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Performance Prediction of Commercial Thermoelectric Cooler
Modules using the Effective Material Properties
HoSung Lee, Alaa M. Attar, Sean L. Weera
Mechanical and Aerospace Engineering, Western Michigan University,
1903 W. Michigan Ave, Kalamazoo, Michigan 49008-5343, USA
Office (269) 276-3429
Fax (269) 276-3421
Email: [email protected]
Abstract
This work examines the validity of formulating the effective thermoelectric material
properties as a way to predict thermoelectric module performance. The three maximum
parameters (temperature difference, current, and cooling power) of a thermoelectric
cooler were formulated on the basis of the hot junction temperature. Then, the effective
material properties (Seebeck coefficient, electrical resistance, and thermal conductivity)
were defined in terms of the three maximum parameters that were taken from either a
commercial thermoelectric cooler module or the measurements. It is demonstrated that
the simple standard equation with the effective material properties predicts well the
performance curves of the four selected commercial products. Normalized parameters
over the maximum parameters were also formulated to present the characteristics of the
2
thermoelectric coolers along with the normalized charts. The normalized charts would be
universal for a given thermoelectric material.
Keywords: Thermoelectric cooler, thermoelectric module, effective material
properties, maximum parameters, normalized parameters, and normalized charts.
Nomenclature
A cross-sectional area of thermoelement (m2)
COP the coefficient of performance, dimensionless
I electric current (A)
maxI maximum current (A)
j
electric current density vector (A/m2)
K thermal conductance (W/K)
L length of thermoelement (m)
k thermal conductivity (W/mK)
n the number of thermocouples
q
heat flux vector (W/m2)
cQ cooling power, heat absorbed at cold junction (W)
hQ heat liberated at hot junction (W)
maxcQ maximum cooling power (W)
R electrical resistance ()
T temperature (°C)
cT low junction temperature (°C)
3
hT high junction temperature (°C)
T average temperature 2ch TT (°C)
V Voltage of a module (V)
maxV maximum voltage (V)
W work per unit time RITIW 2 (W)
x distance of thermoelement leg (m)
Z the figure of merit (K-1), kZ 2
T temperature difference ch TT (°C),
maxT maximum temperature difference (°C)
Greek symbols
Seebeck coefficient (V/K)
electrical resistivity (cm)
gradient operator vector
Subscript
p p-type element
n n-type element
Superscript
* effective quantity
4
1. Introduction
Thermoelectric coolers have comprehensive applications [1-5] in electronic devices,
medical instruments, automotive air conditioners, and refrigerators. Thermoelectric
phenomena are often described by a simple standard equation, which has been widely
used in the literature [1-5], sometimes in good agreement with experiment [6,9,11]. The
simple standard equation is herein called the ideal equation, which is virtually formulated
under three assumptions that the electrical and thermal contact resistances, the Thomson
effect (temperature-dependent Seebeck coefficient), and the radiation and convection heat
transfer are negligible [11,12]. The radiation and convection heat transfer is small for the
moderate temperature differences between the hot and cold junction temperatures and the
surrounding temperature in typical commercial cooler modules. The Thomson effect
rather slightly improves the performance [6,7]. The major errors between the
measurements and the ideal equation lie on the electrical and thermal contact resistances
[11,13].
Commercial thermoelectric cooler modules consist of a number of thermoelement
couples (or thermocouples), electrically connected in series and thermally sandwiched in
parallel between two ceramic plates. The manufacturers usually provide the performance
curves along with the maximum parameters such as the temperature difference Tmax, the
current Imax, the cooling power Qmax, and the voltage Vmax. However, the material
properties of the modules such as the Seebeck coefficient , the electrical resistivity ,
and the thermal conductivity k are not usually provided as manufacturers’ proprietary
information. Therefore, system designers find it difficult to obtain the material properties.
5
Huang et al. [14] measured the material properties of a commercial module for the
optimum design using an evacuated and insulated test apparatus. They confirmed that the
measurements were in good agreement with the performance curves provided by the
manufacturer. Nevertheless, they were not able to fit the measured data to the ideal
equation, which was deemed mainly due to the electrical and thermal contact resistances
not counted for within the ideal equation.
Lineykin and Ben-Yaakov [15] formulated the theoretical maximum parameters
from the ideal equation using the definitions used by manufacturers and then expressed
the physical module properties (m, Rm, and Km) in terms of the three parameters (Tmax,
Imax, and Vmax) out of the four theoretical maximum parameters (Tmax, Imax, Qmax, and
Vmax). In this way, the module properties contain information of the number of
thermoelement couples and geometric ratio. Lineykin and Ben-Yaakov extracted the
physical module properties by substituting the manufacturers’ maximum parameters for
the theoretical maximum parameters. Luo [16] used two methods to determine the
physical module properties: not only the combination (Tmax, Imax, and Vmax) used by
Lineykin and Ben-Yaakov, but also the different combination (Tmax, Imax, and Qmax) out
of the four maximum parameters. When the two methods were compared to each other
over four selected commercial modules, the physical module properties over the four
modules varied within a 5% discrepancy range. Zhang [17] obtained the physical module
properties of a commercial module using the three parameters (Tmax, Imax, and Vmax) for
application to an electronic cooling system and performed evaluation and optimization
onto the system design, including the heat sinks.
6
Simons [21] showed a capability of the module properties (m, Rm, and Km) with a
different set of the maximum parameters (Tmax, Imax, and Qmax) to predict the
performance of an electronic module. Tan and Fok [10] evaluated the module properties
for commercial modules using the three maximum parameters (Tmax, Imax, and Vmax) and
compared the predicted results with the manufacturers’ performance curves. The
comparisons showed fair agreement and the errors increased with increasing current or
temperature difference. Recently, Ahiska and Ahiska [18] developed a new economic
method of measurement for thermoelectric outputs and properties providing formulas
based on the ideal equation by measuring the maximum parameters (Tmax, Imax, and
Vmax) and experimentally proved to be reasonably accurate.
Most of the above mentioned works tried to extract the physical module properties
(m, Rm, and Km) from either the three parameters (Tmax, Imax, and Vmax) or the other set
of parameters (Tmax, Imax, and Qmax), which imposes the uncertainties on the cooling
power prediction. On the other hand, the present work extracts the effective material
properties (and k) from the manufacturers’ maximum parameters (Tmax, Imax, and
Qmax), which imposes the uncertainties on the voltage prediction, particularly being good
at module design for specific systems. Note that, although the differences between the
module properties and the effective material properties appear minuscule, the results and
applications are of great consequence: the module properties are constrained to have a
validity for use of the module, but the effective material properties are not, which is the
uniqueness of the present paper. The optimal design [8] using the ideal equation with the
effective material properties will now be simple and robust. The present work studies to
verify in detail the effective material properties comparing with the performance curves
7
of four major manufacturers’ products. Hence, the usually intractable temperature
dependence of the material properties and the subtle thermal and electrical contact
resistances can be examined with the effective material properties that are constant.
The normalized charts with the maximum parameters were presented by Buist [19]
and later Uemura [20] for the purpose of the design of thermoelectric devices. However,
theoretical formulas for the normalized charts were not found to the authors’ knowledge.
Therefore, the present work studies the normalized formulas over the maximum
parameters providing the two normalized charts, which coherently reveal the elusive
general characteristics of thermoelectric coolers.
p
n
p
n
np
p
pn
Positive (+)
Negative (-)
Heat Absorbed
Heat Rejected
Electrical Conductor (copper)Electrical Insulator (Ceramic)
p-type Semiconcuctor
n-type Semiconductor
Figure 1. Cutaway of a typical thermoelectric module
1. Ideal Equation
8
A typical thermoelectric module is shown in Figure 1. Suppose that the upper junction
temperature (upper electrical conductor) is at Tc and the lower junction temperature is at
Th. The cooling power at the junction of temperature Tc is given by
TKRIITnQ cc
2
2
1 (1)
where n is the number of thermocouples, a the Seebeck coefficient, I the current, R the
electrical resistance, K the thermal conductance, and T = (Th - Tc). From now on,
Equation (1) is called the ideal equation. The current for the optimum COP can be
obtained by differentiating COP and setting it to zero.
11
TZR
TICOP
(2)
where kZ 2 and T is the average temperature of cT and hT . On the basis of Th,
TZ is expressed by
h
hT
TZTTZ
21 (3)
2. Maximum Parameters
Let us consider a thermoelectric module shown in Figure 1 for the theoretical
maximum parameters with the ideal equation. The module consists of a number of
thermoelement couples as shown. As mentioned before, the ideal equation assumes that
there are no the electrical and thermal contact resistances, no Thomson effect, and no
radiation or convection. It is noted that the theoretical maximum parameters might differ
with the manufacturers’ maximum parameters that are usually obtained by measurement.
9
The maximum current Imax is the current that produces the maximum possible
temperature difference Tmax , which always occurs when the cooling power is at zero.
This is obtained by setting cQ = 0 in Equation (1), replacing Tc with (Th – T) and taking
derivative of T with respect to I and setting it to zero. The maximum current is finally
expressed by
ZT
ZT
RI hh
11 2
2
max
(4)
Or, equivalently in terms of Tmax,
R
TTI h max
max
(5)
The maximum temperature difference Tmax always occurs when the cooling power
is at zero and the current is at maximum. This is obtained by setting cQ = 0 in Equation
(1), substituting both I and Tc by Imax and Th – Tmax, respectively, and solving for Tmax.
The maximum temperature difference is obtained as
2
2
max
11hhh T
ZT
ZTT
(6)
The maximum cooling power maxcQ is the maximum thermal load which occurs at
T = 0 and I = Imax. This can be obtained by substituting both I and Tc in Equation (1) by
Imax and Th (since Tc = Th ), respectively, and solving for maxcQ . The maximum cooling
power for a thermoelectric module with n thermoelement couples is
10
R
TTnQ h
c2
2
max
22
max
(7)
The maximum voltage is the DC voltage which delivers the maximum possible
temperature difference Tmax when I = Imax. The maximum voltage is given by
hTnV max (8)
3. Normalized Parameters
If we divide the actual values by the maximum values, we can normalize the
characteristics of the thermoelectric cooler. The normalized cooling power can be
obtained by dividing Equation (1) by Equation (7), which is
RTTn
TKRIITTn
Q
Q
h
h
c
c
2
2
1
2
max
22
2
max
(9)
which, in terms of the normalized current and normalized temperature difference, reduces
to
2
max
max
max
max
2
max
max
max
max
max
max
max
1
2
1
1
1
12
h
h
h
h
h
h
h
c
c
T
TZT
T
T
T
T
T
T
I
I
T
T
T
T
I
I
T
T
T
T
Q
Q
(10)
where
11
11
11
1
2
max
hhh ZTZTT
T (11)
The coefficient of performance in terms of the normalized values is
2
max
max
max
max
max
max
max
max
2
max
max
max
max
max
1
1
12
11
I
I
T
T
I
I
T
T
T
T
T
TZT
T
T
T
T
I
I
T
T
I
I
T
T
T
T
COP
hh
h
h
h
hh
(12)
The normalized voltage is
max
maxmax
maxmax
1I
I
T
T
T
T
T
T
V
V
hh
(13)
The normalized current for the optimum COP is obtained from Equation (2).
111 max
max
max
max
TZT
T
T
T
T
T
I
I
h
hCOP (14)
where TZ is expressed using Equation (3) by
12
max
max
2
11
T
T
T
TZTTZ
h
h (15)
Note that the above normalized values in Equations (10), (11), (12) and (13) are functions
only of three parameters, which are maxTT , maxII and ZTh.
4. Effective Material Properties
The effective material properties are defined here as the material properties that are
extracted from the maximum parameters provided by the manufacturers or from
measurements. The effective figure of merit is obtained from Equation (6), which is
2max
max2
TT
TZ
h
(16)
The effective Seebeck coefficient is obtained using Equations (5) and (7), which is
maxmax
max2
TTnI
Q
h
c
(17)
The effective electrical resistivity can be obtained using Equation (5), which is
max
max
I
LATTh
(18)
13
The effective thermal conductivity is now obtained, which is
Zk
2
(19)
The effective material properties include all the losses such as the contact resistances.
Hence, the effective figure of merit appears slightly less than the intrinsic figure of merit
as shown in Table 1. Since the material properties were obtained for a p-type and n-type
thermoelement couple, the material properties of a thermoelement should be obtained by
dividing by 2.
5. Results and Discussion
In the previous reports [15-17], the physical module properties (m, Rm, and Km)
were extracted from a combination (Tmax, Imax, and Vmax) among the four manufacturer’s
maximum parameters (Tmax, Imax, maxcQ , and Vmax). In the present work, the effective
material properties (, , and k*) were extracted from a different combination (Tmax,
Imax, and maxcQ ) among the manufacturers’ maximum parameters. Therefore, the physical
module properties hold information of the number of thermoelement couples and the
geometric ratio (A/L), while the effective material properties do not.
In order to examine the status of the ideal equation with the effective material
properties, several major manufacturers were chosen as shown in Table 1. The effective
material properties were first calculated using the manufacturer’s maximum parameters
using Equations (16) - (19). The geometry of A and L were actually measured. Only one
14
set of the intrinsic material properties was provided by the manufacturer, which is shown
in Table 1.
In the column of Module CP10-127-05, the effective material properties obtained
appear very close to the intrinsic material properties. It should be noted that the
dimensionless intrinsic figure of merit of 0.803 exhibits slightly larger than the
dimensionless effective figure of merit of 0.744, which is reasonable because the contact
resistances are conceptually imposed on the effective material properties. No appreciable
improvement was found even though the intrinsic material properties were used in
calculation because the contact resistances exist anyway. It is noted that the maximum
temperature differences provided by different manufactures may not be consistent with
one another. The manufacturability and contact resistances may be responsible for the
inconsistency.
Table 1 Comparison of the properties and dimensions for the commercial products of
thermoelectric modules
Description TEC Module (Bismuth Telluride)
Symbols CP10-127-05
(Th=298 K)
RC12-4
(Th=298 K)
TB-127-1.0-1.3
(Th=298 K)
C2-30-1503
(Th=298 K)
# of thermocouples n 127 127 127 127
Intrinsic material
properties (provided
by manufacturers)
V/K 202.17 - - -
cm 1.01 x 10-3 - - -
k (W/cmK) 1.51 x 10-2 - - -
ZTh 0.803 - - -
Effective material
properties (calculated
using commercial
Tmax, Imax, and Qcmax)
V/K 189.2 211.1 204.5 208.5
cm 0.9 x 10-3 1.15 x 10-3 1.0 x 10-3 1.0 x 10-3
k (W/cmK) 1.6 x 10-2 1.7 x 10-2 1.6 x 10-2 1.7 x 10-2
ZTh 0.744 0.673 0.776 0.758
Measured geometry
of thermoelement
A (mm2) 1.0 1.0 1.0 1.21
L (mm) 1.25 1.17 1.3 1.66
G=A/L (cm) 0.080 0.085 0.077 0.073
Dimension (W×L×H) mm 30 × 30 × 3.2 30 × 30 ×
3.4
30 × 30 × 3.6 30 × 30 × 3.7
Manufacturers’
maximum parameters Tmax (°C) 67 66 (63) 69 68
Imax (A) 3.9 3.7 3.6 3.5
Qcmax (W) 34.3 36 34.5 34.1
15
Vmax (V) 14.4 14.7 15.7 15.5
R () -
module
3.36 3.2 3.2 3.85
Figure 2 depicts comparison between the calculations (solid lines) and the
manufacturer’s performance data (triangles) of Module CP10-127-05. The cooling power
in Figure 2 (a) was calculated using Equation (7) by substituting Tc by (Th –T) and using
the effective material properties. The dotted curve indicates the cooling power at the
optimal COP for which Equation (7) was used with substituting I by the current at the
optimum COP in Equation (2). It is seen in Figure 2 (a) that the calculated effective
maximum parameters (Tmax = 67°C, Imax = 3.9 A, and maxcQ = 34.3 W) are in good
agreement with the manufacturer’s performance curves. On the other hand, Figure 2 (b)
depicts that the errors on the voltage-vs-temperature-difference curves increase with
decreasing the temperature difference. The errors are associated with the combination
(Tmax, Imax, and maxcQ ) and partially the inherent contact resistances. The analysis
including the temperature dependence of the material properties and the thermal and
electrical contact resistances are very formidable especially for optimal system design
which requires many iterations of calculations, also not available in the literature to the
authors’ knowledge. Therefore, the errors are a nature of this work. The present work
presents a single module, but system design involves multiple modules. However, the
multiple modules in a system may be effectively handled using a thermal isolation
technique [22]. The marked data of the COP in Figure 2 (c) were not provided by the
manufacturer but generated in this work using the measured data in Figures 2 (a) and (b),
which are in a fair agreement.
16
0 10 20 30 40 50 60 700
5
10
15
20
25
30
35
Temperature Difference, T (°C)
Coo
ling
Pow
er, Q
c (
W)
I = 3.9 A Prediction
Commercial product
3.2 A Optimal COP
2.4 A
1.6 A
0.8 A
(a)
0 10 20 30 40 50 60 700
2
4
6
8
10
12
14
16
18
Temperature Difference (°C)
Volt
age (
V)
Prediction
Commercial productI = 3.9 A
3.2 A
2.4 A
1.6 A
0.8 A
(b)
17
0 1 2 3 40
0.5
1
1.5
2
2.5
3
Current (A)
CO
PPrediction
Commercial product
T = 10°C
20 °C
30 °C
40 °C
50 °C
(c)
Figure 2. (a) Cooling power versus T, (b) Voltage versus T, as a function of current,
and (c) COP versus current as a function of T. The original performance data (triangles)
of the commercial module (Module CP10-127-05) are compared to the prediction (solid
lines). The dotted line in (a) indicates the cooling powers at the optimum COP.
Figures 3 (a) and (b) depict comparison between the calculations and the
performance data of Module RC12-4. In general, the calculations are in good agreement
with the manufacturer’s performance data. Figure 3 (c) shows only the calculations (solid
lines) wherein the COP data (dotted lines) were not able to be generated due to the lack
of information from the manufacturer.
18
0 0.5 1 1.5 2 2.5 3 3.5 40
10
20
30
40
50
60
70
Prediction Qc = 0 W
Commercial product
Qc = 5 W
Qc = 10 W
Qc = 15 W
T (°C)
Qc = 20 W
Qc = 25 W
Qc = 30 W
Qc = 35 W
I (A)
(a)
0 1 2 3 4 50
5
10
15
20
25
30
Prediction, Qc = 0
Prediction, T = 0
Comm. product, Qc = 0
Comm. product, T = 0
Current (A)
Vo
ltag
e (
V)
Qc = 0
T 0
(b)
19
0 1 2 3 40
0.5
1
1.5
2
2.5
3
Current (A)
CO
PPrediction
No commercial product
T = 13.2°C
26.4°C
39.6°C
52.8°C
Figure 3. (a) T versus current as a function of cooling powers, (b) Voltage versus
current for Qc = 0 and T = 0, respectively, and (c) COP versus current. The original
performance data (triangles and squares) in (a) and (b) of the commercial module
(Module RC12-4) are compared to the prediction (solid lines).
Figures 4 (a), (b) and (c) depict comparison between the calculations and the
performance data of Module TB-127-1.0-1.3, with an excellent agreement.
20
0 10 20 30 40 50 60 700
5
10
15
20
25
30
35
Temperature Difference, T (°C)
Coo
ling
Pow
er, Q
c (
W)
Prediction I = 3.6 A
Commercial product
Optimal COP
2.7 A
1.8 A
0.9 A
(a)
0 1 2 3 40
2
4
6
8
10
12
14
16
Current (A)
Vo
ltag
e (
V)
T = 69°C
T = 51.75°C
T = 34.5°C
T = 17.25°C
Prediction
Commercial product
(b)
21
0 1 2 3 40
0.4
0.8
1.2
1.6
2
Current (A)
CO
PPrediction
Commercial product
T = 17.25°C
34.5°C
51.75°C
(c)
Figure 4 (a) Cooling power versus T as a function of current, (b) Voltage versus current
as a function of T, and (c) COP versus current as a function of T. The original
performance data (triangles) of the commercial module (Module TB-127-1.0-1.3)
compared to the prediction (solid lines). The dotted line in (a) indicates the cooling
powers at the optimum COP.
Figures 5 (a), (b) and (c) depicts comparison between the calculations and the
performance data of Module C2-30-1503, with a good agreement.
22
0 10 20 30 40 50 60 700
5
10
15
20
25
30
35
Temperature Difference, T (°C)
Coo
ling
Pow
er, Q
c (
W)
I = 3.5 APrediction
Commercial product3 A
Optimal COP
2.5 A
2 A
1.5 A
1 A
(a)
0 10 20 30 40 50 60 700
2
4
6
8
10
12
14
16
Temperature Difference (°C)
Volt
age (
V)
I = 3.5 A
3 A
2.5 A
2 A
1.5 A
1 A
Prediction
Commercial product
(b)
23
0 1 2 3 40
0.5
1
1.5
2
2.5
3
Current (A)
CO
PT = 10°C Prediction
Commercial product
20°C
30°C
40°C
50°C
(c)
Figure 5. (a) Cooling power versus T as a function of current, (b) voltage versus T, as
a function of current, and (c) COP versus current as a function of T. The original
performance data (triangles) of the commercial module (Module C2-30-1503) are
compared to the prediction (solid lines). The dotted line in (a) indicates the cooling
powers at the optimum COP.
24
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
I/Imax = 1.0 I/Imax = 1.0
0.8 0.8
0.6 0.6
Qc/Qcmax 0.4 V/Vmax
0.4
0.2
0.2
T/Tmax Figure 6. Normalized chart I: cooling power and voltage versus T as a function of
current. The solid lines depict the data at ZTh = 0.75, while the dotted lines depict the
alternate current ratios at ZTh = 0.4. The dashed line depicts the cooling power ratios at
the optimum COP.
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.5
1
1.5
2
2.5
3
T/Tmax = 0 T/Tmax = 0
0.2 0.2
0.4
Qc/Qcmax COP
0.6
0.4
0.8 0.6
0.8
I/Imax Figure 7. Normalized chart II: cooling power and COP versus current as a function of T.
The solid lines depict the data at ZTh = 0.7, while the dotted lines depict the alternate
temperature difference ratios at ZTh = 0.4.
Figures 6 and 7 depict the normalized cooling power maxcc QQ , COP, and voltage
maxVV , which were plotted using Equations (27), (29), and (30), respectively. The above
three dependent parameters are only functions of three independent parameters: I/Imax,
T/Tmax, and ZTh as shown in the equations. From the previous discussion, we learned
that the ideal equation with the effective material properties predicts well the real
performance of a thermoelectric cooler module. These normalized charts should also
predict well the performance with a given ZTh. The solid lines depict the predictions at
ZTh = 0.75, which is a typical dimensionless figure of merit used in the commercial
26
products. In order to see the effect of ZTh, the predictions at ZTh = 0.4 were plotted as the
dotted lines for comparison. We find from the figures that the normalized charts are not
significantly influenced by ZTh. These charts are then considered being universal to
approximately represent the performance of most thermoelectric cooler modules in the
present market. With inserting the maximum parameters provided by the manufacturers
into the charts, the reasonable cooling power, COP and voltage could be obtained as
functions of current and temperature difference.
6. Conclusions
The accuracy of the ideal equation in connection with the effective material
properties is demonstrated by comparing with several manufacturers’ performance data
(which are usually obtained by the measurements), being in good agreement. Usually, the
analysis of thermoelectric devices, including the temperature-dependence of the material
properties and the electrical and thermal contact resistances, is very formidable. However,
when one uses the ideal equation with the effective material properties for moderate
temperature differences, the analysis becomes simple and robust and could be a platform
for optimal system design. The maximum temperature differences given by
manufacturers may not be consistent.
Normalized charts are constructed using the ideal equation and the maximum
parameters defined in this work. The normalized charts I and II represent well the
performance of any thermoelectric modules at a given dimensionless figure of merit.
27
References
[1] A.F. Ioffe, Semiconductor thermoelements and thermoelectric cooling, Infoserch
Limited, London, UK (1957).
[2] D.M. Rowe, CRC Handbook of Thermoelectrics, CRC Press, Boca Raton, FL, USA,
(1995).
[3] H.J. Goldsmid, Introduction to thermoelectricity, Spriner, Heidelberg, Germany
(2010).
[4] Nolas GS, Sharp J, Goldsmid HJ, Thermoelectrics, 2001, Springer, Heidelberg,
Germany.
[5] H. Lee, Thermal design: heat sinks, thermoelectrics, heat pipes, compact heat
exchangers, and solar cells, John Wiley & Sons, Inc., Hoboken, New Jersey, USA,
(2010).
[6] C.Y. Du, C.D. Wen, Experimental investigation and numerical analysis for one-stage
thermoelectric cooler considering Thomson effect, Int. J. Heat Mass Transfer, 54: 4875-
4884, (2011).
[7] H. Leea, The Thomson effect and the ideal equation on thermoelectric coolers, Energy,
56, 61-69 (2013)
[8] H. Leeb, Optimal Design of thermoelectric devices with dimensional analysis, Appled
Energy, 106, 79-88 (2013)
[9] R. Palacios, A. Arenas, R.R. Pecharroman, F.L. Pagola, Analytical procedure to
obtain internal parameters from performance curves of commercial thermoelectric
modules, Applied Thermal Engineering, 29, 3501-3505 (2009)
28
[10] F.L. Tan, S.C. Fok, Methodology on sizing and selecting thermoelectric cooler from
different TEC manufacturers in cooling system design, Energy Conversion and
Management, 49, 1715-1723 (2008).
[11] S.A. Omer, D.G. Infield, Design optimization of thermoelectric devices for solar
power generation, Solar Energy Materials and Solar Cells, 53, 67-82 (1998).
[12] M.J. Huang, R.H. Yen, A.B. Wang, The influence of the Thomson effect on the
performance of a thermoelectric cooler, Int. J. Heat and Mass Transfer, 48, 413-418
(2005).
[13] G. Min, D.M. Rowe, O. Assis, S.G.K. Williams, Determining the electrical and
thermal contact resistance of a thermoelectric module, Proceedings of the International
Conference on thermoelectrics, 210-212 (1992).
[14] B.J. Huang, C.J. Chin, C.L. Duang, A design method of thermoelectric cooler,
International Journal of Refrigeration, 23, 208-218 (2000).
[15] S. Lineykin, S. Ben-Yaakov, Modeling and Analysis of Thermoelectric Modules,
IEEE Transactions of Industry Applications, 43, 2, 505-512 (2007).
[16] Z, Luo, A simple method to estimate the physical characteristics of a thermoelectric
cooler from vendor datasheets, Electronics Cooling Magazine, 14, 3, 22-27 (2008).
[17] H.Y. Zhang, A general approach in evaluating and optimizing thermoelectric coolers,
International Journal of Refrigeration, 33, 1187-1196 (2010).
[18] R. Ahiska, K. Ahiska, New Method for Investigation of Parameters of Real
Thermoelectric Modules, Energy Convs. Manag. 51, 338-345 (2010).
[19] R.J. Buist, Universal thermoelectric design curves, 15th International Energy
Conversion Engineering Conference, Seattle, Washington, 18-22 (1980).
29
[20] K. Uemura, Universal characteristics of Bi-Te thermoelements with application to
cooling equipments, International Conference on Thermoelectrics, Barbrow Press,
Cardiff, UK, Ch.12:69-73 (1991).
[21] R. Simons, Calculation corner: Using vendor data to estimate thermoelectric module
cooling performance in an application environment, Electronics Cooling Magazine, 16, 2,
4-6 (2010).
[22] A. Attar, H. Lee, and S. Weera, Optimal design of automotive thermoelectric air
conditioner, Journal of Electronic Materials, 43, 6, 2179-2187 (2014)
