Energy 233 (2021) 121113
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Energy
journal homepage: www.elsevier.com/locate/energy
Optimized output electricity of thermoelectric generators by matching
phase change material and thermoelectric material for intermittent
heat sources
Yuanyuan Tian a, Anbang Liu b, Junli Wang a, Yajie Zhou a, Chengpeng Bao a, Huaqing Xie a,
Zihua Wu a, Yuanyuan Wang a, c, *
a
b
c
School of Environmental and Materials Engineering, Shanghai Polytechnic University, 2360 Jinhai Road, Shanghai, 201209, China
School of Energy and Power Engineering, Nanjing University of Science & Technology, Nanjing, 210094, China
Shanghai Engineering Research Center of Advanced Thermal Functional Materials, 2360 Jinhai Road, Shanghai, 201209, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 18 November 2020
Received in revised form
25 May 2021
Accepted 29 May 2021
Available online 31 May 2021
Thermoelectric generators (TEGs) are usually working in intermittent heat source environments, and
thus the phase change material (PCM) has been widely adopted in to maintain relatively stable temperature difference. The property matching between the PCM and the TEGs is one of the crucial problems
to influence the performance of the PCM-TEG system. In this work, the influence of the phase change
temperature of the PCM on the output power and generated electricity of PCM-TEG system is studied.
Classic Enthalpy model and three-dimensional coupled thermo-electric equations are applied to study
the heat transfer and energy conversion mechanisms. Our results show that the output electric energy of
a PCM-TEG system can be optimized by tuning the phase change temperature of PCM. The total
generated electricity can be enhanced as large as 15.6% by matching the PCM with the thermoelectric
properties of the thermoelement. Moreover, by comparing three cases with different thermoelectric
materials, we give relationship between the optimal phase change temperature of PCM and the temperature for maximum figure of merit (ZT) of the thermoelement, which provides a selection criterion of
PCM for TEG module. Our work could be helpful to realize further high efficiency thermoelectric generators for intermittent heat sources.
© 2021 Elsevier Ltd. All rights reserved.
Keywords:
Thermoelectric generator
Phase change material
Output power
Electricity generation
Energy harvesting
1. Introduction
In the background of energy shortage all over the world in
recent years, thermoelectric generator (TEG), a kind of solid-state
energy conversion device that can convert low grade heat into
electricity directly, has attracted increasing interest. Regarding the
unique advantages including compact construction, no moving
parts, long service life, very low maintenance cost, no leakage of
liquid, it has shown great application potential in aerospace [1],
solar power generation [2], waste heat utilization [3] and ocean
power generation [4]. High-performance TEGs not only rely on the
availability of high-quality TE materials, but also require efficiency
and feasible TEG devices using those existing TE materials [5]. Large
* Corresponding author. School of Environmental and Materials Engineering,
Shanghai Polytechnic University, 2360 Jinhai Road, Shanghai, 201209, China.
E-mail address: wangyuanyuan@sspu.edu.cn (Y. Wang).
https://doi.org/10.1016/j.energy.2021.121113
0360-5442/© 2021 Elsevier Ltd. All rights reserved.
and stable temperature difference between hot- and cold-ends is
pursued to enhance the performance of TEGs. However, the TEGs
are usually working under transient or periodic operating condition
mainly determined by imposed heat sources, such as automobile
exhaust [6,7], waste heat of the photovoltaic cell [8] and so on.
Although the efficiency can be enhanced by periodically input
thermal power, the fluctuation of output power induced by transient or periodic hot sources lead to inconveniency for application
[5,9e12]. A TEG system with a long-time sustainable and stable
working is required in transient operating condition.
Phase change materials (PCMs), which has numerous advantages such as high density, high phase change latent heat, stable
temperature when absorbing and releasing heat, is a feasible mean
to maintain the relatively stable temperature difference between
the hot- and cold-ends in TEGs. A lot lieteratures have disccused the
PCM-TEG coupled system. Some works focused on the couple
method between the PCM and TEG modules, one of which is that
PCM is sandwiched between the heat source and the hot-end of the
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
P
E
U
m
in
PCM
C
H
L
p
l
s
a
1
ZT
TEG
a
Nomenclature
Symbols
T
Q
T
t
I
R
H
q_
k
r
C
h
f
r0
C0
[P]
J
½k0 [ε]
[s]
f
[S]
DT
Temperature
Heat energy
Average temperature
Time
Current
Resistance
Enthalpy
Heat generation rate per unit volume
thermal conductivity of the PCM
density of the PCM
Heat capacity
latent heat
Phase ratio
Density of thermoelectric material
Specific heat of thermoelectric material
Peltier coefficient
Electric current density
Thermal conductivity matrix of thermoelectric
material
Dielectric permittivityf
Electrical conductivity matrix
Scalar electric potential
Seebeck coefficient matrix
Difference between the optimal phase change
temperature and the temperature for maximum of ZT
Output power
Total electric energy
Voltage
Melting point
Absorb in
Phase change materials
Cold-end
Hot-end
Load
Phase change region
Liquid
Solid
Thase change radius
End time of the cooling period
Figure of merit
Thermoelectric generator
Average
Superscript
max
Maximum
O
Optimal
Abbreviation
TEG
Thermoelectric generator
TE
Thermoelectric
PCMs
Phase change materials
ZT
Figure of merit
PCM-TEG Phase change material- Thermoelectric generator
be determined by the temperature for maximun ZT of the
thermoelement.
In this work, we will study the influence of the phase change
temperature of PCMs on the generation performance of the
coupling system to find the optimal phase change temperature. The
classic Enthalpy model and three-dimensional coupled thermoelectric equations based on the finite-element method are
applied to calculate the generated electricity. Three cases with
different temperatures of hot source are considered, which are
550 K, 800 K and 950 K, respectively. Furthermore, the relationship
between the optimal phase change temperature of PCMs and the
temperature for maximum ZT of the thermoelectric material will be
given to guide the selection of optimal PCM for the PCM-TEG
system.
TEG [13e16]. This coupling structure affects the power generation
performance of TEG since heat transfers from the hot source to the
hot-end of the TEG by crossing the PCM. Then Jo et al. [17] and Liu
et al. [18] proposed a new type of couple method with PCMs around
the thermoelement, which improves the performance of the system since the PCMs and thermoelement contact with the heat
source simutaneously. The properties of PCM, including the thermal conductivity, latent heat, volume, and phase change temperature, are also crucail to determin the performance of the PCM-TEG
system. Some works found that PCMs with high thermal conductivity can greatly improve the thermal energy utilization of TEGs
since the heat transfer rate from the heat source to the hot-end of
TEGs is improved [13e15]. Carneiro et al. [16] and Elefsiniotis et al.
[19] found larger latent heat of the PCM is beneficial to obtain larger
output power of the PCM-TEG system since more heat energy can
be convert into electricity by TEG. Zhu et al. [20] studied the thermal conductivity, phase transition temperature and mass of PCM on
the performance of PCM-TEG power generation, and found
maximum output electricity can be generated when phase change
temperature approximately equates the average temperature of the
hot- and cold-ends of thermoelements. Although these literatures
give trends for choosing optimized PCM to enhance the peformance
of the PCM-TEG system, the selection method of phase change
temperature is still obscure and needs further investigation. In
PCM-TEG system, the PCM provides heat to the hot-end of TEG
during the phase change peorid once the hot source is removed. To
assure the thermelectric materials work in most efficiency condition, the temperature for maximum figure of merit (ZT) should lie
within the temperatures of hot- and cold-ends of TEG. The phase
change temperature of the PCM and the temperature for maximun
ZT of the thermoelement must have stronge correlation. Therefore,
the selection of optimal phase change temperature of PCM shoud
2. Models and methods
In Fig. 1 (a), the model of a PCM-TEG system is proposed, which
is composed of a TEG with a single leg and a PCM module wrapping
around the hot-end of the thermoelement. The spatial coordinate is
also labeled in Fig. 1 (a), where the plane of the cold-end of TEG is
the x-y plane and the direction from cold-to the hot-end is the zdirection. All the sizes can be found in the side view figure (Fig. 1
(b)). The length and width of the PCM are 20 mm and 5 mm
respectively, while the corresponding sizes of the thermoelement
are 5 mm and 20 mm, respectively. The depths of PCM and TEG are
20 mm and 5 mm respectively. Due to long enough contact time
with the hot source, PCM reaches heat equilibrium and the temperature of all the part within PCM equals to that of the hot source.
After removing the hot source when is defined as time zero (t ¼ 0),
the PCM with phase change temperature Tm performs as heat
source and provides heat energy Qin to the TEG. Consequently, the
2
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Now the temperature distribution of the PCM can be obtained
based on Eq. (3) once the enthalpy function is obtained by solving
Eq. (1).
The coupled thermoelectric equations are applied to describe
the TEG, which can be written as [22,23].
r0 C 0
hYi vT
þV
, J V , ð½k0 , VTÞ ¼ q_
vt
vf
þ V , ð½s , ½S , VTÞ þ Vð½s , VfÞ ¼ 0
V ½ε , V
vt
temperature of the PCM decreases gradually and a temperature
distribution exists within PCM. The average temperature of PCM is
labeled as T PCM . All surfaces exposed to the environment except the
cold-end of the TEG are summed to be heat insulated and the
thermal convection and radiation are neglect, which can be realized
approximately by using heat insulating materials at these surfaces
in experiments. When the temperature of the cold-end TC is lower
than that of the hot-end TH, a current I will be generated in close
circuit by the Seebeck effect once a load RL is applied. The external
resistance always equals to the internal resistance of the TEG to
maximize the output power of TEG.
The classic Enthalpy model is used to describe the transient heat
transfer of the PCM module. The differential equation about the
enthalpy field H (x, y, z, t) of the PCM can be expressed as [21].
P ¼ UI
E¼
Pdt
(7)
t¼0
where t1 is the end time of the cooling period when the PCM-TEG
system reaches heat equilibrium with the environment.
(1)
3. Results and discussion
In the intermittent hot source environment, the PCM storages
heat energy when the heat source is in working state, and provides
heat to TEG module once the heat source stops working. We now
consider the performance of the PCM-TEG system once the heat
source is removed and the PCM acts as the hot source. In Sec. 3.1,
the computational model is firstly verified. We study the influence
of the phase change temperature of PCMs on the output power and
total electric energy generated of PCM-TEG system to find the
optimal phase change temperature of the PCM in Sec 3.2. Three
temperatures of hot source are considered. Consequently, three
typical thermoelectric materials are applied and three series of
PCMs with appropriate phase change temperature are chosen
accordingly. Then in Sec. 3.3, the relationship between the optimized phase change temperature of PCM and the temperature for
maximum ZT to optimize the output electricity of the system is
studied by comparing the three cases with different temperature of
the hot sources. The temperature of the cold-end TC is fixed to be
room temperature (300 K) all throughout this work.
(2)
where Cp ¼ ðCl þCs Þ =2 is equivalent heat capacity in phase change
region, Cl and Cs are the specific heat of liquid and solid, respectively. fl is the liquid phase ratio. Then the temperature can be
derived as a function of enthalpy field:
8
>
H Hs
>
>
;
H Hs
>
>
Cs
>
>
>
>
< H C T h=2
p m
; Hs H Hl
T Tm ¼
> Cp þ h=2Ta
>
>
>
>
>
H Hl
>
>
>
H > Hl
: Ta þ C ;
l
(6)
tð1
where q_ represents heat generation rate per unit volume, k is the
thermal conductivity of the PCM, r is the density of the PCM, and T
is the absolute temperature. Once the boundary and initial conditions are given, the enthalpy field can be numerically calculated.
The Enthalpy function also has relationship with the heat capacity C
and the latent heat h of phase change, which can be written as [21].
H ¼ Cp T þ hf l
(5)
where r0 is the density of thermoelectric material, C 0 is the specific
heat of thermoelectric material, [P] denotes Peltier coefficient, J
denotes the electric current density, ½k0 represents thermal conductivity matrix of thermoelectric material, [ε] is the dielectric
permittivity, f is the scalar electric potential, [s] is the electrical
conductivity matrix, and [S] is the Seebeck coefficient matrix.
Three-dimensional Finite-Element Method via TransientThermal and Thermal-Electric modules of ANSYS 19.0 software
are applied to numerically solve above coupled equations. The
instantaneous output current I and voltage U of the TEG can be
obtained. Then the instantaneous output power P and the total
electric energy E generated during the cooling period are calculated
by the following equations:
Fig. 1. (Color online) (a) Three-dimensional schematic and (b) side view of the PCMTEG system, where a single leg TEG is wrapped by a PCM module around the hotend. The depths of the PCM and the TEG are 20 mm and 5 mm respectively. Heat
energy Qin is transfer from the PCM to the hot-end of TEG. When the temperature of
the cold-end TC is smaller than that of the hot-end TH, a current I will be generated in
the close circuit due to the Seebeck effect. (For interpretation of the references to
colour in this figure legend, the reader is referred to the Web version of this article.)
v
vT
v
vT
v
vT
vH
þ
þ
þ q_ ¼ r
k
k
k
vx
vx
vy
vy
vz
vz
vt
(4)
(3)
3.1. Verification of the computational model
In order to verify the mesh convergence of the finite element
approach applied in this work, the influence of the number of the
meshes on the output power of the TEG is studied. It can be seen
that the output power increases rapidly with the mesh number N
when N is smaller than 25000 and then keeps almost unchanging.
Therefore, in the following calculation, N is chosen to be larger than
where Tm is phase change temperature. Hs and Hl are the saturation
enthalpies of solid and liquid, whose expressions are Hs ¼
Cs ðTm Ta Þ and Hl ¼ Cl ðTm þ Ta Þ þ h, respectively. Ta ¼ ðTl Ts Þ =2
is the temperature of phase change radius, where Ts and Tl are the
start and end temperatures of phase change process, respectively.
3
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
35000. To further verify our computational model, we conducted a
numerical calculation following a published work [24]. The calculation condition and parameters are taken the same with those of
Fig. 3 in that work. We calculated the case with temperature difference between hot and cold ends being 150 K. The comparison
between our and their results is shown in Fig. 2 (b). It can be found
that the results are in good agreement, which indicates that our
calculation is effective and accurate.
Table 1
Physical parameters of the PCMs applied for the case with hot source temperature
550 K [26e28].
physical quantity (unit)
C (kJ/kg)
k (W/(mK))
r (kg/m3)
h (kJ/kg)
Solid
liquid
1.69
2.05
0.73
0.44
1550
1045
255
e
(b), respectively. In Fig. 4 (a), it can be found that for all cases with
different phase change temperature Tm, the average temperatures
of PCM T PCM firstly decrease dramatically from time zero, then
reach a phase change platform for a period, and finally decreases
fast again until reaching the cold-end temperature (300 K). For
example, for the case with Tm ¼ 413 K, T PCM decreases from 550 K to
414 K quickly from time zero due to heat transfer from PCM to TEG
and then reaches a platform at t ¼ 1500 s when the solidifying
process of PCM begins. Finally, from t ¼ 3600 s, T PCM continues
decreasing until reaches the cold-end temperature. In Fig. 4 (a), it
can also be found that the time for the phase change platform
becomes shorter with the increase of phase change temperature.
For example, when Tm ¼ 413 K, the duration time of phase change
platform is about 2100 s. When Tm is increased to 533 K, the platform lasts for only about 510 s. This result comes from that the heat
transfer velocity from the PCM to the TEG is faster when the temperature of the PCM is higher. Then the duration time of the platform becomes shorter with the increase of the phase change
temperature of the PCM. The property of the average temperature
of PCM determines the hot-end temperature and hence the
instantaneous output power of the TEG. What should be noticed
here is that once the latent heat h of phase change material varies,
the phase change platform will shift. However, the properties of
PCM with different phase change temperature in Fig. 4(a) still hold.
Fig. 4 (b) shows that the output power for the case with larger
phase change temperature is larger at the platform stage but the
duration time of the platform is much shorter. Consequently, in
consideration that the total output electricity is the integral of
output power via time (Eq. (7)), there must be an optimal phase
change temperature to maximize the total energy generated by the
PCM-TEG system. Fig. 4 (c) gives the total generated electric energy
of PCM-TEG system varying with different phase change temperature. The total output electricity E indeed has a maximum at
Tm ¼ 513 K, when the optimal value of E is about 15.6% larger than
O is introthat without optimization at Tm ¼ 413 K. The symbol Tm
duced to represent the optimal phase change temperature and thus
3.2. Influence of phase change temperature on electricity
generation of PCM-TEG system
We firstly consider the properties of PCM-TEG system when the
temperature of the hot source is 550 K. In order to assure the
max should locate
thermoelectric material to work efficiently, TZT
within 300 K and 550 K. A typical thermoelectric material
Bi0.5Sb1.5Te3 is applied, whose thermoelectric properties are based
on the experimental data and maximum ZT exists at 373 K [25]. By
max to represent the temperature for
introduce a symbol TZT
max is 373 K here. In
maximum ZT of thermoelectric material, TZT
consideration that the phase change temperature of the PCM
should be lower than the temperature of the hot source
(Tm < 550 K), seven values of phase change temperature are
adopted, which are 413 K, 433 K, 453 K, 473 K, 493 K, 513 K, 533 K,
respectively. Other parameters of the PCMs, including the specific
heat capacity C, thermal conductivity k, density r, and latent heat of
phase change h, are taken as the mid-value based on real experiment values, which can be found in Table 1.
We take one case with Tm ¼ 413 K as an example to show the
temperature distribution of the PCM-TEG system at t ¼ 1500 s in
the phase change stage. Fig. 3 (a) and (b) show the temperature
distributions of PCM and thermoelement modules, respectively. It
can be seen in Fig. 3 (a) that there is a temperature distribution
within PCM, where the temperature near to the contact interface
between PCM and thermoelement is relatively low. The average
temperature of PCM T PCM is 414 K through our calculation, which is
obviously lower than the beginning temperature (550 K) since the
heat has been transferred from the PCM to the TEG for 1500 s. Fig. 3
(b) shows that the hot-end temperature TH of the TEG is 409 K due
to heat absorption from the PCM and there is a gradually temperature decrease from the hot-end to the cold-end within the
thermoelement.
Then the properties of average temperature of the PCM (T PCM )
and output power (P) with varying time t are shown in Fig. 4 (a) and
Fig. 2. (a) Mesh convergence study for the calculated model used in this paper; (b) comparison between our numerical results and the results in Fig. 3 in a published work [24].
Solid curve and circle dots stand for their and our results respectively.
4
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Fig. 3. (Color online) Temperature distributions of (a) PCM module and (b) Thermoelement respectively for the case with hot source temperature 550 K and phase change
temperature 413 K at t ¼ 1500 s in the phase change stage. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this
article.)
Fig. 4. (Color online) Temperature dependences of (a) average temperature of PCM and (b) output power of PCM-TEG system and (c) influence of the phase change temperature on
the total output electricity when the temperature of the hot source is 550 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web
version of this article.)
5
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
O ¼ 513 Khere. Then the difference between the optimal phase
Tm
Table 2
Physical parameters applied of the PCMs for the case with hot source temperature
800 K [26e28].
O ) and the temperature for maximum of ZT
change temperature (Tm
max
O
max
(TZT ) is DT ¼ Tm TZT ¼ 140 K.
The existence of optimal phase change temperature to obtain
maximum total output electric energy can be further analyzed by
the time-dependent temperature distribution of the thermoelement, which can be found in Fig. 5. Three cases with relatively
smaller phase change temperature (Tm ¼ 413 K), optimal phase
change temperature (Tm ¼ 513 K), and relatively larger phase
change temperature (Tm ¼ 533 K) are given in Fig. 5 (a), (b) and (c)
respectively. Fig. 5 (a) shows that when Tm ¼ 413 K, although the
duration time that the temperature of the thermoelement is larger
than 350 K is longer (~5000 s), the temperature of the whole
thermoelement is relatively low. When Tm ¼ 533 K (Fig. 5 (c)), the
temperature of the thermoelement is the highest, but the maintenance time of high temperature is the shortest, which is only about
3000 s. For the case with optimal phase change temperature (Fig. 5
(b)), the temperature of the thermoelement is higher compared to
the result with smaller Tm and the cooling speed is not as fast as the
result with larger Tm. Therefore, when the phase change temperature is 513 K, the output electricity reaches maximum.
We now turn to consider the case with the hot source being
800 K. Another typical thermoelectric material Tl0.01Pb0.99Te is
applied, whose thermoelectric properties is also based on experimental work [29] and its maximum ZT exists at 660 K. Seven values
of phase change temperature Tm are adopted, which are 640 K,
660 K, 680 K, 700 K, 720 K, 740 K, 760 K, respectively. Other parameters of PCMs can be found in Table 2. The properties of average
temperature of the PCM (T PCM ) and output power (P) with varying
time t are shown in Fig. 6 (a) and (b), respectively. It can be found
that for all cases with different phase change temperature, the
trends of average temperatures of PCM T PCM and output power P
varying with time both have three stages: fast decrease from time
physical quantity (unit)
C (kJ/kg)
k (W/(mK))
r (kg/m3)
h (kJ/kg)
solid value
liquid value
1.17
1.38
0.50
0.95
2250
e
276
e
zero to the time when solidifying of PCM begins; a platform with
slightly decrease during the phase change period; final fast
decrease until the heat release process stops. Moreover, by
comparing cases with different phase change temperature, Fig. 6 (a)
and (b) also show that the duration time for the phase change
platform becomes shorter with the increase of the phase change
temperature of PCM (Tm). These results are accordant with the results shown in Fig. 4 when the hot source temperature is 550 K.
Then the total output electricity can be obtained by integrating the
output power via time. The total output electric energy is plotted as
a function of phase change temperature in Fig. 6 (c). It can be seen
that the total output electricity E has a maximum at 720 K for this
O ¼ 720 K). The optimal output electricity is about 2.4%
case (Tm
larger than that without optimization at Tm ¼ 640 K. Moreover, the
optimized phase change temperature is 60 K larger than the temperature for the maximum ZT (DT ¼ 60 K).
Similarly, we then study the case with the temperature of hot
source being 950 K. Thermoelectric material Mn15Si26e2%SiGe is
applied, whose thermoelectric properties is based on experimental
work [30] and the maximum ZT exists at 803 K. Seven values of
phase change temperature are adopted, which are 783 K, 803 K,
823 K, 843 K, 863 K, 883 K, 903 K, respectively. Other parameters of
PCMs can be found in Table 3. Fig. 7 (a) and (b) give the properties of
average temperature of the PCM (T PCM ) and output power (P)
varying with time t, respectively. As expected, the properties of
Fig. 5. (Color online) Temperature distribution of the thermoelement along z-axis varies with time t when phase change temperature of PCM Tm is (a) 413 K, (b) 513 K, and (c) 533 K,
respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
6
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Fig. 6. (Color online) Temperature dependences of (a) average temperature of PCM and (b) output power of PCM-TEG system and (c) influence of the phase change temperature on
the total output electricity when the temperature of the hot source is 800 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web
version of this article.)
matter the distribution of ZT, the optimal phase change temperature to obtain maximum total output electric energy always exists.
We summarize the optimal phase change temperature and the
corresponding temperature for maximum ZT in Table 4. Then we
O and T max as
can fit these data and give the relationship between Tm
ZT
follows
Table 3
Physical parameters applied of the PCMs for the case with hot source temperature
950 K [26e28].
physical quantity (unit)
C (kJ/kg)
k (W/mK)
r (kg/m3)
h (kJ/kg)
solid value
liquid value
1.41
1.56
1.13
1.73
2465
e
357
e
O
max
Tm
¼ 0:76TZT
þ 226:39K
average temperature of the PCM and output power are in accordance with those obtained in the other two cases. Consequently,
the total output electricity E also has a maximum at Tm ¼ 843 K as
shown in Fig. 7 (c). The optimal value of output electricity is about
1.4% larger than that without optimization at 903 K. The optimized
phase change temperature is 40 K larger than the temperature for
O ¼ 903 K, T max ¼ 803 K, and
maximum ZT for this case. That is Tm
ZT
hence DT ¼ 40 K.
(8)
Moreover, the difference between the optimal phase change
temperature and the temperature for maximum ZT (DT) can also be
max as follows:
fitted as a function of TZT
max
DT ¼ 0:23TZT
þ 226:93K
(9)
O and T max and the fitting curves.
Fig. 8 shows all the values of Tm
ZT
O increases with the increase of T max
It is interesting to find that Tm
ZT
max linlinearly. Consequently, DT decreases with the increase of TZT
early as well. The result can be understood as follows. In consideration that the temperature of the cold-end of TEG is fixed as
300 K, when the temperature of hot source is higher, the temperature gradient per unit length in thermoelement is larger. At the
3.3. Relationship between optimized phase change temperature of
PCM and the temperature for maximum ZT of thermoelectric
material
Based on the investigation in Sec. 3.2, it can be found that no
7
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Fig. 7. (Color online) Temperature dependences of (a) average temperature of PCM and (b) output power of PCM-TEG system and (c) influence of the phase change temperature on
the total output electricity when the temperature of the hot source is 950 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web
version of this article.)
Table 4
Optimal phase change temperature and corresponding temperature for maximum
ZT for three cases with different temperature of the hot source.
Hot source (K)
O (K)
Tm
max (K)
TZT
550
800
950
513
720
843
373
660
803
same time, higher temperature of hot source requires higher
temperature thermoelectric material to achieve better conversion
efficiency. Then the phase change temperature of the PCM should
max of the thermoelectric material to keep the
become closer to TZT
whole thermoelement lie in best working temperature for longer
time. Fig. 9 shows the time-dependent temperature distributions of
the thermoelement for the three cases with optimal phase change
temperatures. When the phase change temperature is 513 K (Fig. 9
(a)), the temperature of the thermoelement is around the temperature for maximum ZT during the phase change platform, which
assures the thermoelectric leg works in the best efficiency. When
the phase change temperature increases to 720 K (Fig. 9 (b)), the
temperature distribution of the thermoelement determines the
temperature for maximum ZT should lies closer to the phase
change temperature. Then for the case with phase change temperature 843 K, the temperature distribution of the thermoelectric
O ) (left
Fig. 8. (Color online) The dependences of optimal phase change temperature (Tm
hand side of the frame) and the difference between the optimal phase change temperature and the temperature for maximum ZT (DT) (right hand side of the frame) on
max ). (For interpretation of the references to colour
the temperature for maximum ZT (TZT
in this figure legend, the reader is referred to the Web version of this article.)
8
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Fig. 9. (Color online) Temperature distribution of the thermoelement along z-axis varies with time t for three cases with optimal phase change temperature Tm (a) 513 K, (b) 720 K,
and (c) 843 K, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
show the total generated electricity can be enhanced as large as
15.6% by choosing PCM with optimal phase change temperature.
Moreover, by comparing three cases with different temperature of
hot source, we also found that the optimal phase change temperature increases linearly with the increase of the temperature for
maximum ZT of the thermoelement, which provides a selection
criterion of PCM for TEG module with a certain thermoelectric
material adopted. Our work opens up new possibilities for
enhancing performance of PCM-TEG system in energy harvesting of
intermittent heat source.
leg determines the thermoelectric material whose maximum ZT
exists at 803 K is the best choice. Therefore, with the increase of the
phase change temperature, the temperature for maximum ZT
should become closer to the phase change temperature. The
optimal phase change temperature and the temperature for
maximum ZT are coupling to achieve maximum output electricity.
It should be noticed that other parameters of PCM and thermoelectric materials, such as the latent heat and thermal conductivity
of the PCM and the distribution of ZT around the maximum, also
affects the performance of the system. The linear relationship between the optimal phase change temperature and the temperature
for maximum ZT still exists except the gradient of the curve will
changes. Our work gives simple guides to select optimal PCM when
the thermoelectric properties of the thermoelement are known in
the PCM-TEG system.
Credit author statement
Yuanyuan Tian: Methodology, Software, Investigation, Writing
e original draft. Anbang Liu: Methodology, Investigation. Junli
Wang: Software. Yajie Zhou: Validation. Chengpeng Bao: Visualization. Huaqing Xie: Writing e review & editing. Zihua Wu:
Funding acquisition. Yuanyuan Wang: Conceptualization; Writing
e review & editing; Supervision; Funding acquisition.
4. Conclusion
In this paper, the influence of the phase change temperature of
PCM on performance the of PCM-TEG system which works in
intermittent heat source environment is studied. The classic
Enthalpy model and three-dimensional coupled thermo-electric
equations based on the finite-element method are applied to
calculate the output power and total output electricity of PCM-TEG
system in detail with three different hot source temperatures.
Three temperatures of hot source is considered as 550 K, 800 K and
950 K. Then three serials of phase change materials and three
typical thermoelectric materials are applied accordingly. We found
the optimal phase change temperature exists when relatively high
phase change temperature and the relatively long duration time of
the phase change platform are satisfied simultaneously. Our results
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grants No. 51876111. Z.W. would like to thank
the “Shu Guang” project supported by Shanghai Municipal
9
Y. Tian, A. Liu, J. Wang et al.
Energy 233 (2021) 121113
Education Commission and Shanghai Education Development
Foundation under Grant No. 18SG54.
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