Heat and Mass Transfer

https://doi.org/10.1007/s00231-022-03280-5

ORIGINAL

An experimental evaluation of thermoelectric generator performance

under cyclic heating regimes
N. P. Williams1 · J. Power1 · D. Trimble1 · S. M. O’Shaughnessy1

Received: 2 February 2022 / Accepted: 10 August 2022

© The Author(s) 2022

Abstract
Thermal cycling is known to adversely affect the performance and lifespan of thermoelectric generators (TEGs) yet has
received limited attention to date. The current study experimentally investigates the effect of thermal cycling on the perfor-
mance of twelve nominally identical TEG modules. Six samples were subjected to the same thermal cycle profile with an
average heating time of 154 s to examine the variation in their outputs. The maximum cycling temperature was varied between
170 °C and 190 °C for a further six samples to investigate the effect of maximum set-point temperature on performance.
Degradation in performance was exhibited by all modules, with maximum power outputs between 28% and 57% of pre-cycling
values and a decrease in the dimensionless figure of merit ZT of 21% to 56% upon cessation of cycling. Sudden ‘break-
downs’ or significant reductions in output power were observed for all TEGs, accompanied by increased electrical resistance,
which is indicative of internal damage to the modules arising from the formation of micro-cracks at the interface between
the semiconductor thermocouples and electrically conductive material. The rate of degradation post-‘breakdown’ appeared
to be influenced by the maximum set-point temperature, with more rapid decreases observed for increasing temperatures.
Nomenclature Subscripts
A Cross-sectional area ­[m2] C TEG cold side
I Current [A] eff Effective
K Thermal conductance [W/K] H TEG hot side
L Length [m] L Electrical load
Q Heat power [W] max Maximum
R Electrical resistance [Ω] OC Open circuit
T Temperature [°C] n N-type semiconductor
V Voltage [V] p P-type semiconductor
W Electrical power [W]
Z Figure of Merit [1/K]
ZT Dimensionless Figure of Merit 1 Introduction
Greek symbols
Thermoelectric generators (TEGs) are solid state semi-
𝛼 Seebeck coefficient [V/K]
conductor devices which convert heat energy to electrical
Δ Gradient
energy through the Seebeck effect, with wide-ranging appli-
𝜆 Thermal conductivity [W/mK]
cations including vehicle exhaust heat recovery systems [1],
𝜌 Density [kg/m3]
low power sensors [2], off-grid electricity generation [3],
𝜎 Electrical conductivity [S/m]
and wearable technologies [4]. Greater voltages across the
electrical terminals of the TEG and higher output power are
generated by the module for increasing temperature differ-
ence between its hot and cold surfaces while the maximum
* N. P. Williams operating temperature is not exceeded. The absence of mov-
nwilliam@tcd.ie ing parts in their construction means that TEGs are often
1 quoted with long lifetimes by manufacturers when assumed
Department of Mechanical, Manufacturing, and Biomedical
Engineering, Parsons Building, Trinity College, The to be operating under stable thermo-mechanical conditions.
University of Dublin, Dublin, Ireland However, their expected lifetimes and output power can

13
Vol.:(0123456789)
 Heat and Mass Transfer

be significantly reduced when the devices are subjected to side was maintained at 23 °C using a heat exchanger. Upon
thermal cycling, which has received limited attention in lit- completion of 45,000 cycles each lasting 60 s, the cyclable
erature to date. There appears to be no standard method to hot side temperature range had decreased to between 20 °C
impose thermal cycling on TEGs, or to evaluate its effects. and 40 °C, indicating failure of the module. A decrease in
Several analytical and/or numerical studies, such as those the figure of merit and significantly increased internal resist-
in Refs. [5–7], have attempted to provide greater insight, ance was attributed to fracture of the TEG leg/solder inter-
but the models are typically limited in their applicability face, detected through infrared (IR) microscopy.
to real life scenarios, and they often do not consider mate- Tatatinov et al. [14] cycled the hot side of a TEG mod-
rial degradation effects. An exception to this is the study of ule between 50 °C and 250 °C while maintaining a cold
Wang et al. [8]. side temperature of 30 °C. For a cycle time of 11 min, the
Regarding experimental studies, Hori et al. [9] were module’s output power was observed to have decreased by
among the first to examine the effect of thermal cycling 11% after 340 cycles, which the authors believed was due to
on TEG performance, investigating three bismuth telluride the degradation of the thermal contact at the solder leg and
­(Bi2Te3) modules of varying thermoelement cross-sectional thermoelement interface.
area. The hot side was cycled to a maximum temperature The use of TEG modules as the hot and/or cold side
of 180 °C, while the cold side was maintained at 30 °C. source when thermal cycling an additional TEG has been
The duration of the thermal cycle was not detailed. Thermal employed by a number of authors. Park et al. [15] utilised
cycling was found to have a detrimental effect on the TEG two TEG modules thermally in series as the hot side source
modules’ performance, attributed to increased internal elec- for the thermal cycling of a module. Thermal cycles of three-
trical resistance, with the power generated decreasing over minute duration between temperatures of 30 °C and 160 °C
successive cycles. The authors observed a sudden decrease were applied to the module, with the cold side maintained at
or ‘breakdown’ in performance for all modules, with greater 20 °C. Decreases of 8% and 11% in the figure of merit and
lifespan linked to increased thermoelement cross-sectional output power respectively were observed after 6,000 cycles.
area. Tenorio et al. [16] alternated the hot and cold sides across
Hatzikraniotis et al. [10] examined the thermal cycling a TEG module between 20 °C and 40 °C for thermal cycles
of ­Bi2Te3 TEGs of 25 mm × 25 mm cross-sectional area lasting approximately 15 min by utilising additional TEG
containing 31 thermoelements. A thermal cycle consisted modules as the hot and cold sources. A decrease in ZT of
of a heating stage of approximately 6 min to a hot side 7% after only 127 cycles was observed, with a 10% increase
temperature of 200 °C, a constant temperature period last- in the internal resistance.
ing approximately 5 min, followed by a cooling stage of Ding et al. [17] examined the effect of varying thermal
approximately 20 min to a minimum hot side temperature cycling conditions on TEG performance, for heat inputs of
of 30 °C. The cold side temperature was fixed at 24 °C. At 80 W and 160 W and heating and cooling times of 15 min-
the end of 6,000 thermal cycles, the module experienced a utes. This corresponded to the thermal cycling ranges 35 °C
drop in output power of approximately 14% and an increase to 85 °C and 55 °C to 165 °C respectively. No change in
in material resistivity of 16.1%. The authors attributed this output performance was determined under the first cycling
degradation to micro-crack formation at the thermoelement range after 500 thermal cycles. However, when subjected
leg/solder interface, as observed through scanning electron to cycling at the higher hot side temperature, the module’s
microscope (SEM) imaging of the module’s internal struc- open-circuit voltage exhibited unexpected fluctuations,
ture post-cycling. The dimensionless figure of merit ZT was which was attributed to degradation of the solder connec-
also observed to have decreased from 0.74 to 0.63 upon the tions within the module. The authors concluded that pro-
cessation of cycling. A larger decrease in ZT of 18.7% was longed cycling of TEG modules at hot side temperatures of
observed by de Cerqueira Veras et al. [11] who developed a approximately 150 °C is detrimental to their performance.
testing platform to investigate thermal cycling effects on a Merienne et al. [18] recently investigated the effect of
single thermoelectric module. The sample was subjected to heating rate on three nominally identical ­Bi2Te3 TEGs as
temperature differences of ± 20 ℃ in the temperature range produced by a single manufacturer. All samples exhibited
of 20 ℃ to 40 ℃, with each cycle lasting 15 minutes. After performance degradation after 600 thermal cycles, with the
548 cycles, the internal resistance, Seebeck coefficient, greatest degradation experienced by the sample subjected to
thermal conductivity, and electrical conductivity changed the most rapid heating rate.
by + 9.8%, -3.9%, -8.6%, and -9.6%, respectively. Harish et al. [19] assessed the impact of thermal cycling on
The hot side temperature of a TEG module was varied eight ­Bi2Te3 modules used in an automotive exhaust thermo-
between -20 °C and 146 °C by Barako et al. [12, 13] through electric generator. Measurements of the open circuit voltage,
the application of a square wave voltage signal to the mod- voltage-current relationship, and matched load output power
ule, replicating both heating and cooling cycles. The cold were obtained in response to three thermal cycling profiles

13
Heat and Mass Transfer

with a maximum heat source temperature of 350 ℃. After There are differences in the number of TEGs investigated
150 cycles, only marginal variations in the measured param- per study, the TEG size and number of p-n pellets, the pel-
eters were observed. However, after 300 cycles a noticeable let length and cross-sectional area, the temperature limits
decrease in maximum output power was observed for two imposed, and the duration and number of thermal cycles per-
TEGs which was due to an increase in internal resistance formed. This leads to differing results. A greater understand-
caused by contact resistance at the cold-side leg–electrode ing of thermal cycling effects on commercially available
joints. Microstructural and compositional analyses indicated modules is required to ensure their sustainable application.
that the cold-side joint contact resistance increase arose from In this work, two distinct investigations were undertaken
the thermochemical degradation of the interface between the to examine the impact of the operating conditions on the
thermocouple legs and Sn-Cu solder alloy. performance degradation of TEG modules. In the first study,
Ziolkowski et al. [20] investigated the short-term (60 h) six TEG samples produced by a single manufacturer were
and long-term (443 h) stability of four TEG samples from subjected to the same thermal cycling profile to examine
different manufacturers using thermal cycling between a fixed the variation in performance between nominally identical
cold side temperature of 50 ℃ and hot side temperatures vary- samples under the same conditions. In the second study, a
ing between 100 ℃ to 200 ℃ and 125 ℃ to 225 ℃ depending further six TEG samples from the same manufacturer were
on the sample studied. Tests were conducted at an applied subjected to different maximum temperature limits during
pressure of 3 MPa and long-term stability was assessed on thermal cycling to determine the effect on module degrada-
the basis of the internal electric resistance. Internal resistance tion. To the authors’ knowledge, this represents the largest
changes of 2.43%, 4.3%, 13.1%, and 9.16% were obtained for number of TEG samples, particularly from a single manu-
the samples identified as A, B, C, and D, respectively. facturer, investigated in a single study.
Riyadi et al. [21] used a similar experimental setup to
Merienne et al. [18] to thermally cycle an SP1848 27145
SA TEG for 100 cycles at four heating rates: 3.92 ℃/s, 2.67
℃/s, 1.64 ℃/s, and 0.91 ℃/s. The average temperature dif- 2 Thermoelectric theory
ference during thermal cycling was 110 ℃ for all tests. An
increasing number of thermal cycles led to an increase in Under the Seebeek effect, when conductors of dissimilar
TEG internal resistance and a corresponding decrease in material are subjected to a thermal gradient, the diffusion of
output voltage, current and power, with greater deterioration charge carriers across this temperature difference develops
at higher heating rates. Lower heating rates resulted in an an electrical potential between the hot and cold ends. This
increase in the Seebeck coefficient. open-circuit voltage VOC can be described in terms of the
Clearly, thermal cycling has a deleterious effect on TEG thermal gradient ΔT = TH − TC and the material’s Seebeck
performance, at least at the macro scale. Although not within coefficient, 𝛼 , which is the difference between the Seebeck
scope of this study, with the advent of thin film TEGs and coefficients of the individual semiconductor materials, as
newer organic and inorganic thermoelectric materials, fur- given by Eq. (1):
ther work is required to assess robustness and reliability over VOC = 𝛼ΔT = 𝛼(TH − TC ) (1)
repeated thermal cycles. For example, Mirhosseini et al.
[22] thermally cycled a zinc antimonide (Zn-Sb) thin film TEG modules consist of several p-n semiconductors
thermoelectric sample, subjecting the sample to different known as thermoelements or thermocouples connected elec-
thermal gradients. They observed no deterioration in per- trically in series and thermally in parallel. These thermocou-
formance; however, only 10 cycles each of 8 min duration ples are connected to an electrical shunt such as copper to
were conducted. Other studies have been performed to miti- conduct the current generated and placed between ceramic
gate thermal cycling effects through, for example, protec- plates of high thermal conductivity but low electrical con-
tive coatings [23]. Gao et al. [24] used nanostructured inter- ductivity. The efficiency of a thermoelectric device in con-
faces based on vertically aligned carbon nanotubes (CNT) verting heat energy to electrical energy is dependent upon
to simultaneously address the issues of mechanical stability the thermoelectric material properties. Desirable properties
and large temperature drops in thin film TEGs. They sub- of a thermoelectric material include low thermal conductiv-
jected their thin film sample to 100 thermal cycles from 30 ity to maintain a thermal gradient across the device, a high
℃ to 200 ℃, finding no significantly detrimental effect on electrical conductivity to avoid electron scattering, and a
the CNT array, whilst acknowledging the need for further high Seebeck coefficient. A thermoelectric material’s per-
studies and sample imaging before and after cycling. formance can be characterised by its figure of merit, Z , as
A summary of the studied parameters from several per- given by Eq. (2) where 𝜎 and 𝜆 are the material’s electrical
tinent TEG thermal cycling studies is provided in Table 1. and thermal conductivity respectively:

13
 Heat and Mass Transfer

Table 1  Summary of pertinent TEG thermal cycling studies

Author(s) Year Cycle Length No. Thermal Cycles Temperature Limits TEG Dimensions No. of Number/Type
[s] [-] [℃] ­[mm3] Thermocouples

Hori et al. [9] 1999 – 50 – 300 30 to 180 47.5 × 47.5 × 5 49 6 × ­Bi2Te3

Hatzikraniotis et al. 2009 1,800 6,000 30 to 200 25 × 25 × 3 31 1 × ­Bi2Te3
[10]
Barako et al. [12, 13] 2012 60 45,000 23 to -20 – – –
23 to 146
Tatarinov et al. [14] 2012 – 340 30 to 250 – – 1 × ­Bi2Te3
Park et al. [15] 2012 180 6,000 30 to 160 39.7 × 39.7 × 4.16 127 1 × ­Bi2Te3
de Cerqueira Veras 2015 900 548 20 to 40 40 × 40 × 3.3 127 1 × ­Bi2Te3
et al. [11]
Ding et al. [17] 2016 1,800 300 – 500 35 to 85 40 × 40 × 2.3 127 1 × ­Bi2Te3
55 to 165
Tenorio et al. [16] 2017 900 127 20 to 40 40 × 40 × 3.9 127 1 × ­Bi2Te3
Merienne et al. [18] 2019 760 – 1,320 600 50 to 165 40 × 40 × 3.3 127 3 × ­Bi2Te3
Williams et al. [25] 2021 990 600 50 to 165 40 × 40 × 3.4 127 6 × ­Bi2Te3
Harish et al. [19] 2021 960 – 1,320 150 – 300 50 to 300 40 × 40 × 5 126 8 × ­Bi2Te3
50 to 350
Ziolkowski et al. [20] 2021 155 – 1,230 3 – 151 50 to 200 40 × 40 × 3.5 – 4 × ­Bi2Te3
50 to 225 51.5 × 51.5 × 4.5
54 × 54 × 3.4
50 × 50 × 3.5
Riyadi et al. [21] 2022 334 – 378 100 30–38 to 163.8 40 × 40 × 3.9 110 4 × ­Bi2Te3
30–38 to 158.3
30–38 to 156.5
30–38 to 155.3
Current study 2022 940 – 1,061 300 – 750 50 to 165 40 × 40 × 3.4 127 12 × ­Bi2Te3
50 to 170
50 to 180
50 to 190

𝛼2𝜎 Assuming one-dimensional conduction through the mod-

Z= (2) ule, the rate of heat absorbed (QH ) and rejected (QC ) can be
𝜆
described as:
The highest figures of merits are observed for TEGs con-
sisting of bismuth telluride thermocouples, with Z values of RI 2
(5)
( ) ( )
QH = K TH −T C + 𝛼p − 𝛼n ITH −
approximately 3.4 × ­10–3 ­K−1. However, they are limited to 2
maximum operating temperatures of approximately 250 °C.
The internal electrical resistance R and thermal conduct- RI 2
(6)
( ) ( )
ance K of a single thermocouple can be defined simply in QC = K TH −T C + 𝛼p − 𝛼n ITC +
2
one-dimension according to the standard model proposed
by Hodes [26], which defined these properties in terms of 𝛼p and 𝛼n are the respective Seebeck coefficients of the p
the material density (𝜌), thermal conductivity, thermocouple and n-type doped semiconductor materials and I is the cur-
length ( L ) and cross-sectional area ( A), as shown in Eqs. (3) rent through the thermocouple. The electrical power (W )
and (4): generated by the thermocouple can be expressed as the prod-
uct of the current through and voltage (V ) across the ther-
2𝜌L mocouple. Applying an energy balance across the module,
R= (3)
A the electrical power can also be expressed as the difference
between the heat absorbed and rejected:
2𝜆A
K= (4) W = IV = QH − QC (7)
L

13
Heat and Mass Transfer

Combining Eqs. (5), (6) and (7): the largest cross-sectional area that can be achieved to obtain
the greatest output power.
W = I 𝛼p − 𝛼n TH −T C − I 2 R (8)
( )( )

The thermocouple’s voltage at a fixed temperature differ-

3 Experimental method
ence ΔT = TH − TC can be determined by dividing Eq. (8)
by the electrical current and combining the Seebeck coef-
Figure 1 illustrates the experimental set-up employed,
ficients into a single parameter 𝛼 = 𝛼p − 𝛼n:
which is comparable to that of Merienne et al. [18]. Two
V = 𝛼ΔT − IR (9) aluminium blocks are utilised as the hot and cold sources,
between which a single TEG module is placed. The set-up
To measure 𝛼 , the TEG is subjected to open-circuit condi-
can accommodate TEG modules of cross-sectional areas
tions and the applied temperature gradient and correspond-
up to 56 × 56 ­mm2. The upper hot block is provided with
ing voltage is measured. By setting the electrical power W
the required heat input by two cartridge heaters of 16 mm
equal to the external load’s electrical power I 2 RL in Eq. (8),
outside diameter connected to an Elektro-Automatik EA-
the thermocouple’s current can be described by Eq. (10),
PSI 8360-10 T power supply. Cooling water at a constant
where RL is the load resistance:
temperature and flow rate from a recirculating chiller
𝛼(ΔT) provides the necessary cooling to the lower cold block.
I= (10) A Thermo Fisher Scientific Accel 500 LC recirculating
R + RL
chiller was employed during the first study, while an S&A
Combining Eqs. (9) and (10) provides the thermocouple’s CW-5200 recirculating chiller was utilised to provide the
power as a function of load resistance and internal resistance cooling requirements for the second study. The entire test
for a given temperature difference: section is insulated with DURATEC-750 calcium silicate
( ) insulation of 25 mm thickness to minimise heat loss. The
2 RL TEG module under test is clamped between the heating
W = (𝛼ΔT) ( (11)
and cooling blocks to reduce thermal contact resistance,
)2
R + RL
which is known to affect module performance. Clamping
The maximum power (Wmax) generated by the thermocou- pressure is applied to aluminium plates at each end of the
ple occurs when the internal resistance matches the resist- test section. These plates are connected by four M6 bolts
ance of the external load: of 150 mm length. An adjustable torque screwdriver is
used to apply the necessary torque of 0.5 Nm to each bolt,
(𝛼ΔT)2 A(𝛼ΔT)2 which corresponds to the TEG module’s maximum oper-
Wmax = = (12)
4R 8𝜌L ating pressure of 1.2 MPa. Conical or Belleville spring
washers are arranged on each bolt to maintain this pres-
From Eq. (12) for a particular thermoelectric material and sure during thermal cycling. The surface temperatures on
fixed temperature difference, the thermocouples within the either side of the TEG are approximated from the averaged
TEG module should be of the shortest length possible with measurements of two calibrated 1.5 mm diameter K-type

Fig. 1  Rendered CAD image of

the experimental test set-up

13
 Heat and Mass Transfer

thermocouple probes placed 1.5 mm from the module’s Table 2  European Thermodynamics (GM250-127–14-10) B ­i2Te3
surfaces. These temperature measurements are recorded TEG module properties for a hot side temperature of 250 °C and a
cold side temperature of 30 °C
through a National Instruments (NI) 9211 data acquisition
module (DAQ). The maximum uncertainty in the tempera- Parameter Value
ture difference measurements in this study is ± 0.27 °C.
Dimensions 40 × 40 × 3.4 ­mm3
As a safety measure, a bi-metallic thermostat installed in
Number of thermocouples 127
the upper hot block prevents the temperature exceeding
Maximum hot side temperature 250 °C
200 °C. It should be noted that the actual temperature dif-
Maximum cold side temperature 175 °C
ference experienced by the semiconductor pellets in the
Open circuit voltage 9.93 V
TEGs will be lower than that measured in the experiment
Matched load output voltage 4.96 V
due to various contact resistances.
Matched load output current 2A
During thermal cycling, the power generated by the TEG
Matched load resistance 2.49 Ω ± 15%
module is consumed by an Elektro-Automatik EA-EL 9080-
Matched load output power 9.9 W
45 T electronic load in constant current mode. The output
voltage of the module is recorded using an NI-DAQ 9215,
a 16-bit analog-to-digital converter (ADC) with a range
of ± 10 V and an uncertainty of 0.02% of reading at room supplied with a small direct current (DC), a small tem-
temperature. The module’s current is indirectly recorded perature gradient is generated across the module due to
by measuring the voltage drop across a 0.04 Ω ± 1% sense the Peltier effect, as well as a voltage difference across the
resistor via an NI-DAQ 9219, a 24-bit ADC with a range terminals. This voltage is comprised of a resistive heating
of ± 125 mV and an uncertainty of 0.1% of reading at room component VJoule and a Peltier effect-induced temperature
temperature, resulting in a current reading with maximum difference component VSeebeck [28]. The dimensionless fig-
uncertainty of ± 0.02 A, and a power measurement maxi- ure of merit ZT at ambient temperature can be determined
mum uncertainty of ± 1.1%. from Eq. (14).
The experimental results uncertainty arises from the
VSeebeck
measured parameters of temperature, electrical resistance, ZT = (14)
and voltage. In accordance with the study of Huang et al. VJoule
[27], if the experimental result R is a function of small Under the Harman test, the TEG is connected to an
variations of n independent variables, vi , the uncertainty external power supply providing a constant 10 mA DC
( wR ) can be expressed as: current. Upon reaching a stable voltage output, the power
√
√ n ( )2 supply is switched off and the voltage decay is observed
until the module reaches thermal equilibrium. As illus-
√∑ 𝛿R ( )2
wR = √ 𝛿vi (13)
i=1
𝛿vi trated in Fig. 2(a), VJoule is determined as the difference
between the exponentially decaying Seebeck voltage and
All calibrated DAQ modules are connected to the NI the steady-state voltage. The test must be conducted out-
LabVIEW programme via an NI-cDAQ 9174 chassis. The side of the experimental set-up and therefore can only be
heater block and chiller set-point temperatures are PID performed pre- and post-cycling. The test is performed
controlled through state machine architecture employed at least ten times for each TEG sample and the average is
by a LabVIEW virtual instrument (VI) to regulate the taken for the estimated value of ZT .
heating and cooling times, with the Ziegler-Nichols tun- The characterisation test evaluates the performance of
ing method implemented to determine the parameters of each TEG module before the initiation of thermal cycling
the PID control. and after every 50 thermal cycles by maintaining a fixed
The TEG modules investigated in this study were manu- temperature difference across the module and increas-
factured by European Thermodynamics, model GM250- ing the electronic load’s current draw from 0.5 A to 1.6
127–14-10, with a cross-sectional area of 40 × 40 m ­ m2 A. Joule heating is induced by this variation in current,
and containing 127 thermocouples. The properties of the with the hot side temperature maintained at ± 2 °C of the
modules are summarised in Table 2. desired set-point. During the first study, the hot side was
All TEG samples were subjected to three performance cycled between 50 °C and 165 °C for all modules with the
evaluation tests to examine the effect of the thermal cold side temperature fixed at 30 °C. For the investigation
cycling on their output parameters. Under the Harman of the influence of maximum cycling temperature, hot side
test, the material properties of the module can be non- set-point temperatures of 170 °C, 180 °C and 190 °C were
destructively evaluated both pre- and post-cycling. When applied, with the cold side temperature fixed at 25 °C. Two

13
Heat and Mass Transfer

Fig. 2  (a) Example of a TEG

voltage response during Harman
test (b) Thermal cycle profiles
for maximum hot side tempera-
ture investigation (c) Determina-
tion of TEG open circuit voltage
VOC and internal resistance R
from the characterisation test,
and (d) TEG output power pre-
thermal cycling as a function of
electronic load resistance RL

samples were tested at each temperature set-point. The maximum set-point temperature, under a constant current
heating profile for each of these set-point temperatures is draw of 1.4 A. Upon reaching the set-point temperature,
illustrated in Fig. 2(b). the desired temperature difference is maintained for at least
The TEG open circuit voltage VOC can be determined as 60 s to account for fluctuations arising from the Peltier,
the y-intercept from a plot of TEG voltage against current, Joule, and Thomson effects. The voltage and current of
while the internal resistance R is taken as the modulus of both the TEG module and electronic load are recorded,
the gradient of a line of best fit applied to the data, as illus- as well as the heating time required to meet the set-point.
trated in Fig. 2(c). The maximum TEG output power Wmax in Upon reaching user defined limits for the hot side mean
Fig. 2(d) occurs when the resistances of both the module and temperature (< 0.3 ℃) and its standard deviation (< 0.1 ℃),
electronic load are equal. As detailed by Hsu et al. [29] for the cooling phase of the thermal cycle is initiated. The
real test conditions, the effective Seebeck coefficient 𝛼eff can average duration of the thermal cycle profiles employed
be determined as the ratio of the open circuit voltage of the during the investigation, including the average heating and
TEG VOC and the temperature difference maintained across cooling times, are summarised in Table 3. As a safety pre-
the module’s surfaces: caution, and due to the automation of the testing procedure,
testing ceased when the maximum power generated by the
VOC
𝛼eff = (15) TEG fell below half of its pre-cycling output. This automa-
T H − TC tion was implemented to mitigate against the TEG recovery
Under the conditions of the thermal cycling test, the hot effect when thermal cycling is interrupted, as observed by
side of the TEG is cycled between 50 °C and the required Merienne et al. [18].

Table 3  Thermal cycle profile Maximum Cycle Average Average Average Cooling Average Cooling Total Cycle
parameters Temperature [°C] Heating Time Heating Rate Time [s] Rate [°C/s] Duration [s]
[s] [°C/s]

165 (TEGs 1 – 6) 154 0.75 660 0.17 940

170 (TEG 7, 8) 169 0.71 691 0.17 984
180 (TEG 9, 10) 182 0.71 699 0.19 1016
190 (TEG 11, 12) 205 0.68 734 0.19 1061

13
 Heat and Mass Transfer

4 Results of 14% and 30% after 150 cycles and 200 cycles respec-
tively. Thermal cycling ceased for both samples after 300
4.1 Single set‑point temperature study cycles. More gradual power reductions were observed for
TEG 1, TEG 4 and TEG 6, with ‘breakdown’ occurring
Characterisation and thermal cycling test results for all after 300, 350 and 450 cycles respectively. The substan-
samples investigated during the single set-point tem- tial increase in the modules’ internal resistance as shown
perature study are presented in Fig. 3. The normalised in Fig. 3(b) and decreased effective Seebeck coefficient
maximum output power (Wmax,norm ) of the TEGs and their of Fig. 3(c) corresponding to these ‘breakdown’ events
normalised internal electrical resistance ( Rnorm ) are pre- may be indicative of internal structural damage through
sented relative to their pre-cycling values. Table 4 sum- the formation of micro-cracks at the interface between the
marises the modules’ pre- and post-cycling characteristics, thermocouples and the conductive copper substrate, in line
including the ZT values as determined from the Harman with the findings of Hatzikraniotis et al. [10]. Damage
test. Despite nominally identical properties for all sam- to the TEG’s structure as a result of thermal cycling was
ples with very similar ZT values pre-cycling for TEGs investigated through microscopic imagery of the leg-solder
1–5, significant variation in their performance character- interface, as illustrated in Fig. 4. The formation of a crack
istics was determined. As illustrated in Fig. 3(a) decreas- in a thermocouple leg of TEG 5 is evident, emanating from
ing maximum output power was observed as the number the soldered connection at the copper substrate and prop-
of thermal cycles increased, as expected. Furthermore, agating toward the opposing leg-solder interface. More
rapid decreases in output power were experienced by all substantial damage post-thermal cycling was observed in
samples, in line with the ‘breakdown’ in performance as TEG 6, with through-thickness fracture of a thermocou-
outlined by Hori et al. [9]. However, despite their similar ple leg resulting in the failure of the entire TEG. Further
characteristics pre-cycling, the TEG modules experienced indication of the damage to the internal structure of the
this event at varying cycle numbers. The maximum power TEGs because of thermal cycling was the inability of the
generated by TEG 2 was significantly reduced after only electronic load to draw the maximum set-point current
200 cycles, with the minimum power threshold of 50% from the module during the final characterisation test
reached after 350 cycles. More extreme behaviour was performed. Reductions in ZT were determined for TEGs
exhibited by TEG 3 and TEG 5, with reduced output power 1–5 upon completion of thermal cycling, dominated by

Fig. 3  Performance of all TEG

samples from the single set-
point temperature investigation
characterisation tests including
(a) normalised maximum output
power (b) normalised internal
electrical resistance (c) effective
Seebeck coefficient and (d) nor-
malised output power from the
thermal cycling test

13
Heat and Mass Transfer

Table 4  Characteristics of the Pre-cycling Post-cycling

TEG samples investigated for
the single set-point temperature VOC [V] 𝛼eff [V/K] Rpre [Ω] Wmax [W] ZTpre ZTpost ZTdecrease Rpost [Ω]
study. Maximum uncertainties ± 0.02% ± 0.17% ± 1.2% ± 1.1% ± 1.4% ± 1.4% ± 1.2%
for each parameter are presented
TEG 1 5.95 0.0440 1.87 4.73 0.594 0.303 49% 2.39
TEG 2 5.78 0.0428 1.90 4.40 0.580 0.416 28% 2.59
TEG 3 5.81 0.0430 1.95 4.34 0.597 0.471 21% 2.54
TEG 4 5.86 0.0434 1.90 4.53 0.596 0.342 43% 2.20
TEG 5 5.72 0.0423 2.03 4.03 0.602 0.359 40% 3.25
TEG 6 5.83 0.0430 2.01 4.21 –a 0.079 – 2.83
a
Value for ZTpre unavailable due to hardware failure

the increased Joule voltage VJoule arising from the rise in TEG 3 approached zero during a single cycle during thermal
the TEG modules’ internal electrical resistance. TEG 1 cycling as a result of poor electrical connections to the DAQ
was found to have experienced the greatest ZT decrease of module. Upon rectification, they returned to values in line
49%. A hardware failure prevented the determination of a with their preceding and proceeding cycles.
ZT value for TEG 6 pre-cycling; however, the substantial
degradation of this module was evident from the low value 4.2 Maximum cycle temperature study
post-cycling.
This degradation in performance is further apparent Figure 5 presents the results from the characterisation and
from the modules’ output power during thermal cycling, thermal cycling testing of all samples (TEGs 7—12) investi-
normalised by the output power recorded after the first gated during the maximum set-point temperature study, with
thermal cycle, as shown in Fig. 3(d). All samples exhibited both the maximum power and internal electrical resistance
reduced output as cycling increased, in line with the results values normalised with respect to their pre-cycling values.
of their respective characterisation test. Upon occurrence The characteristics of the modules pre- and post-cycling are
of performance ‘breakdown’, fluctuations in output power summarised in Table 5. The ZT values for the TEG samples
between successive cycles were observed as the module’s before the initiation of thermal cycling were in line with
internal structure deteriorated. For TEG 1 and TEG 4, the TEGs 1—6. As in the single set-point temperature inves-
output power appeared to stabilise after the initial ‘break- tigation, all modules experienced a sudden ‘breakdown’ in
down’ point, before experiencing additional material dam- performance after varying number of cycles, with signifi-
age and further decreases in performance. In contrast, both cant reductions in the maximum generated power as illus-
TEG 2 and TEG 5 experienced continuous deterioration in trated in Fig. 5(a). The occurrence of this decreased output
their output after the initial performance drop. Reductions did not appear to correlate with the maximum temperature
in the heating time required for all modules to reach their applied to the modules. The power reduction of TEG 7 and
set-point temperature were observed for increasing thermal TEG 8, both cycled to a maximum temperature of 170 °C,
cycle number, which we believe to be indicative of lower was observed after 250 cycles, in comparison to after 400
material thermal conductivity resulting from internal crack cycles for TEG 11, which experienced a greater hot side
formation. The normalised power output for both TEG 2 and temperature of 190 °C. Furthermore, the generated power of

Fig. 4  Microscopic images of

thermoelement legs post-
thermal cycling, illustrating
the presence of a crack in TEG
5 leg (left) and the through-
thickness failure of a TEG 6 leg
(right)

13
 Heat and Mass Transfer

Fig. 5  Performance of all TEG

samples from the maximum set-
point temperature investigation
characterisation tests including
(a) normalised maximum output
power (b) normalised internal
electrical resistance (c) effective
Seebeck coefficient and (d) nor-
malised output power from the
thermal cycling test

the modules subjected to a hot side temperature of 180 °C, the application of insufficient clamping pressure on TEG 12
i.e., TEG 9 and TEG 10, dropped after 350 and 250 cycles at the beginning of testing, reduced output properties were
respectively. determined as a result of high thermal contact resistance.
The rate of performance deterioration post-‘breakdown’ Upon correction of the clamping pressure after 50 cycles,
appears to be affected by the set-point temperature, with the module’s properties were in line with the other samples
more rapid degradation observed for higher set-point investigated. The ‘breakdown’ event for this sample was
temperatures. TEG 7’s generated power remained above found to occur after 300 cycles.
the 50% output threshold for a further 200 cycles, while The sharp increase in internal resistance for all mod-
thermal cycling ceased after only 100 additional cycles for ules as illustrated in Fig. 5(b) corresponded to the occur-
TEG 11 with a 30% decrease in output power across these rence of their individual ‘breakdown’ events, indicative
cycles. This increased degradation rate is further evident of material degradation at the contact interface. The
in the modules’ normalised power outputs during thermal greatest increase in post-cycling resistance of 73% was
cycling, as presented in Fig. 5(d). These observations are in experienced by TEG 8; in comparison, TEG 11 exhibited
line with the findings of Ding et al. [17], in which greater a resistance increase of 35%, despite being subjected to
performance deterioration was observed for modules oper- the highest set-point temperature. The average effective
ated closer to their maximum operating temperature. Due to Seebeck coefficient (Fig. 5(c)) remained constant during

Table 5  Characteristics of Pre-cycling Post-cycling

the TEG samples investigated
for the maximum set-point VOC [V] 𝛼eff [V/K] Rpre [Ω] Wmax [W] ZTpre ZTpost ZTdecrease Rpost [Ω]
temperature investigation. ± 0.02% ± 0.17% ± 1.2% ± 1.1% ± 1.4% ± 1.4% ± 1.2%
Maximum uncertainties for each
parameter are presented TEG 7 6.37 0.0439 2.24 4.55 0.594 0.478 20% 3.56
TEG 8 6.09 0.0420 2.09 4.45 0.591 0.368 38% 3.61
TEG 9 6.57 0.0424 2.25 4.81 0.580 0.254 56% 2.78
TEG 10 6.60 0.0426 2.10 5.16 0.584 0.326 44% 3.31
TEG 11 7.17 0.0435 2.28 5.65 0.596 0.399 33% 3.07
TEG 12 6.29 0.0381 2.26 4.39 0.596 0.287 52% 2.62

13
Heat and Mass Transfer

Fig. 6  Thermal cycling (a) heat-

ing times and (b) cooling times
for TEGs, normalised by the
heating/cooling time for the
fiftieth thermal cycle. Two TEG
samples for each hot side set-
point temperature are presented

the initial period of thermal cycling, before decreasing in 5 Conclusion

response to module deterioration as a reduced open cir-
cuit voltage was generated across the terminals. Examin- The performance characteristics of 12 thermoelectric gener-
ing the post-cycling dimensionless figure of merit values, ator (TEG) modules of nominally identical properties under
the largest decrease was observed for TEG 9, which may thermal cycling conditions was experimentally investigated.
have been expected due to its subjection to the great- For 6 samples, the cold side temperature was fixed at 30 °C
est number of thermal cycles. For the samples which while the hot side was cycled between 50 °C and 165 °C,
underwent 500 cycles, TEG 12, subjected to the highest with an average heating time (rate) of 154 s (0.75 °C/s). For
set-point temperature, experienced a decrease in ZT of a further 6 samples, the cold side temperature was fixed at
52%, indicating the deleterious effect of thermal cycling 25 °C and the hot side temperature was varied from 50 °C
at elevated temperatures. to set-points of 170 °C, 180 °C and 190 °C, corresponding
to average heating times (rates) of 169 s (0.71 °C/s), 182 s
(0.71 °C/s) and 205 s (0.68 °C/s) respectively.
4.3 Analysis of heating and cooling times Performance degradation of all samples was observed with
an increasing number of thermal cycles, with maximum out-
The heating and cooling times for the thermal cycle pro- put power reductions between 36% and 72% in combination
files investigated in the study are presented in Fig. 6 at 50 with increased internal electrical resistances of 16% to 73%.
cycle intervals. As the heating time for the first thermal The output power exhibited a sudden, significant decrease or
cycle is longer due to heating from ambient conditions, ‘breakdown’ consistent with the findings of previous stud-
the times are normalised to those measured at the fifti- ies, which occurred at cycle numbers which varied between
eth cycle. Two datasets are shown for each maximum set- samples. Furthermore, the heating times were observed to
point temperature. There is a general decrease in the heat- decrease with an increasing number of thermal cycles, while
ing time with an increase in the number of thermal cycles, the cooling times increased. This is attributed to a decrease
indicating that the TEG presents a larger thermal resist- in effective thermal conductivity of the TEG samples. This
ance to heat throughput, and therefore a shorter period degradation in performance was attributed to the formation
of time is required to reach the desired set-point hot side of micro-cracks at the interface of the p-n thermocouples
temperature. The cooling times increase as it becomes and the conductive material to which they are attached.
more difficult to extract the heat through the sample. This Microscope imaging identified evidence of damage to mul-
is indicative of a decrease of thermal conductivity of the tiple samples. This separation equates to significant internal
TEG, likely brought about by material degradation and structural damage of the TEGs. While no correlation was
structural deterioration such as that shown in Fig. 4. Both found between the occurrence of these significant degrada-
the heating and cooling times show the greatest change tion events and the magnitude of the maximum cycle set-
after the ‘breakdown’ has occurred, which reinforces point temperature, more rapid performance deterioration was
the belief that the TEG fails through internal damage. observed post-‘breakdown’ for those samples exposed to the
Wang et al. [8] predicts that interface damage growth can higher set-point temperatures. In such cases, the temperature
be divided into three stages: (i) microcracks grow and gradients through the semiconductor pellets of the TEG are
nucleate into macrocracks, (ii) macrocracks propagate and the largest. The somewhat stochastic nature of the point of
cause interface delamination, and (iii) delamination leads ‘breakdown’ suggests that existing intrinsic material and/or
to structural failure. structural defects in the samples, perhaps resulting from the

13
 Heat and Mass Transfer

manufacturing processes, play a significant role in deter- need to obtain permission directly from the copyright holder. To view a
mining the lifespan of TEGs. However, additional study of copy of this licence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.
TEG module performance under thermal cycling, and post-
breakdown material and structural analysis, is required to
better determine this relationship. References
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