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Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law
Accepted Manuscript Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law Hongbo Tan, Hua Fu, Jianlin Yu PII: DOI: Reference:
S1359-4311(17)32120-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.182 ATE 10497
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
30 March 2017 29 May 2017
Please cite this article as: H. Tan, H. Fu, J. Yu, Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.182
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Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law Hongbo Tan, Hua Fu and Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’anJiaotongUniversity, Xi’an 710049, China
Abstract This paper presents a theoretical analysis based on the second law of thermodynamics to evaluate the optimal performances of a single-stage thermoelectric cooling system. The cold exergy and exergy efficiency are chosen as the optimization objectives, and a new entropy generation number associated with entropy generation, cold exergy and cooling temperature is proposed. The influences of several key parameters such as electric current, thermal conductance allocation ratio and cooling temperature on the cooling performance are theoretically investigated. The results indicate that the criterion of entropy generation number could be used as a new dimensionless measure of TEC system irreversibility. Furthermore, the cooling temperature can be considered as an important variable for TEC system to be optimized. It is found that an optimal cooling temperature exists, leading to the maximum cooling capacity and exergy efficiency, respectively. Thus, the cooling temperature should be considered in the design and application for practical TEC systems in order to obtain the maximum performance benefit. The present study can provide guidelines for the design and application of practical thermoelectric cooling
Corresponding author. Tel.:+86-29-82668738. Fax: +86-29-82668725. Email: [email protected] 1
systems. Highlights: Thermodynamic 2nd law analysis of a thermoelectric cooling (TEC) system is conducted. A new entropy generation number for evaluating the TEC irreversibility is proposed. An optimal cooling temperature exists, leading to the maximum 2nd law performance.
Keywords: thermoelectric cooling system; thermodynamic second law; entropy generation number; optimization. Nomenclature
A
area (m2)
COP
coefficient of performance
EQc
exergy of cooling capacity (W)
I
electrical current (A)
Km
total thermal conductance ( W K -1 )
L
length (m)
N
number of thermoelectric couples
Ns
entropy generation number
Q
heat transfer rate (W)
Rm
total electric resistance ( )
Sg
entropy generation ( J kg -1K -1 )
Tc
cold junction temperature (K) 2
Th
hot junction temperature (K)
Tc
temperature of cooled object (K)
Th
cooling fluid inlet temperature (K)
W
power (W)
x
thermal conductance allocation ratio
ex
exergy efficiency
Greek symbols
Seebeck coefficient ( VK -1 )
thermal conductivity ( W m1K 1 )
electric resistivity ( m )
Subscripts
c
cold side
h
hot side
max
maximum value
min
minimum value
n
n-type semiconductor elements
opt
optimum value
p
p-type semiconductor elements
1. Introduction Over the past decade, researchers have been increasingly concerned with developing and applying thermoelectric coolers (TECs) in the fields of electronic cooling, small refrigeration and air conditioning devices, due to their good 3
compactness, high reliability, long life span，rapid thermal response and quiet operation characteristic [1]. It is reported that thermoelectric domestic heat pumps and air conditioners will become competitive in the world market in view of the increasing energy costs and the rising environmental concerns [2]. Besides, TECs has been widely applied for domestic and portable refrigerators, cooling for medical and scientific devices, electronic cooling and automobile refrigeration, such as temperature-control car seats. And Huang et al. [3] provided a rapid and simple method to estimate the power generated from a waste heat recovery system with thermoelectric generators (TEGs) by three-dimensional (3D) thermal resistance. Zhao and Tan [4] summarized the development of modelling and optimizing of TECs in the past decade, and pointed out that the COP for both domestic and portable refrigerators is usually less than 0.5 when operating at a system temperature lift of 20-25 K. He et al. [5] reviewed recent application of TECs including the thermoelectric model and its application areas. The main drawback of TEC is its low coefficient of performance (COP) due to the limitations of current thermoelectric materials. Thus, in addition to relying on advances in thermoelectric materials science, optimization of TEC design and operation has become the most effective way to improve the performance of TECs in practice. Therefore, this situation has motivated researchers to carry out relevant studies on the design and application of TECs. Basically, the optimization of TECs is based on the first and second law of thermodynamics with various optimization objectives, constraints and methods. In 4
this respect, many optimization studies for TECs have been conducted by a number of investigators. Meng et al. [6] performed the optimization for a proposed two-stage thermoelectric refrigerator driven by a two-stage thermoelectric generator according to maximum cooling load and COP, and showed that there exists the optimum configuration relationship between two thermoelectric devices. Recently, David et al. [7] conducted the optimization of thermoelectric heat pumps based on coupling thermoelectric modules to heat exchangers, and revealed there exists one optimal thermal power leading to the maximal COP of the device studied. Rao and Patel [8] applied
a
modified
teaching–learning-based
algorithm
to
multi-objective
optimization of a two stage TEC, and demonstrated the effectiveness and accuracy of the proposed algorithm for the TEC optimization. Jeong [9] optimized a thermoelectric cooling module by using a novel one-dimensional analytic model, where the maximal COP is selected as the objective function for a given cooling capacity. Through the optimization, the optimum current and thermoelement length were obtained analytically. Wang et al. [10] used a three-dimensional multi-physics model to optimize the performance of three kinds of two-stage TECs, indicated that the optimal cooling capacity, COP, and maximum temperature difference can be achieved by properly configuring thermoelement number ratio and current ratio. Tian-Hu Wang et al. [11] proposed a simplified conjugated-gradient method that was coupled into the multiphysics model to optimize the TECs, for seeking the maximum cooling capacity. The results show that the maximum cooling capacity at T = 0, 20, 40, and 60 K can be enhanced by 19.62%, 21.30%, 25.49%, and 43.83%, 5
respectively. Ma et al. [12] used a validated numerical model for TEC operated with continuous current pulses to obtain the temperature evolution profile with time, and results obtained showed that the periodical supercooling effect could be achieved if the current period is properly designed. Manikandan and Kaushik [13] presented an exoreversible thermodynamic model of the annular thermoelectric cooler using exergy analysis to derive the maximum energy/exergy efficiency, maximum cooling power conditions and dimensionless irreversibilities in the annular thermoelectric cooler. Hao Lv et al. [14] developed a three-dimensional Multiphysics transient model to analyze and optimize the supercooling characteristics of a two-stage TEC, and the cold-end temperature drop is significantly improved by the optimization. S. Soprani et al. [15] developed a 3D topology optimization model to design a thermoelectric system, and the model predictions reproduced the experimental results of the final optimized system with good agreement. Shen et al. [16] developed a thermal physical model combined thermoelectric effect and radiation law and presented an optimization design configuration of thermoelectric (TE) radiant panel, the results show that the optimal thickness of thermoelectric radiant panels is 4 mm, and the number of thermoelectric modules (TEM) is 16 per square meter, which also could solve the issues about dew formation and uniformity of inner surface temperature. Karwa et al. [17] demonstrated a low thermal resistance water cooled heat sink design for the hot side of a commercial low-cost thermoelectric refrigerator which can increase the performance of the thermoelectric coolers. It can be realized from the above works that the improvement in the 6
performances of TECs is possible through using optimization approaches. As well known, thermoelectric cooling systems mainly including thermoelectric module, hot and cold side heat exchangers, are subject to internal and external irreversibilitieas. From a thermodynamic point of view, the second law analysis method has proved to be a very powerful tool in the optimization of TEC systems [18] and heat exchangers [19]. Moreover, Shama et al [20] conducted the 2nd law analysis of single- and multi-stage TECs with the help of entropy generation. Tipsaenporm et al [21] investigated the thermodynamic chracteristics of a compact thermoelectric (TE) air conditioner based on the exergy analysis approach. It was found that the exergy efficiency of the TE air conditioner was very low comparing with the respective COP. It leads researchers to employ the second law for the optimization study of TECs, such as exergy analysis and entropy generation analysis [22, 24]. The second law analysis may provide a more realistic view of the operating process of TEC systems and give much better guidance for system improvement [25, 26]. This clearly means that the second law analysis is more useful for optimal design and operation of irreversible TECs. So far, the operational optimization of a single-stage TEC system has been carried out based on the first and second laws of thermodynamics. Maximum cooling capacity, COP, temperature difference and exergy efficiency were chosen as optimizing objects in many optimization studies of single-stage TEC using different models, such as energy equilibrium models, one- and three-dimensional numerical models. It was found that the optimal performance of a single-stage TEC can be 7
achieved by changing the operating current and configuration of TEC. However, relevant theoretical study on optimizing the cooling temperature has not yet received much attention. Thus, a particular attention is paid on considering the cooling temperature as an optimization variable which maximizes the exergy of cooling capacity or the exergy efficiency at specified conditions in the present study. In addition, a new entropy generation number definition is proposed to assess the single-stage TEC system irreversibility, which is related to the system entropy generation and the exergy of cooling capacity. The present study can provide guidelines for the design and application of practical thermoelectric cooling systems, especially when need to consider the cooling temperature. The objective of this paper is to provide useful insight in single-stage TEC applications with thermodynamic second law study. The relevant detailed theoretical analysis and the obtained results will be presented in the following sections. 2. Analytical model The schematic view of a typical single-stage TEC system is shown in Fig. 1, which consists of a heat source (cooled object), a heat sink, a thermoelectric module (TEM), cold and hot side heat exchangers. As shown in Fig. 1 (a), the TEM is comprised of a number of p-n thermoelectric couples connected electrically in series but thermally in parallel. The p-n thermoelectric couples are sandwiched between two electrically insulating but thermally conducting ceramic plates. The TEC system operates between the heat source at temperature Tc (cooled object temperature) and the heat sink at temperature Th as shown in Fig. 1 (b). In a steady state operation of 8
TEC system with DC power, the absorbed heat Qc (cooling capacity) is transferred from the heat source to the cold junction of TEM at temperature Tc , and the rejected heat Qh is transferred from the hot junction of TEM at temperature Th to the heat sink. The two heat transfer processes through the cold and hot side thermal conductance ( K c and K h ) are involved in the external irreversibility due to the finite temperature differences while the internal irreversibility occurs in the TEM. Thus, the operation process of TEC system is characterized by irreversibilities, which needs to be examined in terms of the second law of thermodynamic analysis.
a
b Fig. 1 A typical single-stage TEC system: a) The structural diagram of single-stage TEC system; b) The schematic representation of a single-stage TEC 9
system In order to carry out thermodynamic analyses of the TEC system, a mathematical model is presented based on the basic one-dimensional energy equilibrium equations of the TEM and heat transfer equations for heat exchangers. The main assumptions considered in the model are as follows: the TEC system has one dimensional steady state operation; the Thomson effect is neglected; the analysis and optimization results are only valid for the considered operating temperature, at which the properties have been considered constant. Energy balance equations for the hot and cold junctions of the TEM can be written as: 1 Qh m ITh K m (Th Tc ) Rm I 2 2 1 Qc m ITc K m (Th Tc ) Rm I 2 2
(1) (2)
where m is the total Seebeck coefficient of the TEC module, I is the electric current; K m is the overall thermal conductance, Rm is the total electric resistance. The m , K m and Rm are given as follows:
m N ( p n )
(3)
A L L Rm N ( n p ) A K m N ( n )p
(4) (5)
where N is the number of thermoelectric couples, is Seebeck coefficient, is the thermal conductivity, is the electric resistivity of the thermoelectric material,
A is the cross-sectional area of a thermoelement leg and L is the thermoelement leg length. Subscripts p and n designate p and n-type thermoelement legs, 10
respectively. Considering heat transfer through the heat exchangers, i.e. from the hot and cold junctions to the heat sink /source, the heat transfer rates Qh and Qc can be also written as
Qh Kh (Th Th)
(6)
Qc Kc (Tc Tc )
(7)
In terms of the energy balance, the power input to the TEC system is given as
W Qh Qc
(8)
Accordingly, the COP of the TEC system is given by COP
Qc W
(9)
Following the second law of thermodynamics, the total entropy generation rate in the TEC system can be expressed as [27-29]: Sg
Qh Qc Th Tc
(10)
By performing exergy accounting in the TEC system, the exergy input to the system is the electrical power ( W ), and the exergy flux into the TEC system, i.e. the exergy of cooling capacity, is defined as [15, 23]:
EQc Qc (Th / Tc 1)
(11)
Note that inhere the heat sink temperature Th is assumed to be a reference environment temperature. Therefore, the exergy efficiency of the TEC system can be written as:
ex
EQc COP Th / Tc 1 W
(12)
As well known, the dimensionless entropy generations have been applied to the 11
analyses of thermodynamic processes, such as the entropy generation numbers and the revised entropy generation number [30]. Similarly, the proposed entropy generation number expressed in terms of entropy generation, cold exergy and cooled object temperature is given as, Ns Sg /( EQc / Tc)
(13)
It is noticed that the proposed entropy generation number can be used to assess the performance of a single-stage TEC system. As a matter of fact, to design and operate a single-stage TEC system for practical applications would usually require the specification of cooled object temperature and cooling capacity (corresponding to cooling capacity exergy). Thus, relating the entropy generation number to the operation requirement of a single-stage TEC system may be meaningful to thermoelectric cooling applications. From the above equations, it can be seen that the entropy generation and performance criterion of a single-stage TEC system are also associated with external heat transfer irreversibilities, i.e. relative to the cold and hot side thermal conductance
K h and K c besides other operation parameters. Each thermal conductance is proportional to each heat transfer area and its corresponding overall heat transfer coefficient. Since K h and K c are usually finite for a single-stage TEC system, the allocation of total thermal conductance inventory is introduced by:
K h Kc K t x
Kc , Kt
1 x
(14) Kh Kt
(15)
where K t is some finite constant, x is the thermal conductance allocation ratio. 12
The allocation ratio x can be used as a parameter to assess the merit of the TEC system configuration. In general, the above equations (eq.1-15) provide a complete description of the thermodynamic model of the TEC system, including the proposed performance parameter. Note that since the expressions for the hot and cold junction temperatures
Th and Tc are complex, they will not be presented here for brevity. However, the Th and Tc can be determined with those equations. The upcoming section is devoted to performance optimization of the TEC system based on this model, and the effects of main parameters on optimal performance are discussed. 3. Results and discussion In the following simulations, a commercial Bi2Te3-based TEM (CP2-127-06L) is selected as the case for analysis. The detailed geometry parameters such as the element cross-sectional area, length and thermocouple number are summarized in Table 1 [31]. The material properties of the thermoelement used in this work are assumed
to
be:
n p 2.03 104 VK -1 , kn kp 0.0176 W cm1K 1 and n p 9.37 104 cm. The total thermal conductance of the cold side K c is set to be in the range of
0.12 0.18 W K-1cm-2 , including the heat spreaders, the ceramic substrate and the thermal grease. The total thermal conductance for the hot sides K h is set to be in the range of 0.0174 0.2874 W K-1cm-2 , representing different cooling conditions [32]. Finally, the heat sink of temperature Th is set 35℃ and the cooled object temperature at the cold side of the TEC system, Tc , is considered as an operational parameter, 13
relevant to electronic cooling and small refrigerator . Table 1 Thermoelectric parameters of the TEM Module [21]
Parameters Dimension
mm 3
62 62 4.6
Pellet size mm3
2.0 2.0 1.42
I max A
14.0
U max V
15.4
Qmax W
140.5
Tmax
C o
67
Fig. 2 shows the variations of the exergy of cooling capacity EQc and the exergy efficiency of the TEC system ex with the current I conductance allocation ratios x . As I
under different thermal
continuously increases, the maximum
ex,max can be situated at the approximate same current I opt =6A, while the maximum EQc,max can be achieved when I
opt
are 15A、14A and 12A, respectively for
allocation ratios of 0.4, 0.6 and 0.8. As displayed in Fig. 2, the optimum values of the current corresponding to ex are affected slightly by the x , but EQc,max are obviously influenced by the x . It is clear that a larger x will result in the smaller EQc,max and ex,max . This is because the larger x implies the thermal conductance of
the heat sink is relatively smaller. The heat sink with low thermal conductance can cause a rise in the heat transfer irreversibility on hot side of TEC (i.e. larger temperature difference) and eventually leads to the decrease of the maximum performances of TEC. Thus, it is important to ensure that the TEC design has 14
sufficient hot side thermal conductance for expected performance.
Fig. 2 The variations of EQc and ex with I Fig. 3 presents the effects of I
under different x
on the proposed entropy generation number N s
and the total entropy generation rate S g under the various thermal conductance allocation ratio x . It is clearly displayed that in Fig. 3, S g monotonically increases as I
increases, while the minimum Ns,min can be obtained at the relevant optimal
currents under the setting conditions. It is revealed that for the TEC system, the internal irreversibility due to the Joule effect and heat conduction losses through the TEM plays a key role in determining the total entropy generation rate, which is proportional to the electric current. Thus, the S g increases in more prominent way with increasing internal irreversibility, than external irreversibility. Obviously, internal irreversibility is dominant factor for overall entropy generation rate. On the other hand, the proposed entropy generation number N s is related to the entropy generation, cooling capacity exergy and cooled object temperature according to its definition. Consequently, it is related not only to internal irreversibility, but also to the interaction between the TEM and the heat exchangers. For this reason, there exists one optimal electric current leading to the minimum Ns,min as shown in Fig. 3. 15
Fig. 3 The effects of I
on the N s and S g under the various x
It is worth noting that the minimum Ns,min criterion correlates with the maximum
ex,max criterion while optimizing the operating electric current I . Fig. 4
shows the entropy generation number N s and the exergy efficiency ex with the electric current I . It can be seen that the minimum Ns,min and maximum
ex,max
occurs at same electric current. In other words, maximization of the ex is equivalent to minimization of N s when the operating electric current for a TEC system, I , is considered as the optimization parameter. Actually, the link between the proposed entropy generation number and the exergy efficiency of a TEC system is given by thermodynamic second law. Thus, the introduction of the proposed entropy generation number as a new optimization criterion may be useful because it is related to both the irreversiblitities occurring in the TEC system and cooling requirements (cooling capacity exergy and cooled object temperature).
16
Fig. 4 The N s and ex with the electric current I As seen in Fig. 2, both the thermal conductance allocation ratios x and electrical current has an effect on the best performances EQc and ex as well as the correspondent optimal electrical currents. Fig. 5 shows the variations of the maximum EQc,max , maximum exergy efficiency of the TEC system ex,max
and their
corresponding optimal currents I cor with the allocation ratio x . It is obvious that the best cooling performances, EQc,max and ex,max , can be obtained for x values from 0.1 to 0.8 when an optimum x is chosen, respectively. In addition, the optimal current corresponding to ex,max is almost constant for all values of x but the optimal current corresponding to EQc,max decreases with x . Under the setting conditions in the simulation, the values of the optimal allocation ratio x for the best EQc,max and ex,max are 0.37 and 0.44, respectively. These results may be of interest
and importance to designers when making decisions on selecting an appropriate heat exchanger configuration and electrical current for designing and operating TEC systems.
17
Fig. 5 The variations of the EQc,max , ex,max and optimal currents with x As known, the application of a thermoelectric cooling system is mainly characterized by the required cooling temperature and cooling capacity. For a TEC system with the determined system configuration, however, the cooling capacity usually reduces with decreasing cooling temperature under fixed other conditions. Obviously, the variation of cooling temperature would also has influence in the irreversibility and efficiency of the TEC system. Thus, it is important realize here that the optimization of a TEC system for optimum cooling temperature and maximum efficiency should be examined. In Fig. 6, the variations of the parameters EQc and
ex are plotted as functions of the cooling temperature. It shows that the optimum cooling temperatures at maximum cooling capacity exergy and exergy efficiency of the TEC system can be obtained, respectively, under different conditions. This means that the cooling temperature can be considered as an optimization variable for the optimization problem of a TEC system. In addition, it can be found that the optimal cooling temperatures corresponding to the maximization of EQc and ex range from 13 to 15
o
C , and the optimal cooling temperature for ex is slightly higher
than the one for EQc . However, the thermal conductance allocation ratio x has a 18
larger influence on the maximum cooling capacity exergy and exergy efficiency. When x increases from 0.4 to 0.8, the maximum EQc decreases from 2.16W to 1.78W, i.e. by 17.6%. As respected, the maximum ex also decreases from 0.0766 to 0.0613. As mentioned previously, larger x means the thermal conductance of the heat sink is smaller than at the cooling load, which leads to the decrease of the maximum EQc,max and ex,max . Overall, the results reveal that the operational cooling temperature regime of a TEC system should be between the optimum regimes obtained by maximizing the EQc and maximizing the ex . Also, it can be found the same variations of the parameters EQc and ex with different cooling temperature when we change the current from 5A to 10A.
Fig. 6 The variations of EQc and ex versus the cooling temperature ( I 5 A )
19
Fig. 7 The variations of EQc and ex versus the cooling temperature ( I 10 A ) 4. Conclusion In this paper, the theoretical analysis based on the second law of thermodynamics is conducted to study the optimization problems of single-stage TEC systems. The exergy of cooling capacity and the exergy efficiency of a TEC system are suggested to be the optimization objective functions. Furthermore, a new entropy generation number associated with the entropy generation, the cooling capacity exergy and cooling temperature is introduced. The effects of the thermal design and operating parameters, including the operation electric current, thermal conductance allocation ratio and cooling temperature, on the cooling capacity exergy, entropy generation number and the exergy efficiency are evaluated. The obtained results indicate the equivalence of minimum entropy generation number and maximum exergy efficiency in the optimization of a TEC system. Thus, it is possible to optimize the TEC system by the criterion of entropy generation number, which may provide a new dimensionless measure of TEC system irreversibility. The maximum cooling capacity exergy and maximum exergy efficiency of the TEC system at their corresponding optimal currents are dependent on the thermal conductance allocation ratio between the cold and hot sides. For given temperature conditions, there exists one optimal allocation ratio leading to the best maximal cooling capacity exergy and exergy efficiency, respectively. Moreover, the cooling temperature can be considered as an optimization variable for TEC system optimization, and an optimal cooling temperature exists, leading to the maximum cooling capacity exergy and exergy 20
efficiency, respectively. Thus, the most important contribution of the present investigation is that the cooling temperature should be considered in the design and application for practical TEC systems to obtain the maximum performance benefit. It should be noted that the thermal conductance allocation ratio and the operating current must be carefully designed to achieve the optimal cooling temperature. For a real TEC application, the cold and hot sides heat exchangers must be precisely manufactured, and the operating current should also be adjusted carefully. The results obtained herein may provide guides for the design and application of practical TEC systems.
Acknowledgements This study is financially supported by the National Natural Science Foundation of China (NSFC) under the grant No. 51276135. The authors would like to thank NSFC for the sponsorship.
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Figure captions Fig. 1 A typical single-stage TEC system: a) The structural diagram of single-stage TEC system; b) The schematic representation of a single-stage TEC system Fig. 2 The variations of EQc and ex with I Fig. 3 The effects of I
under different x
on the N s and S g under the various x
Fig. 4 The N s and ex with the electric current I Fig. 5 The variations of the EQc,max , ex,max and optimal currents with x Fig. 6 The variations of EQc and ex versus the cooling temperature ( I 5 A ) Fig. 7 The variations of EQc and ex versus the cooling temperature ( I 10 A ) Table captions Table 1 Thermoelectric parameters of the TEM
26
Table 1 Thermoelectric parameters of the TEM
Module [21]
Parameters Dimension
mm 3
62 62 4.6
Pellet size mm3
2.0 2.0 1.42
I max A
14.0
U max V
15.4
Qmax W
140.5
Tmax
C o
67
27
Abstract This paper presents a theoretical analysis based on the second law of thermodynamics to evaluate the optimal performances of a single-stage thermoelectric cooling system. The cold exergy and exergy efficiency are chosen as the optimization objective functions, and a new entropy generation number associated with entropy generation, cold exergy and cooling temperature is proposed. The influences of several key parameters such as electric current, thermal conductance allocation ratio and cooling temperature on the cooling performance are theoretically investigated. The results indicate that the criterion of entropy generation number could be used as a new dimensionless measure of TEC system irreversibility. Furthermore, the cooling temperature can be considered as an optimization variable for TEC system optimization, and an optimal cooling temperature exists, leading to the maximum cooling capacity exergy and exergy efficiency, respectively. Thus, the cooling temperature should be considered in the design and application for practical TEC systems in order to obtain the maximum performance benefit. The present study can provide guidelines for the design and application of practical thermoelectric cooling systems.
28
Highlights: Thermodynamic 2nd law analysis of a thermoelectric cooling (TEC) system is conducted. A new entropy generation number for evaluating the TEC irreversibility is proposed. An optimal cooling temperature exists, leading to the maximum 2nd law performance.
29
S1359-4311(17)32120-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.182 ATE 10497
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
30 March 2017 29 May 2017
Please cite this article as: H. Tan, H. Fu, J. Yu, Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.05.182
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law Hongbo Tan, Hua Fu and Jianlin Yu Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’anJiaotongUniversity, Xi’an 710049, China
Abstract This paper presents a theoretical analysis based on the second law of thermodynamics to evaluate the optimal performances of a single-stage thermoelectric cooling system. The cold exergy and exergy efficiency are chosen as the optimization objectives, and a new entropy generation number associated with entropy generation, cold exergy and cooling temperature is proposed. The influences of several key parameters such as electric current, thermal conductance allocation ratio and cooling temperature on the cooling performance are theoretically investigated. The results indicate that the criterion of entropy generation number could be used as a new dimensionless measure of TEC system irreversibility. Furthermore, the cooling temperature can be considered as an important variable for TEC system to be optimized. It is found that an optimal cooling temperature exists, leading to the maximum cooling capacity and exergy efficiency, respectively. Thus, the cooling temperature should be considered in the design and application for practical TEC systems in order to obtain the maximum performance benefit. The present study can provide guidelines for the design and application of practical thermoelectric cooling
Corresponding author. Tel.:+86-29-82668738. Fax: +86-29-82668725. Email: [email protected] 1
systems. Highlights: Thermodynamic 2nd law analysis of a thermoelectric cooling (TEC) system is conducted. A new entropy generation number for evaluating the TEC irreversibility is proposed. An optimal cooling temperature exists, leading to the maximum 2nd law performance.
Keywords: thermoelectric cooling system; thermodynamic second law; entropy generation number; optimization. Nomenclature
A
area (m2)
COP
coefficient of performance
EQc
exergy of cooling capacity (W)
I
electrical current (A)
Km
total thermal conductance ( W K -1 )
L
length (m)
N
number of thermoelectric couples
Ns
entropy generation number
Q
heat transfer rate (W)
Rm
total electric resistance ( )
Sg
entropy generation ( J kg -1K -1 )
Tc
cold junction temperature (K) 2
Th
hot junction temperature (K)
Tc
temperature of cooled object (K)
Th
cooling fluid inlet temperature (K)
W
power (W)
x
thermal conductance allocation ratio
ex
exergy efficiency
Greek symbols
Seebeck coefficient ( VK -1 )
thermal conductivity ( W m1K 1 )
electric resistivity ( m )
Subscripts
c
cold side
h
hot side
max
maximum value
min
minimum value
n
n-type semiconductor elements
opt
optimum value
p
p-type semiconductor elements
1. Introduction Over the past decade, researchers have been increasingly concerned with developing and applying thermoelectric coolers (TECs) in the fields of electronic cooling, small refrigeration and air conditioning devices, due to their good 3
compactness, high reliability, long life span，rapid thermal response and quiet operation characteristic [1]. It is reported that thermoelectric domestic heat pumps and air conditioners will become competitive in the world market in view of the increasing energy costs and the rising environmental concerns [2]. Besides, TECs has been widely applied for domestic and portable refrigerators, cooling for medical and scientific devices, electronic cooling and automobile refrigeration, such as temperature-control car seats. And Huang et al. [3] provided a rapid and simple method to estimate the power generated from a waste heat recovery system with thermoelectric generators (TEGs) by three-dimensional (3D) thermal resistance. Zhao and Tan [4] summarized the development of modelling and optimizing of TECs in the past decade, and pointed out that the COP for both domestic and portable refrigerators is usually less than 0.5 when operating at a system temperature lift of 20-25 K. He et al. [5] reviewed recent application of TECs including the thermoelectric model and its application areas. The main drawback of TEC is its low coefficient of performance (COP) due to the limitations of current thermoelectric materials. Thus, in addition to relying on advances in thermoelectric materials science, optimization of TEC design and operation has become the most effective way to improve the performance of TECs in practice. Therefore, this situation has motivated researchers to carry out relevant studies on the design and application of TECs. Basically, the optimization of TECs is based on the first and second law of thermodynamics with various optimization objectives, constraints and methods. In 4
this respect, many optimization studies for TECs have been conducted by a number of investigators. Meng et al. [6] performed the optimization for a proposed two-stage thermoelectric refrigerator driven by a two-stage thermoelectric generator according to maximum cooling load and COP, and showed that there exists the optimum configuration relationship between two thermoelectric devices. Recently, David et al. [7] conducted the optimization of thermoelectric heat pumps based on coupling thermoelectric modules to heat exchangers, and revealed there exists one optimal thermal power leading to the maximal COP of the device studied. Rao and Patel [8] applied
a
modified
teaching–learning-based
algorithm
to
multi-objective
optimization of a two stage TEC, and demonstrated the effectiveness and accuracy of the proposed algorithm for the TEC optimization. Jeong [9] optimized a thermoelectric cooling module by using a novel one-dimensional analytic model, where the maximal COP is selected as the objective function for a given cooling capacity. Through the optimization, the optimum current and thermoelement length were obtained analytically. Wang et al. [10] used a three-dimensional multi-physics model to optimize the performance of three kinds of two-stage TECs, indicated that the optimal cooling capacity, COP, and maximum temperature difference can be achieved by properly configuring thermoelement number ratio and current ratio. Tian-Hu Wang et al. [11] proposed a simplified conjugated-gradient method that was coupled into the multiphysics model to optimize the TECs, for seeking the maximum cooling capacity. The results show that the maximum cooling capacity at T = 0, 20, 40, and 60 K can be enhanced by 19.62%, 21.30%, 25.49%, and 43.83%, 5
respectively. Ma et al. [12] used a validated numerical model for TEC operated with continuous current pulses to obtain the temperature evolution profile with time, and results obtained showed that the periodical supercooling effect could be achieved if the current period is properly designed. Manikandan and Kaushik [13] presented an exoreversible thermodynamic model of the annular thermoelectric cooler using exergy analysis to derive the maximum energy/exergy efficiency, maximum cooling power conditions and dimensionless irreversibilities in the annular thermoelectric cooler. Hao Lv et al. [14] developed a three-dimensional Multiphysics transient model to analyze and optimize the supercooling characteristics of a two-stage TEC, and the cold-end temperature drop is significantly improved by the optimization. S. Soprani et al. [15] developed a 3D topology optimization model to design a thermoelectric system, and the model predictions reproduced the experimental results of the final optimized system with good agreement. Shen et al. [16] developed a thermal physical model combined thermoelectric effect and radiation law and presented an optimization design configuration of thermoelectric (TE) radiant panel, the results show that the optimal thickness of thermoelectric radiant panels is 4 mm, and the number of thermoelectric modules (TEM) is 16 per square meter, which also could solve the issues about dew formation and uniformity of inner surface temperature. Karwa et al. [17] demonstrated a low thermal resistance water cooled heat sink design for the hot side of a commercial low-cost thermoelectric refrigerator which can increase the performance of the thermoelectric coolers. It can be realized from the above works that the improvement in the 6
performances of TECs is possible through using optimization approaches. As well known, thermoelectric cooling systems mainly including thermoelectric module, hot and cold side heat exchangers, are subject to internal and external irreversibilitieas. From a thermodynamic point of view, the second law analysis method has proved to be a very powerful tool in the optimization of TEC systems [18] and heat exchangers [19]. Moreover, Shama et al [20] conducted the 2nd law analysis of single- and multi-stage TECs with the help of entropy generation. Tipsaenporm et al [21] investigated the thermodynamic chracteristics of a compact thermoelectric (TE) air conditioner based on the exergy analysis approach. It was found that the exergy efficiency of the TE air conditioner was very low comparing with the respective COP. It leads researchers to employ the second law for the optimization study of TECs, such as exergy analysis and entropy generation analysis [22, 24]. The second law analysis may provide a more realistic view of the operating process of TEC systems and give much better guidance for system improvement [25, 26]. This clearly means that the second law analysis is more useful for optimal design and operation of irreversible TECs. So far, the operational optimization of a single-stage TEC system has been carried out based on the first and second laws of thermodynamics. Maximum cooling capacity, COP, temperature difference and exergy efficiency were chosen as optimizing objects in many optimization studies of single-stage TEC using different models, such as energy equilibrium models, one- and three-dimensional numerical models. It was found that the optimal performance of a single-stage TEC can be 7
achieved by changing the operating current and configuration of TEC. However, relevant theoretical study on optimizing the cooling temperature has not yet received much attention. Thus, a particular attention is paid on considering the cooling temperature as an optimization variable which maximizes the exergy of cooling capacity or the exergy efficiency at specified conditions in the present study. In addition, a new entropy generation number definition is proposed to assess the single-stage TEC system irreversibility, which is related to the system entropy generation and the exergy of cooling capacity. The present study can provide guidelines for the design and application of practical thermoelectric cooling systems, especially when need to consider the cooling temperature. The objective of this paper is to provide useful insight in single-stage TEC applications with thermodynamic second law study. The relevant detailed theoretical analysis and the obtained results will be presented in the following sections. 2. Analytical model The schematic view of a typical single-stage TEC system is shown in Fig. 1, which consists of a heat source (cooled object), a heat sink, a thermoelectric module (TEM), cold and hot side heat exchangers. As shown in Fig. 1 (a), the TEM is comprised of a number of p-n thermoelectric couples connected electrically in series but thermally in parallel. The p-n thermoelectric couples are sandwiched between two electrically insulating but thermally conducting ceramic plates. The TEC system operates between the heat source at temperature Tc (cooled object temperature) and the heat sink at temperature Th as shown in Fig. 1 (b). In a steady state operation of 8
TEC system with DC power, the absorbed heat Qc (cooling capacity) is transferred from the heat source to the cold junction of TEM at temperature Tc , and the rejected heat Qh is transferred from the hot junction of TEM at temperature Th to the heat sink. The two heat transfer processes through the cold and hot side thermal conductance ( K c and K h ) are involved in the external irreversibility due to the finite temperature differences while the internal irreversibility occurs in the TEM. Thus, the operation process of TEC system is characterized by irreversibilities, which needs to be examined in terms of the second law of thermodynamic analysis.
a
b Fig. 1 A typical single-stage TEC system: a) The structural diagram of single-stage TEC system; b) The schematic representation of a single-stage TEC 9
system In order to carry out thermodynamic analyses of the TEC system, a mathematical model is presented based on the basic one-dimensional energy equilibrium equations of the TEM and heat transfer equations for heat exchangers. The main assumptions considered in the model are as follows: the TEC system has one dimensional steady state operation; the Thomson effect is neglected; the analysis and optimization results are only valid for the considered operating temperature, at which the properties have been considered constant. Energy balance equations for the hot and cold junctions of the TEM can be written as: 1 Qh m ITh K m (Th Tc ) Rm I 2 2 1 Qc m ITc K m (Th Tc ) Rm I 2 2
(1) (2)
where m is the total Seebeck coefficient of the TEC module, I is the electric current; K m is the overall thermal conductance, Rm is the total electric resistance. The m , K m and Rm are given as follows:
m N ( p n )
(3)
A L L Rm N ( n p ) A K m N ( n )p
(4) (5)
where N is the number of thermoelectric couples, is Seebeck coefficient, is the thermal conductivity, is the electric resistivity of the thermoelectric material,
A is the cross-sectional area of a thermoelement leg and L is the thermoelement leg length. Subscripts p and n designate p and n-type thermoelement legs, 10
respectively. Considering heat transfer through the heat exchangers, i.e. from the hot and cold junctions to the heat sink /source, the heat transfer rates Qh and Qc can be also written as
Qh Kh (Th Th)
(6)
Qc Kc (Tc Tc )
(7)
In terms of the energy balance, the power input to the TEC system is given as
W Qh Qc
(8)
Accordingly, the COP of the TEC system is given by COP
Qc W
(9)
Following the second law of thermodynamics, the total entropy generation rate in the TEC system can be expressed as [27-29]: Sg
Qh Qc Th Tc
(10)
By performing exergy accounting in the TEC system, the exergy input to the system is the electrical power ( W ), and the exergy flux into the TEC system, i.e. the exergy of cooling capacity, is defined as [15, 23]:
EQc Qc (Th / Tc 1)
(11)
Note that inhere the heat sink temperature Th is assumed to be a reference environment temperature. Therefore, the exergy efficiency of the TEC system can be written as:
ex
EQc COP Th / Tc 1 W
(12)
As well known, the dimensionless entropy generations have been applied to the 11
analyses of thermodynamic processes, such as the entropy generation numbers and the revised entropy generation number [30]. Similarly, the proposed entropy generation number expressed in terms of entropy generation, cold exergy and cooled object temperature is given as, Ns Sg /( EQc / Tc)
(13)
It is noticed that the proposed entropy generation number can be used to assess the performance of a single-stage TEC system. As a matter of fact, to design and operate a single-stage TEC system for practical applications would usually require the specification of cooled object temperature and cooling capacity (corresponding to cooling capacity exergy). Thus, relating the entropy generation number to the operation requirement of a single-stage TEC system may be meaningful to thermoelectric cooling applications. From the above equations, it can be seen that the entropy generation and performance criterion of a single-stage TEC system are also associated with external heat transfer irreversibilities, i.e. relative to the cold and hot side thermal conductance
K h and K c besides other operation parameters. Each thermal conductance is proportional to each heat transfer area and its corresponding overall heat transfer coefficient. Since K h and K c are usually finite for a single-stage TEC system, the allocation of total thermal conductance inventory is introduced by:
K h Kc K t x
Kc , Kt
1 x
(14) Kh Kt
(15)
where K t is some finite constant, x is the thermal conductance allocation ratio. 12
The allocation ratio x can be used as a parameter to assess the merit of the TEC system configuration. In general, the above equations (eq.1-15) provide a complete description of the thermodynamic model of the TEC system, including the proposed performance parameter. Note that since the expressions for the hot and cold junction temperatures
Th and Tc are complex, they will not be presented here for brevity. However, the Th and Tc can be determined with those equations. The upcoming section is devoted to performance optimization of the TEC system based on this model, and the effects of main parameters on optimal performance are discussed. 3. Results and discussion In the following simulations, a commercial Bi2Te3-based TEM (CP2-127-06L) is selected as the case for analysis. The detailed geometry parameters such as the element cross-sectional area, length and thermocouple number are summarized in Table 1 [31]. The material properties of the thermoelement used in this work are assumed
to
be:
n p 2.03 104 VK -1 , kn kp 0.0176 W cm1K 1 and n p 9.37 104 cm. The total thermal conductance of the cold side K c is set to be in the range of
0.12 0.18 W K-1cm-2 , including the heat spreaders, the ceramic substrate and the thermal grease. The total thermal conductance for the hot sides K h is set to be in the range of 0.0174 0.2874 W K-1cm-2 , representing different cooling conditions [32]. Finally, the heat sink of temperature Th is set 35℃ and the cooled object temperature at the cold side of the TEC system, Tc , is considered as an operational parameter, 13
relevant to electronic cooling and small refrigerator . Table 1 Thermoelectric parameters of the TEM Module [21]
Parameters Dimension
mm 3
62 62 4.6
Pellet size mm3
2.0 2.0 1.42
I max A
14.0
U max V
15.4
Qmax W
140.5
Tmax
C o
67
Fig. 2 shows the variations of the exergy of cooling capacity EQc and the exergy efficiency of the TEC system ex with the current I conductance allocation ratios x . As I
under different thermal
continuously increases, the maximum
ex,max can be situated at the approximate same current I opt =6A, while the maximum EQc,max can be achieved when I
opt
are 15A、14A and 12A, respectively for
allocation ratios of 0.4, 0.6 and 0.8. As displayed in Fig. 2, the optimum values of the current corresponding to ex are affected slightly by the x , but EQc,max are obviously influenced by the x . It is clear that a larger x will result in the smaller EQc,max and ex,max . This is because the larger x implies the thermal conductance of
the heat sink is relatively smaller. The heat sink with low thermal conductance can cause a rise in the heat transfer irreversibility on hot side of TEC (i.e. larger temperature difference) and eventually leads to the decrease of the maximum performances of TEC. Thus, it is important to ensure that the TEC design has 14
sufficient hot side thermal conductance for expected performance.
Fig. 2 The variations of EQc and ex with I Fig. 3 presents the effects of I
under different x
on the proposed entropy generation number N s
and the total entropy generation rate S g under the various thermal conductance allocation ratio x . It is clearly displayed that in Fig. 3, S g monotonically increases as I
increases, while the minimum Ns,min can be obtained at the relevant optimal
currents under the setting conditions. It is revealed that for the TEC system, the internal irreversibility due to the Joule effect and heat conduction losses through the TEM plays a key role in determining the total entropy generation rate, which is proportional to the electric current. Thus, the S g increases in more prominent way with increasing internal irreversibility, than external irreversibility. Obviously, internal irreversibility is dominant factor for overall entropy generation rate. On the other hand, the proposed entropy generation number N s is related to the entropy generation, cooling capacity exergy and cooled object temperature according to its definition. Consequently, it is related not only to internal irreversibility, but also to the interaction between the TEM and the heat exchangers. For this reason, there exists one optimal electric current leading to the minimum Ns,min as shown in Fig. 3. 15
Fig. 3 The effects of I
on the N s and S g under the various x
It is worth noting that the minimum Ns,min criterion correlates with the maximum
ex,max criterion while optimizing the operating electric current I . Fig. 4
shows the entropy generation number N s and the exergy efficiency ex with the electric current I . It can be seen that the minimum Ns,min and maximum
ex,max
occurs at same electric current. In other words, maximization of the ex is equivalent to minimization of N s when the operating electric current for a TEC system, I , is considered as the optimization parameter. Actually, the link between the proposed entropy generation number and the exergy efficiency of a TEC system is given by thermodynamic second law. Thus, the introduction of the proposed entropy generation number as a new optimization criterion may be useful because it is related to both the irreversiblitities occurring in the TEC system and cooling requirements (cooling capacity exergy and cooled object temperature).
16
Fig. 4 The N s and ex with the electric current I As seen in Fig. 2, both the thermal conductance allocation ratios x and electrical current has an effect on the best performances EQc and ex as well as the correspondent optimal electrical currents. Fig. 5 shows the variations of the maximum EQc,max , maximum exergy efficiency of the TEC system ex,max
and their
corresponding optimal currents I cor with the allocation ratio x . It is obvious that the best cooling performances, EQc,max and ex,max , can be obtained for x values from 0.1 to 0.8 when an optimum x is chosen, respectively. In addition, the optimal current corresponding to ex,max is almost constant for all values of x but the optimal current corresponding to EQc,max decreases with x . Under the setting conditions in the simulation, the values of the optimal allocation ratio x for the best EQc,max and ex,max are 0.37 and 0.44, respectively. These results may be of interest
and importance to designers when making decisions on selecting an appropriate heat exchanger configuration and electrical current for designing and operating TEC systems.
17
Fig. 5 The variations of the EQc,max , ex,max and optimal currents with x As known, the application of a thermoelectric cooling system is mainly characterized by the required cooling temperature and cooling capacity. For a TEC system with the determined system configuration, however, the cooling capacity usually reduces with decreasing cooling temperature under fixed other conditions. Obviously, the variation of cooling temperature would also has influence in the irreversibility and efficiency of the TEC system. Thus, it is important realize here that the optimization of a TEC system for optimum cooling temperature and maximum efficiency should be examined. In Fig. 6, the variations of the parameters EQc and
ex are plotted as functions of the cooling temperature. It shows that the optimum cooling temperatures at maximum cooling capacity exergy and exergy efficiency of the TEC system can be obtained, respectively, under different conditions. This means that the cooling temperature can be considered as an optimization variable for the optimization problem of a TEC system. In addition, it can be found that the optimal cooling temperatures corresponding to the maximization of EQc and ex range from 13 to 15
o
C , and the optimal cooling temperature for ex is slightly higher
than the one for EQc . However, the thermal conductance allocation ratio x has a 18
larger influence on the maximum cooling capacity exergy and exergy efficiency. When x increases from 0.4 to 0.8, the maximum EQc decreases from 2.16W to 1.78W, i.e. by 17.6%. As respected, the maximum ex also decreases from 0.0766 to 0.0613. As mentioned previously, larger x means the thermal conductance of the heat sink is smaller than at the cooling load, which leads to the decrease of the maximum EQc,max and ex,max . Overall, the results reveal that the operational cooling temperature regime of a TEC system should be between the optimum regimes obtained by maximizing the EQc and maximizing the ex . Also, it can be found the same variations of the parameters EQc and ex with different cooling temperature when we change the current from 5A to 10A.
Fig. 6 The variations of EQc and ex versus the cooling temperature ( I 5 A )
19
Fig. 7 The variations of EQc and ex versus the cooling temperature ( I 10 A ) 4. Conclusion In this paper, the theoretical analysis based on the second law of thermodynamics is conducted to study the optimization problems of single-stage TEC systems. The exergy of cooling capacity and the exergy efficiency of a TEC system are suggested to be the optimization objective functions. Furthermore, a new entropy generation number associated with the entropy generation, the cooling capacity exergy and cooling temperature is introduced. The effects of the thermal design and operating parameters, including the operation electric current, thermal conductance allocation ratio and cooling temperature, on the cooling capacity exergy, entropy generation number and the exergy efficiency are evaluated. The obtained results indicate the equivalence of minimum entropy generation number and maximum exergy efficiency in the optimization of a TEC system. Thus, it is possible to optimize the TEC system by the criterion of entropy generation number, which may provide a new dimensionless measure of TEC system irreversibility. The maximum cooling capacity exergy and maximum exergy efficiency of the TEC system at their corresponding optimal currents are dependent on the thermal conductance allocation ratio between the cold and hot sides. For given temperature conditions, there exists one optimal allocation ratio leading to the best maximal cooling capacity exergy and exergy efficiency, respectively. Moreover, the cooling temperature can be considered as an optimization variable for TEC system optimization, and an optimal cooling temperature exists, leading to the maximum cooling capacity exergy and exergy 20
efficiency, respectively. Thus, the most important contribution of the present investigation is that the cooling temperature should be considered in the design and application for practical TEC systems to obtain the maximum performance benefit. It should be noted that the thermal conductance allocation ratio and the operating current must be carefully designed to achieve the optimal cooling temperature. For a real TEC application, the cold and hot sides heat exchangers must be precisely manufactured, and the operating current should also be adjusted carefully. The results obtained herein may provide guides for the design and application of practical TEC systems.
Acknowledgements This study is financially supported by the National Natural Science Foundation of China (NSFC) under the grant No. 51276135. The authors would like to thank NSFC for the sponsorship.
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thermoelectric cooling systems: a review, Int. J. Energy Res. 28(2004) 753–768.
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Figure captions Fig. 1 A typical single-stage TEC system: a) The structural diagram of single-stage TEC system; b) The schematic representation of a single-stage TEC system Fig. 2 The variations of EQc and ex with I Fig. 3 The effects of I
under different x
on the N s and S g under the various x
Fig. 4 The N s and ex with the electric current I Fig. 5 The variations of the EQc,max , ex,max and optimal currents with x Fig. 6 The variations of EQc and ex versus the cooling temperature ( I 5 A ) Fig. 7 The variations of EQc and ex versus the cooling temperature ( I 10 A ) Table captions Table 1 Thermoelectric parameters of the TEM
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Table 1 Thermoelectric parameters of the TEM
Module [21]
Parameters Dimension
mm 3
62 62 4.6
Pellet size mm3
2.0 2.0 1.42
I max A
14.0
U max V
15.4
Qmax W
140.5
Tmax
C o
67
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Abstract This paper presents a theoretical analysis based on the second law of thermodynamics to evaluate the optimal performances of a single-stage thermoelectric cooling system. The cold exergy and exergy efficiency are chosen as the optimization objective functions, and a new entropy generation number associated with entropy generation, cold exergy and cooling temperature is proposed. The influences of several key parameters such as electric current, thermal conductance allocation ratio and cooling temperature on the cooling performance are theoretically investigated. The results indicate that the criterion of entropy generation number could be used as a new dimensionless measure of TEC system irreversibility. Furthermore, the cooling temperature can be considered as an optimization variable for TEC system optimization, and an optimal cooling temperature exists, leading to the maximum cooling capacity exergy and exergy efficiency, respectively. Thus, the cooling temperature should be considered in the design and application for practical TEC systems in order to obtain the maximum performance benefit. The present study can provide guidelines for the design and application of practical thermoelectric cooling systems.
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Highlights: Thermodynamic 2nd law analysis of a thermoelectric cooling (TEC) system is conducted. A new entropy generation number for evaluating the TEC irreversibility is proposed. An optimal cooling temperature exists, leading to the maximum 2nd law performance.
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