the entropy generation rate and entropy generation rate ratio with various cooling load for the TAC system and TSC system. It can be seen that a similar trend is observed for Sgen and Ns in comparison to the Fig. 7. As shown, the all Ns values are also above 0.9, concluding that the internal irreversibility is also dominant factor for overall entropy generation rate in comparison to the external irreversibility. The reason behind such variation is most likely due to the finite heat transfer rate between the electric device and the cold side of TAC system or hot side of TSC system, which is found to have a strong influence on the chip temperature by previously theoretical analysis. In the meantime, the lower Sgen value can be achieved at 0.014 W/K when the absorbed load is set to be 40 W for TSC system. Clearly, the minimum entropy production rate is according with the result in Fig. 7 under a certain condition. The system efficiencies of TAC system and TSC system with the

Fig. 9. Effect of thermal conductance in hot absorbed end on the chip temperature with various cooling loads for the TAC system and TSC system respectively. 409

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Fig. 10. Effect of thermal conductance in hot absorbed end on the entropy generation rate and entropy generation rate ratio with various cooling loads for the TAC system and TSC system respectively.

Fig. 13. Effect of chip temperature on the entropy generation rate and entropy generation rate ratio with various heat sinks for the TAC system and TSC system respectively.

Fig. 11. Effect of thermal conductance in hot absorbed end on the system efficiency with various cooling loads for the TAC system and TSC system respectively.

Fig. 14. Effect of chip temperature on the system efficiency with various heat sinks for the TAC system and TSC system respectively.

effective ranges. Referring to these figures, the cooling load and system efficiency would be obviously enhanced through using heat pipe cooling. This occurs due to the thermal conductance being augmenting in the heat dissipater side in this study. Moreover, the increment of Qin and COP from water cooling to heat pipe cooling is obviously lower than that of air cooling to water cooling, which also indicates that the improvement of system performance is finite by the improvement of heat dissipation way. 3.5. Effect of thermoelectric module parameters According to Eqs. (4)–(6), the module parameters of thermoelectric device (S, K, R) could be determined if the variables s, k, ρ, N, and G are given. In fact, the value of Z (Z = S2/KR) would be able to remain constant if the variables S, K and R change in a certain principle simultaneously, such as increasing the couple number of p-n junction. To further indentify the effect of the module parameters on the two thermoelectric systems, the new module parameters at N = 127 (S′ = 0.055 V/K, K′ = 0.488 W/K, R′ = 2.48 Ω) are adopted to simulate the system performance and irreversibility characteristic as a comparison of current module parameters. Figs. 15–17 present the effect of thermoelectric module parameters on the evaluation indexes (Tj, Sgen, Ns, and COP) for the TAC system and TSC system respectively when the ZT value of thermoelectric material is maintained as constant. According to the simulation results in Figs. 15

Fig. 12. Effect of chip temperature on the absorbed load with various thermal sinks for the TAC system and TSC system respectively.

the effective range of Tj for heat pipe cooling is more widespread than that of air cooling. For instance, in the case of I = 0.4 A, the effective Tj ranges are about 46–80, 42.8–80 and 42.2–80 °C for Qin, Sgen, and Ns. According to Fig. 14, the system efficiency of TSC system is far lower than that of TAC system when the chip temperature remains in the 410

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module parameters (S, K, R and S′, K′, R′) show relatively greater differences, which suggests that the module parameters have direct effects on the chip temperature and system efficiency for two thermoelectric systems. For instance, the corresponding differences are 42.5 °C/0.0064 and 35.74 °C/10.17 for I = 0.4 A and I = 2 A respectively. For the TSC system, if the new module parameters (S′, K′, R′) are adopted, the entropy generation rate and entropy generation rate ratio are greater than that of using parameters (S, K, R). However, the almost opposite results are obtained for TAC system, especially for entropy generation rate. Also, the Ns value ranges from 0.89 to 0.95 when I changes from 0 to 3.6 A and the lower Ns value can be achieved at the value of I = 0.96 A. Although the values of ZT remain the same in this two cases, the geometry parameters of thermoelectric module could change the entire values of S, K, R and further influence the system performance. 4. Analysis of environmental impacts Assessments of exergy destruction and waste exergy emission offer the opportunity to quantify the environment impact and the sustainability of any energy system [44,46]. Generally, the degradation of exergy resource is a form of environment damage during the utilization of the exergy source. This is due to the fact that the using of the source containing exergy would result in the disequilibrium with the environment. According to second law of thermodynamics, the destroyed exergy can be represented by the product of entropy generation rate and reference temperature (Ed = To·Sgen). Thus, the minimum destroyed exergy corresponds to the entropy generation minimization as illustrated in the Bejan’s theory [52]. Furthermore, the emitted exergy causes a change that could be damaging to the environment, such as greenhouse effect due to the release of a large amount of heat. By considering the values of the destroyed exergy and emitted exergy, the environment impacts of thermoelectric system applied in electronic cooling are numerically quantified and fully evaluated in view of thermodynamic analysis. Moreover, the results and discussions are presented later. Fig. 18 shows the destroyed exergy as a function of the electric current with various cooling load for the TAC system and TSC system respectively. As shown in Fig. 18, the destroyed exergy decreases continuously as the electric current value increases for TSC system. For Qin = 40 W, 60 W, and 80 W, the lower destroyed exergy are 4.02 W, 8.54 W, 14.35 W at the corresponding current of 0.66 A, 0.98 A and 1.28 A. Compared to results from Fig. 4, minimum values of Ed and Sgen for each cooling load occur at the same amount of the electric current, which represents the optimal current leading to destroyed exergy minimization. As analyzed in the previous section, the neighboring

Fig. 15. Effect of thermoelectric module parameters on the chip temperatures for the TAC system and TSC system respectively when the ZT value of thermoelectric material is maintained constant.

Fig. 16. Effect of thermoelectric module parameters on the entropy generation rate and entropy generation rate ratio for the TAC system and TSC system respectively when the ZT value of thermoelectric material is maintained constant.

Fig. 17. Effect of thermoelectric module parameters on the system efficiency for the TAC system and TSC system respectively when the ZT value of thermoelectric material is maintained constant.

and 17, the clearly higher chip temperature and system efficiency can be achieved through making use of new module parameters when the operating current is fixed as constant. It can be seen from the present results that the chip temperature and system efficiency in various

Fig. 18. Destroyed exergy as a function of the electric current with various cooling loads for the TAC system and TSC system respectively. 411

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Tj = 34.2 °C at 59.6 W is obtained here for the air cooled cases with and without TEC enhancement. Likewise the similar cross-over point for the Sgen can be found at 0.206 W/K for Tj = 89.2 °C with and without TEC enhancement. According to results in Fig. 23, a critical area that is used to evaluate the TEC enhanced performance has been identified through combining energy analysis with entropy generation minimization analysis. In fact, the cross-over point of Tj for the energy analysis would increase with the number of thermoelectric modules [26], which suggests the cooling potential of thermoelectric system. Furthermore, the operating current could be a key factor on the minimization of Sgen due to the reduction of cross-over point for the Sgen dramatically, as shown in Fig. 24. The effective range of the chip temperature, corresponding to normal operating condition for TEG module, is higher than that of results in Fig. 23.

region around the thermoelectric system would be affected due to discharging the spent hot stream, further resulting in the environmental condition change. Similarly to the destroyed exergy, the emitted exergy can be expressed as a function of heat rejection Qo (Ee = Qo·(1 − To/ Tout)). Fig. 19 indicates the variation of the emitted exergy (Ee) as a function of the electric current with various cooling load for the TAC system and TSC system respectively. By increasing the electric current, Ee of TSC system reduces at first and then increases, slightly. The lower values of Ee can be achieved at the values of 0.26 W, 0.57 W, and 1.0 W When the corresponding currents are 0.32 A, 0.46 A, and 0.6 A respectively. However, the Ee of TAC system would increase consecutively until it reaches its maximum. It reveals that at higher current a great amount of exergy absorbed from electronic device is wasted inevitably due to the irreversibility process in the thermodynamic system. Moreover, the environment impact of thermoelectric system should be paid attention in order to develop a sustainable energy system, particularly in the utilization of exergy source.

7. Conclusions In order to propose some information about energy efficiency and entropy generation rate in electronic cooling, a coupled analysis including energy and entropy generation minimization analysis is performed for two representative thermoelectric systems (TAC system and TSC system). The combined module through considering the chip temperature, system efficiency and entropy generation rate has been set up, aiming to assess the system performance and further identify the relationship between internal irreversibility and external irreversibility. Furthermore, a comprehensive comparison of TAC system and TSC system involved with main decision parameters, environmental impact and application potential is developed based on the coupling model. The conclusions that can be obtained from the present work are listed as follows. The chip temperature decreases gradually with an increase of continuous current from 0 to 3.6 A whereas the Sgen and Ns simultaneously reduce for the TSC system and increase for the TAC system. The operating modes for TAC system and TSC system can be completely switched when the corresponding chip temperatures are 54.56 °C, 70.32 °C and 86.15 °C for I = 0.66 A, 0.98 A and 1.28 A, respectively. Also, the Ns values are over 0.88 in the range of 0–3.6 A, significantly indicating the total irreversibility is dominated by interior irreversibility for the entire thermoelectric systems. With a rise in the operating current, the COP of TSC system is first increased and then decreased. There exist peak values of COP at 0.018, 0.026 and 0.034 when the electric current are 0.32 A, 0.48 A and 0.62 A respectively. With the change of heat dissipater side thermal conductance, the chip temperature is decreasing quickly before UA < 20 W/K and after UA > 20 W/K maintained almost constant. Increasing the value of heat

5. Application potential of thermoelectric system As mentioned previously, the performance of thermoelectric system is subject to semiconductor materials due to that the current ZT value of thermoelectric material is fairly low. Indeed, if the ZT value is further improved and commercialized, then it is definitely possible for the thermoelectric system to achieve higher quality system performance. The results on the prediction of the system performance have been presented with a range of ZT value from 0.5 to 3, as shown in Figs. 20–22. The absorbed load, operating currents for the TAC system and TSC system remain at approximately 60 W, 1.6 A and 0.4 A respectively. By increasing the ZT value from 0.5 to 3.0, the chip temperature decreases continuously from 63.04 °C to 10.94 °C for the TAC system and 92.44 °C to 74.55 °C for the TSC system respectively. Observing from Fig. 21, for the TSC system both Sgen and Ns decrease by ZT enlargement, which indicates the reduction of internal irreversibility in this condition. It is noted that, for the TAC system, the Sgen would be decreased at beginning and then increased. Thus a peak value of Sgen can be reached at the value of 0.037 W/K for ZT = 1.6. When the electric current and absorbed load are fixed as constants, the system efficiency for the TSC system is 0.044 at ZT = 3 which is more than doubled than that of ZT = 0.5 (COP = 0.02). It is worth noting that the COP decreases inversely by an increase in ZT for the TAC system. This is because, an increase of the temperature difference between the hot and cold sides of thermoelectric cooler occurs with an increase of ZT and further results in the increment of power input. This suggests that the enlargement of ZT may be perceived to be beneficial or disadvantageous for thermoelectric systems, which larger depends on specific finite conditions. 6. Comparison with former published studies The present research coupled energy and entropy generation analysis is compared with previous studies in Ref. [28] based on a general air cooling way. In order to display the current results better, the results of Qin and Sgen have been presented with two representative sets of electric currents (0.98/0.4 A and 3.6/1.6 A) for the TSC system and TAC system respectively. Figs. 23 and 24 show the comparison between present analytical results and literature for ITSC = 0.98 A, ITAC = 3.6 A and ITSC = 0.4 A, ITAC = 1.6 A respectively. As shown in Fig. 23, the Qin for the TAC system with air cooling is higher than that of previous study using TEC223 and 330 when the chip temperature below the cross-over point (about 75 °C). For the case of the TSC system, the chip temperatures are completely lower than that of TEC223 or 330 when the effective range of chip temperature varies from 80 °C to 100 °C, which is due to the temperature difference requirement of regular work for TEG module. It is also seen that, the same intersecting temperature point of

Fig. 19. Emitted exergy as a function of the electric current with various cooling loads for the TAC system and TSC system respectively. 412

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Fig. 23. Comparison between analytical results and published ones for ITSC = 0.98 A, ITAC = 3.6 A.

Fig. 20. Variations of chip temperatures of thermoelectric systems with the ZT value. All changes in ZT were assumed to be affected only by S at the range of 0.5 and 3.0.

Fig. 24. Comparison between present analytical results and published ones for ITSC = 0.4 A, ITAC = 1.6 A. Fig. 21. Variations of entropy generation rate and entropy generation rate ratio of different thermoelectric systems with the value of ZT. All changes in ZT were assumed to be affected only by S at the range of 0.5 and 3.0.

for TSC system when the absorbed loads are set to be 40 W, 60 W, and 80 W respectively. Constant values of COP in the case of absorbed side thermal conductance are obtained with 4.28, 9.48, 24.26 being achieved for TAC system and 0.017, 0.026, 0.03 being achieved for TSC system respectively. The effective range of Tj for heat pipe cooling is broader than that of air cooling. In the case of I = 0.4 A, the effective Tj ranges are about 46–80, 42.8–80 and 42.2–80 °C for Qin, Sgen, and Ns. The system efficiency of TSC system is far lower than that of TAC system when the chip temperature remains in the effective ranges. Moreover, the increment of Qin and COP from water cooling to heat pipe cooling is obviously lower than that of air cooling to water cooling and the improvement of system performance is finite by the improvement of heat dissipation way. The geometry parameters and ZT value of thermoelectric module have heavily effects on the system performance. By increasing the ZT value from 0.5 to 3.0, the chip temperature decreases continuously from 63.04 °C to 10.94 °C for the TAC system and 92.44 °C to 74.55 °C for the TSC system respectively. When the electric current and absorbed load are fixed as constants, the system efficiency for the TSC system is 0.044 at ZT = 3 which is more than doubled than that of ZT = 0.5 (COP = 0.02). For Qin = 40 W, 60 W, and 80 W, the lower destroyed exergy are 4.02 W, 8.54 W, 14.35 W at the corresponding current of 0.66 A, 0.98 A and 1.28 A. The lower values of Ee can be achieved at the values of 0.26 W, 0.57 W, and 1.0 W When the corresponding currents are 0.32 A, 0.46 A, and 0.6 A respectively. Furthermore, the same intersecting temperature point of Tj = 34.2 °C at 59.6 W is obtained here for the air cooled cases with and without TEC enhancement. Likewise the similar

Fig. 22. Variation of system efficiency of two thermoelectric systems with the ZT values. All changes in ZT were assumed to be affected only by S at the range of 0.5 and 3.0.

dissipater side thermal conductance results in a decrease of Sgen and simultaneously an increase of Ns at first and then the values of Sgen and Ns tend to be stable. In the meantime, a higher absorbed side thermal conductance has very little effect on the Tj and the stable values of Tj are 29.7 °C, 52.9 °C, 76.1 °C for TAC system and 62.3 °C88.6 °C, 114.9 °C 413

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cross-over point for the Sgen can be found at 0.206 W/K for Tj = 89.2 °C with and without TEC enhancement. Overall, the present work makes a global comparison of two typical thermoelectric systems applied in electronic cooling on the basis of the coupling thermodynamics analysis. The future research on the thermoelectric cooling system should be focus on the operating strategy that is used to regulate the high effective module of TAC system and TSC system.

2015;159:458–68. [20] Wang T, Luan W, Liu T, Tu S-T, Yan J. Performance enhancement of thermoelectric waste heat recovery system by using metal foam inserts. Energy Convers Manage 2016;124:13–9. [21] Zhang X, Zhao LD. Thermoelectric materials: Energy conversion between heat and electricity. J Materiomics 2015;1:92–105. [22] Zhao D, Tan G. A review of thermoelectric cooling: Materials, modeling and applications. Appl Therm Eng 2014;66:15–24. [23] Cai Y, Mei S-J, Liu D, Zhao F-Y, Wang H-Q. Thermoelectric heat recovery units applied in the energy harvest built ventilation: Parametric investigation and performance optimization. Energy Convers Manage 2018;171:1163–76. [24] Cai Y, Liu D, Zhao FY, Tang JF. Performance analysis and assessment of thermoelectric micro cooler for electronic devices. Energy Convers Manage 2016;124:203–11. [25] Esfahani JA, Rahbar N, Lavvaf M. Utilization of thermoelectric cooling in a portable active solar still-An experimental study on winter days. Desalination 2011;269:198–205. [26] Zhang HY. A general approach in evaluating and optimizing thermoelectric coolers. Int J Refrig 2010;33:1187–96. [27] Zhang HY, Mui YC, Tarin M. Analysis of thermoelectric cooler performance for high power electronic packages. Appl Therm Eng 2010;30:561–8. [28] Chang YW, Chang CC, Ke MT, Chen SL. Thermoelectric air-cooling module for electronic devices. Appl Therm Eng 2009;29:2731–7. [29] Hu HM, Ge TS, Dai YJ, Wang RZ. Experimental study on water-cooled thermoelectric cooler for CPU under severe environment. Int J Refrig 2016;62:30–8. [30] Chein R, Chen Y. Performances of thermoelectric cooler integrated with microchannel heat sinks. Int J Refrig 2005;28:828–39. [31] Li G, Zhang G, He W, Ji J, Lv S, Chen X, et al. Performance analysis on a solar concentrating thermoelectric generator using the micro-channel heat pipe array. Energy Convers Manage 2016;112:191–8. [32] Gharbi S, Harmand S, Jabrallah SB. Experimental comparison between different configurations of PCM based heat sinks for cooling electronic components. Appl Therm Eng 2015;87:454–62. [33] Roberts NS, Al-Shannaq R, Kurdi J, Al-Muhtaseb SA, Farid MM. Efficacy of using slurry of metal-coated microencapsulated PCM for cooling in a micro-channel heat exchanger. Appl Therm Eng 2017;122:11–8. [34] Sun X, Zhang L, Liao S. Performance of a thermoelectric cooling system integrated with a gravity-assisted heat pipe for cooling electronics. Appl Therm Eng 2017;116:433–44. [35] Karwa N, Stanley C, Intwala H, Rosengarten G. Development of a low thermal resistance water jet cooled heat sink for thermoelectric refrigerators. Appl Therm Eng 2017;111:1596–602. [36] Ahammed N, Asirvatham LG, Wongwises S. Thermoelectric cooling of electronic devices with nanofluid in a multiport minichannel heat exchanger. Exp Therm Fluid Sci 2016;74:81–90. [37] Nuwayhid RY, Moukalled F, Noueihed N. On entropy generation in thermoelectric devices. Energy Convers Manage 2000;41(9):891–914. [38] Bejan A. Advanced engineering thermodynamics. 4th ed New York: Wiley; 2016. [39] Manikandan S, Kaushik SC. The influence of Thomson effect in the performance optimization of a two stage thermoelectric generator. Energy 2016;100:227–37. [40] Kaushik SC, Manikandan S, Hans R. Energy and exergy analysis of thermoelectric heat pump system. Int J Heat Mass Trans 2015;86:843–52. [41] Manikandan S, Kaushik SC. Energy and exergy analysis of an annular thermoelectric cooler. Energy Convers Manage 2015;106:804–14. [42] Zhu L, Yu J. Optimization of heat sink of thermoelectric cooler using entropy generation analysis. Int J Therm Sci 2017;118:168–75. [43] Martínez A, Astrain D, Rodríguez A, Aranguren P. Thermoelectric self-cooling system to protect solar collectors from overheating. J Electron Mater 2014;43:1480–6. [44] Kiflemariam R, Lin CX. Numerical simulation of integrated liquid cooling and thermoelectric generation for self-cooling of electronic devices. Int J Therm Sci 2015;94:193–203. [45] Martínez A, Astrain D, Rodríguez A. Experimental and analytical study on thermoelectric self cooling of devices. Energy 2011;36:5250–60. [46] Kiflemariam R, Lin CX. Experimental investigation on heat driven self-cooling application based on thermoelectric system. Int J Therm Sci 2016;109:309–22. [47] Martinez A, Astrain D, Aranguren P. Thermoelectric self-cooling for power electronics: Increasing the cooling power. Energy 2016;112:1–7. [48] Sahin AZ, Yilbas BS. Thermodynamic irreversibility and performance characteristics of thermoelectric power generator. Energy 2013;55:899–904. [49] Ali H, Yilbas BS, Al-Sharafi A. Innovative design of a thermoelectric generator with extended and segmented pin configurations. Appl Energy 2017;187:367–79. [50] Zhao Y, Wang S, Ge M, Li Y, Yang Y. Energy and exergy analysis of thermoelectric generator system with humidified flue gas. Energy Convers Manage 2018;156:140–9. [51] Nuwayhid RY, Moukalled F. Evolution of power and entropy in a temperature gap system with electric and thermoelectric influences. Energy Convers Manage 2003;44:647–65. [52] Bejan A. Entropy generation through heat and fluid flow. New York: Wiley; 1982. [53] Bilgen S, Sarıkaya İ. Exergy for environment, ecology and sustainable development. Renew Sustain Energy Rev 2015;51:1115–31. [54] Rosen MA, Dincer I, Kanoglu M. Role of exergy in increasing efficiency and sustainability and reducing environmental impact. Energy Policy 2008;36:128–37.

Conflict of interests We declare that there is no conflict of interests regarding the publication of this manuscript. Acknowledgements Authors would gratefully acknowledge the financial supports of National Key Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2018YFC0705201, Grant No. 2018YFB0904200), Natural Science Foundation of China (NSFC Grant No. 51778504, Grant No. U1867221), Joint Zhuzhou - Hunan Provincial Natural Science Foundation (Grant No. 2018JJ4064), National Defense Research Funds of Wuhan University (Grant No. 2042018gf0031), and Fundamental Research Projects from Shenzhen Council (Grant No. JCYJ20160523160857948). References [1] McGlen RJ, Jachuck R, Lin S. Integrated thermal management techniques for high power electronic devices. Appl Therm Eng 2004;24(8):1143–56. [2] Bar-Cohen A, Kraus AD, Davidson SF. Thermal frontiers in the design and packaging of microelectronic equipment. Mech Eng 1983;105:53–9. [3] Zhang HY, Pinjala D, Teo PS. Thermal management of high power dissipation electronic packages: from air cooling to liquid cooling. In: IEEE, 5th electronics packaging technology conference (EPTC). p. 620–5. [4] Chein R, Huang G. Thermoelectric cooler application in electronic cooling. Appl Therm Eng 2004;24:2207–17. [5] Wang J, Zhao X-J, Cai Y-X, Zhang C, Bao W-W. Experimental study on the thermal management of high-power LED headlight cooling device integrated with thermoelectric cooler package. Energy Convers Manage 2015;101:532–40. [6] Micheli L, Sarmah N, Luo X, Reddy KS, Mallick TK. Opportunities and challenges in micro- and nano-technologies for concentrating photovoltaic cooling: A review. Renew Sustain Energy Rev 2013;20:595–610. [7] Tang H, Tang Y, Wan Z, Li J, Yuan W, Lu L, et al. Review of applications and developments of ultra-thin micro heat pipes for electronic cooling. Appl Energy 2018;223:383–400. [8] Rowe DM. Handbook of thermoelectrics. CRC Press; 1995. [9] Twaha S, Zhu J, Yan Y, Li B. A comprehensive review of thermoelectric technology: Materials, applications, modelling and performance improvement. Renew Sustain Energy Rev 2016;65:698–726. [10] Montecucco A, Buckle JR, Knox AR. Solution to the 1-D unsteady heat conduction equation with internal Joule heat generation for thermoelectric devices. Appl Therm Eng 2012;35:177–84. [11] Riffat SB, Ma X. Thermoelectrics: a review of present and potential applications. Appl Therm Eng 2003;23:913–35. [12] Liu D, Cai Y, Zhao FY. Optimal design of thermoelectric cooling system integrated heat pipes for electric devices. Energy 2017;128:403–13. [13] Lv S, He W, Hu D, Zhu J, Li G, Chen H, et al. Study on a high-performance solar thermoelectric system for combined heat and power. Energy Convers Manage 2017;143:459–69. [14] Fraisse G, Ramousse J, Sgorlon D, Goupil C. Comparison of different modeling approaches for thermoelectric elements. Energy Convers Manage 2013;65:351–6. [15] Wang X-D, Huang Y-X, Cheng C-H, Ta-Wei Lin D, Kang C-H. A three-dimensional numerical modeling of thermoelectric device with consideration of coupling of temperature field and electric potential field. Energy 2012;47:488–97. [16] Tan H, Fu H, Yu J. Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law. Appl Therm Eng 2017;123:845–51. [17] Liu D, Zhao FY, Yang HX, Tang GF. Thermoelectric mini cooler coupled with micro thermosiphon for CPU cooling system. Energy 2015;83:29–36. [18] Liu Z, Zhang L, Gong G. Experimental evaluation of a solar thermoelectric cooled ceiling combined with displacement ventilation system. Energy Convers Manage 2014;87:559–65. [19] Liu D, Zhao F-Y, Yang H, Tang G-F. Theoretical and experimental investigations of thermoelectric heating system with multiple ventilation channels. Appl Energy

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