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Article
Thermoelectric cyclic-thermal regulation: A
new operational mode of thermoelectric
materials with high energy efficiency
Yupeng Wang (王玉鹏), Xinzhi
Wu (吴新志), Mao Yu (于茂), ...,
Huan Li (李欢), Zuotai Zhang (张
作泰), Weishu Liu (刘玮书)
zhangzt@sustech.edu.cn (Z.Z.)
liuws@sustech.edu.cn (W.L.)
Highlights
A new operational mode,
thermoelectric cyclic-thermal
regulation, is first proposed
Its actual algebraic model is
derived based on the finite
difference method
It is employed in the gasseparation system, featuring
remarkable energy efficiency
An empirical figure of merit is
proposed to guide material
optimization in this mode
Thermoelectric materials, commonly used for power generation and refrigeration,
have an exciting hidden potential application: efficient thermal regulation. Our
study introduces a new approach called thermoelectric cyclic-thermal-regulation
mode, demonstrating how thermoelectric devices can significantly improve
energy efficiency when two objects are cycled between two temperatures.
Notably, they save energy consumption by 42% in gas-separation systems
compared with traditional electrical heaters. This work sets the stage for
developing practical applications and optimizing materials across various thermal
conditions and device modes.
Wang et al., Joule 8, 3201–3216
November 20, 2024 ª 2024 The Author(s).
Published by Elsevier Inc.
https://doi.org/10.1016/j.joule.2024.08.002
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Article
Thermoelectric cyclic-thermal regulation: A new
operational mode of thermoelectric materials
with high energy efficiency
Yupeng Wang (王玉鹏),1 Xinzhi Wu (吴新志),1 Mao Yu (于茂),1 Xuehua Shen (沈雪华),2
Shuaihua Wang (王帅华),1 Huan Li (李欢),1 Zuotai Zhang (张作泰),2,* and Weishu Liu (刘玮书)1,3,4,*
SUMMARY
CONTEXT & SCALE
The thermoelectric cyclic-thermal-regulation (TEcR) system was
defined as cyclical heat pumping between two vessels in a transient
mode, which has emerged as a new application in gas separation
and temperature-driven soft robots. Here, we provided systematic
theoretical fundamentals relative to the TEcR system and proposed
the determining factors and performance scales. We have also designed and fabricated a thermoelectric CO2-gas-separation system
based on low-temperature adsorption and high-temperature
desorption, verifying the feasibility of the TEcR system. Our experiments unequivocally demonstrate the significant potential of the
TEcR system, with energy consumption savings of 42% and cycle frequency improvements of 2.5 times compared with electrical heater
systems. We also proposed an empirical figure of merit to guide the
thermoelectric material optimization strategies for the TEcR application. Our work sheds light on the new application of thermoelectric materials, which would generate implications for a wide range of
industrial applications that use multi-plate thermal energy.
Thermal energy has been a vital
energy source throughout the
progress of human civilization.
Heat transfer preserves our body
temperature and enables the
creation of farming tools, which
lead to the Agricultural Age. Heat
transformation was the driving
force behind machinery during
the Industrial Age. Thermoelectric
materials can realize the direct
conversion between heat and
electricity, achieving the dual
purpose of heat transfer and
energy transformation. A novel
and more efficient heat-transfer
system, which utilizes a cyclical
heat-pumping arrangement
between two vessels, has a rapid
thermal response and a wide
range of potential uses. This
innovative system can save
electricity consumption by 42%
and increase the cycle speed by
2.3 times relative to traditional
systems, indicating extremely
promising applications for gas
separation, temperature-driven
actuators, and others.
INTRODUCTION
Thermal energy can be either transformed or transferred. Heat transformation is the
conversion of thermal energy to other forms of energy, such as electrical,1 mechanical,2 or chemical energy,3 whereas heat transfer entails the exchange of heat between two objects at different temperatures. Heat flow from a high temperature
to a lower temperature occurs passively, but heat flow in the opposite direction
(from cold to hot) is an active process requiring energy input. Thermal regulation involves both processes. Thermoelectric (TE) effects, describing the reversible direct
conversion between heat and electricity, have emerged as a promising means of utilizing thermal energy while meeting the sustainability demands of global energy.4–6
TE generators (TEGs), which utilize TE effects for the direct conversion of heat to
electricity, are commonly employed as durable electric power supplies for equipment in space,7 remote areas, and other harsh environments, and for energy recovery of low-to-medium-temperature waste heat from automotive exhaust,8,9 biomass
furnaces,10,11 and even the human body.12–15 Meanwhile, heat-transfer devices are
exemplified by TE coolers (TECs), an active cooling technology that consumes electricity. TECs have been commercialized in domestic refrigerators, which can cool
their contents to 5 C in a room-temperature environment (25 C).16 Multistage
TECs combined with traditional compression refrigeration can achieve ultra-low
temperatures (70 C).17 Another potential application of TECs is heat dissipation
in electronic chips,18 which is pertinent because the number of chips has sharply
Joule 8, 3201–3216, November 20, 2024 ª 2024 The Author(s). Published by Elsevier Inc. 3201
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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increased following Moore’s law.19 Additional applications of TEGs and TECs are reviewed in Champier20 and Zhao and Tan.21
Thermal regulation (or thermal management) is a broad field encompassing passive
heat transfer, active cooling, and heat storage. Thermal regulation plays vital roles in
preventing overheating of batteries in electric vehicles,22 dissipating heat from electronic devices,23 and regulating human body temperature.24 Regulation of thermal
energy is essential for optimizing the performance, improving the energy efficiency,
and ensuring the safety of industrial and scientific equipment. Thermal regulation requires a smart dual-mode device with both heating and active cooling capabilities to
attain and maintain the desired temperature of an object. TE regulators (TERs),
which incorporate TE materials for prompt and accurate temperature control,
reverse the direction of heat flow in response to a current reversal. Therefore,
TERs are widely applied in situations requiring strict temperature control within a
limited space. TERs can realize smart walls25 or windows26 in zero-energy buildings
combined with photovoltaic technology, woven textiles that maintain comfortable
temperatures in diverse temperature environments,27 an electronic skin that maintains constant body temperature in artificial limbs,28 and temperature sensing by
game players in virtual reality.29 Although the potential applicability of TERs
matches those of TEGs or TECs, further in-depth explorations of TERs are required.
A TE cyclic-thermal regulator (TEcR) periodically oscillates the temperature of a
target between two values. For instance, TEcRs control the thermal cycling process
of the polymerase chain reaction (PCR) in molecular biology.30 They also control the
temperature-swing adsorption cycling of mini-type fixed beds that separate gases in
particular environments and drive temperature-responsive soft robots for human
healing. By recycling the waste heat from a high-temperature object while heating
a low-temperature object, a TEcR can efficiently and simultaneously control the temperatures of two target objects. The target temperatures correspond to the denaturation and annealing temperatures in a PCR system, as well as the desorption and
adsorption temperatures in a gas-separation system. Unlike TEGs and TECs, which
operate under steady-state conditions, TERs must provide temperature control under constantly changing and transient conditions. This fundamental difference separates TERs from conventional heat-transfer methods. The transient characteristics
of TERs defy analysis through traditional steady-state heat-transfer equations, which
primarily explains the need for more in-depth research on TERs.
This study investigates the potential of TEcRs commonly employed in gas-separation systems, PCR systems, and similar systems. The transient characteristics of
TEcRs are predicted using a mathematical model based on the finite difference
method (FDM). Our theoretical study encompasses a well-defined set of operating
characteristics, an evaluation index of system performance, and application scenarios. Additionally, we compare the thermal performances of the TEcRs system
and an electrically heated temperature control system in a mini-type gas-separation
system developed for that purpose. Finally, we suggest strategies for optimizing the
TE materials of TEcR systems.
RESULTS AND DISCUSSION
Definition of the TEcR system
Figure 1A is a schematic of TE cyclic-thermal regulation by which two objects are
cycled between two temperatures. The heat-flow direction is periodically reversed
by changing the current direction in the TE device. By this mechanism, one object
3202 Joule 8, 3201–3216, November 20, 2024
1Department of Materials Science and
Engineering, Southern University of Science and
Technology, Shenzhen, Guangdong 518055,
China
2School of Environmental Science and
Engineering, Guangdong Provincial Key
Laboratory of Soil and Groundwater Pollution
Control, Southern University of Science and
Technology, Shenzhen, Guangdong 518055,
China
3Guangdong Provincial Key Laboratory of
Functional Oxide Materials and Devices,
Southern University of Science and Technology,
Shenzhen, Guangdong 518055, China
4Lead contact
*Correspondence:
zhangzt@sustech.edu.cn (Z.Z.),
liuws@sustech.edu.cn (W.L.)
https://doi.org/10.1016/j.joule.2024.08.002
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Figure 1. Schematics of the TEcR system and its mathematical model
(A) Equipment of the TEcR system and a temperature curve of the target object.
(B) Establishment of the FDM-based model.
(C) Validation of the TEcR model.
is heated while the other is cooled. Once the system has reached the cyclic-steady
state, the temperature changes in each cycle are identical, and the temperatures
of both objects oscillate between two cycling temperatures, Th* and Tc*, which
correspond to the desorption and adsorption temperatures, in a gas-separation system. Both Th* and Tc* depend on the cycling period tp. As tp approaches infinity, the
temperatures of the two objects approach the hot and cold limit temperatures (Th,lim
and Tc,lim, respectively) of the system, which are fixed under identical boundary conditions. In a fixed TEcR system, Th,lim and Tc,lim are essential parameters that prevent
the TEcR system from arbitrarily controlling the target cycling temperature. Furthermore, TEcR systems inevitably exchange heat with the surrounding environment.
This portion of heat dissipation, governed by the convection heat-transfer coefficient (h) and the ambient temperature (Ta), can be used to adjust the cycle temperature and limit the temperature of the TEcR system. Overall, the TEcR system reliably
and efficiently controls temperature cycling in PCR apparatus, gas-separation systems, and similar systems.
Controlled temperature cycling in a TEcR requires periodic reversal of the current,
necessitating the use of a transient model rather than a steady model. However,
the transient performance of TE devices is usually studied on discretized domains using the FDM31,32 or finite volume method (FVM),33 which is computationally intensive. Furthermore, as the FDM and FVM are non-transparent, the researcher cannot
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easily establish a direct correlation between the parameters and results. This section
establishes an FDM-based transient model for TEcR, albeit under some assumptions
that sacrifice accuracy to obtain an analytic expression. The aim is to improve the efficiency of TEcR performance evaluations while minimizing the computational
resources.
To simplify the TE leg calculation process, the developed model considers a single
leg. Convective heat transfer occurs at both the hot and cold sides of the TE leg,
and the surrounding surfaces are assumed to be adiabatic. Further assuming onedimensional energy flow, the temperature distribution within the TE leg is calculated as
Cr
vT
J2
= V$ðkVTÞ + e + Je TVS tJe VT
vt
s
(Equation 1)
where, C, r, S, s, k, and t are the specific heat capacity, density, Seebeck coefficient,
electrical conductivity, thermal conductivity, and Thomson coefficient of the TE material, respectively, t denotes time, and Je is the electric current density. In addition,
the TE leg is discretized into n pieces along the x axis (see Figure 1B). The governing
equation and boundary conditions of the TE leg in the transient state are given in
Equation S2. The temperature distribution in the TE leg is determined using the
FDM, and the transient temperature curve of the TE leg is estimated using Equation S7 (see Note S1 for detailed hypotheses and derivations).
The temperature in a TEcR system periodically varies on both sides of the TE device.
At the beginning and end of each cycle, the temperature at each end reverses while
the TEcR remains in the cyclic-steady state. Consequently, the high and low temperatures during the temperature cycling can be resolved under the following boundary
conditions:
(
Th ðt = 0Þ = Tc t = tp
(Equation 2)
Tc ðt = 0Þ = Th t = tp
The formula for the initial temperature (Equation S12) is complex, and the influence
of each parameter on the temperature is not intuitively obvious. Nevertheless, the
formula requires far fewer computing resources and time than the domain discretization method.
To establish the accuracy of the developed model, we compared the temperatures
obtained by the developed model, an FDM model, and an experimental study. Copper blocks, one placed at each side of the TE leg, act as the target whose temperature needs to be regulated (see schematic in Figure 1C). The TEcR model yields highly accurate results, and its temperature variation trends are consistent with those of
both the FDM model and experiments (see Figures 1C and S1). The model predicts
lower than observed temperatures when the cycling trends toward the cyclic-steady
state. This discrepancy is attributed to the ambient temperature, which rises during
the experiments but remains stable in the model calculation. The calculation assumes commercial n-type Bi2Te3 with the physical parameters presented in Figure S2. The convective heat-transfer coefficient, an essential parameter in the transient model, was evaluated as 21.9–28.6 W m2 K1 (Figure S3).
In previous studies, the steady-state performance was rapidly calculated using
Ioffe’s equation,34 but the transient-state performance could be evaluated only on
a discrete domain. The present analytical expression integrates the simplicity of
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Figure 2. Definition of evaluation index of TEcR system and validation of the model
(A) Diagram of heat fluxes in the TEcR system during a temperature cycle and plots of the evaluation indices over time.
(B) Comparisons of the mathematically modeled and experimental coefficients of performance and thermoregulation powers of the TEcR system.
(C) Comparison of temperature curves of objects periodically cycled at different periods and maintained at steady temperature (i.e., the limit
temperature). The TE material is commercial n-type Bi2 Te 3 , and all results are calculated under the default conditions (L = 2 mm, A obj = 25 mm 2 , F = 0.04,
T a = 20 C, where L denotes the length of TE leg).
the former with the precision of the latter, circumventing the need for extensive
computational resources and time investment.
Evaluation indices of the TEcR system
Figure 2A is a heat flux diagram of the TEcR system during temperature cycling. The
TE device transfers thermal energy from a high-temperature object (object-1 in Figure 2A) to a low-temperature object (object-2) while consuming electrical power
(PTE). Over time, the temperatures of object-1 and object-2 decrease and increase,
respectively, until the temperatures of both objects are reversed. Throughout this
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temperature variation process, the heat flux of each object encompasses both the
heat absorbed/released by the TE device (QTE-O) and the heat exchanged with the
surroundings (Qloss). These two heat fluxes affect the internal energy (ultimately
manifesting as a temperature change, DE = QTE-O Qloss) of each object. The
TEcR system attempts to simultaneously cycle the temperatures of both objects
with the same internal-energy change (EO1 = EO2 = E) and power consumption (w)
during one cycle. The parameters E and w are numerical integrals of the internal-energy change rate and power consumption, respectively, over one cycle period (Figure 2A). In this section, the efficiency, power, and limit-operating thermal conditions
of the system are evaluated in terms of coefficient of performance (COP), thermoregulation power (PTEcR), and limit temperature, respectively. Although this study preliminarily considers a single TE leg configuration, the model is easily extendible to
multi-TE leg systems (see Note S1).
COP of the TEcR system
The TE device is incorporated into the TEcR system as a heat switch, enabling heat
transfer between two objects. The COP, based on the ratio of heat transported to
energy consumed, evaluates the efficacy of a TEcR system. To obtain this evaluation
index, we divide the variation in internal energy of the target object (E) by the electricity consumed by the TE device (w) during one temperature cycle as follows:
COP =
E
w
(Equation 3)
The COP can also be analytically calculated using Equations S12–S16. These expressions are complex but highly accurate (Figure 2B). When determining the
COP from the experimental results, we considered the internal-energy variation
in half of the TE material. Nevertheless, the model may display a relatively large
error at small cycle periods (tp < 5 min) because the model is inaccurate during
the initial stages of temperature change. Notably, all COP values exceed 1 for
different currents and cycle periods (see Figure 2B), indicating that the TEcR system implements a more energy-efficient operating mode than the traditional
temperature-controlling method, which employs an electrical heater and a vapor-compression cooling system. The experimental results confirm the potential
application value of the TEcR system.
Thermoregulation power of the TEcR system
The thermoregulation power of the TEcR system (PTEcR), defined as the rate of internal-energy change during temperature cycling, is calculated as the ratio of internalenergy variation to the cycle period:
PTEcR =
E
tp
(Equation 4)
The high thermoregulation power of the TEcR is attributable to the fast temperature-conversion rate of the system, which shortens the time of reversing a comparatively large temperature difference. Note that PTEcR is distinct from the COP evaluation index, which measures efficiency. Here, we apply an analytical formula of
PTEcR (Equations S12 and S15) and verify its accuracy through experiments (Figure 2B). Both the COP and PTEcR decrease throughout the cycle period, but these
trends are reversed as the current increases. Thus, adjusting the cycle period can
enhance both the COP and PTEcR of the system. However, the TEcR system can
only cycle between a limited range of temperature differences, as discussed later.
When changing the current, the COP and PTEcR must be balanced to meet the demands of the application.
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Limit temperature of the TEcR system
The limit temperature, obtained by Equation S9, plays a vital role in a TEcR system. In
particular, it indicates the possible extent of temperature cycling in the system,
which helps assess whether a particular TE material meets the temperature cycling
requirements of the application. Because it represents the stable temperature at
an infinite cycle period, the limit temperature is affected by all parameters in the
TEcR model except the cycle period. In addition, it is substantially influenced by current (Figure S4). Therefore, enhancing the current can expand the cycling temperature range of the TEcR system. As the cycle period increases, the temperature difference between Th* and Tc* approaches that between the limit temperatures (see
Figure 2C), but owing to the temperature-dependent physical properties of the
TE material, Tc* is slightly lower than Tc,lim. Nevertheless, the steady-state temperature can quickly and usefully indicate the possible temperature-cycling range of
the system.
Operating characteristics of the TEcR system
This study aims to establish a highly accurate mathematical model of the TEcR system and its evaluation indices (COP, PTEcR, and the limit temperatures Th,lim and
Tc,lim). The evaluation parameters are influenced by the structural parameters (F, L,
and h), operating parameters (tp, I), and physical properties of the TE material.
The fill factor F defines the cross-section ratio of the TE material to the target object
(Aobj). The TE material design of the TEcR will be discussed later. This section focuses
on the operating characteristics of TEcR systems with various structures and operating parameters.
The cycling temperature of a fixed TEcR depends mainly on the operating parameters of the system, i.e., the current and cycle period. The average temperature of the
system during one temperature cycle will inevitably rise at high currents due to the
Joule effect. Therefore, the temperature difference is low at low average temperatures and increases at high average temperatures (Figure S5A). At low average temperatures, the COP is relatively high, while the PTEcR is low. To increase the temperature difference during the temperature cycling, one must increase either the cycle
period or the current, which raises the electricity consumption and reduces the COP,
especially when the high and low cycling temperatures are close to their steady-state
values (see Figure 3A). As PTEcR is sensitive to current, increasing the current can
markedly improve the thermoregulation power. In addition, the PTEcR is maximized
when the temperature differential is slight and the average temperature is high (see
Figure 3B). Note that the adjustment strategies for the current and the cycle period
can be non-unique at the same high and low temperatures (Figure S5B). A short-cycle scheme raises the COP but is more challenging to adjust because the temperature sensitively responds to the current or cycle period. The other long-cycle scheme
allows more precise adjustment along with a lower COP.
The operating temperature range of a TEcR system can be achieved by adjusting the
operating parameters but is also influenced by the structural parameters. Increasing
the convective heat-transfer coefficient and length of the TE leg can effectively
widen the temperature range (Figure 3C), but these solutions decrease the COP
(Figures 3D, S6, and S7). Therefore, the operating temperature range and system efficiency cannot be simultaneously enhanced. The PTEcR can be improved by optimizing the heat dissipation of the system and increasing the fill factor of the TE device; the PTEcR is minimally influenced by TE leg length (Figure 3D). The operating
temperature range and COP are little affected by the fill factor (Figure S8). In general, the operating temperature range is inversely related to COP, while PTEcR is
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Figure 3. Operating characteristics of the TEcR under different conditions
(A and B) Contour plots of (A) coefficient of performance and (B) thermoregulation power on high-cycling-temperature versus low-cycling-temperature
planes.
(C) Variations of temperature range at different convective heat-transfer coefficients and TE leg lengths.
(D) Coefficient of performance and thermoregulation power as functions of (top) convective heat-transfer coefficient, (center) length of TE leg, and
(bottom) fill factor. The TE material is commercial n-type Bi2 Te 3 , and all results are calculated under the default conditions (L = 2 mm, A obj = 25 mm 2 , F =
0.04, h = 200 W m 2 K 1 , Ta = 20 C).
highly influenced by the convective heat-transfer coefficient and fill factor. Therefore, the structural parameters should be optimized to meet the specific requirements of a particular evaluation index.
A careful examination of the preceding discussion clarifies that the TEcR system is
better suited to situations with low average temperatures than those with low
average temperatures and wide temperature differences. When the average temperature is low, TEcR systems with minor temperature differences achieve a high
COP, whereas those with large temperature differences achieve a high PTEcR. The
high and low cycling temperatures during temperature cycling must be as far as
possible from their limit values. The operating temperature range is usually broadened by adjusting the operating convective heat-transfer coefficient and length of
the TE leg, but these options increase the energy consumption of the system.
Instead, modifying the fill factor can boost the PTEcR of the TEcR system without degrading the other operating characteristics.
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Figure 4. Schematics and performance of the TEcR-based gas-separation system
(A and B) (A) Structure and (B) gas and temperature control logic of the gas-separation system.
(C) Comparison of the mathematical model and experimental results.
(D) Comparison of thermal performances of the traditional temperature control system and the TEcR system.
TEcR system for a gas-separation system
To verify the practical feasibility of the system, a TEcR system with uniquely low energy consumption was applied to a gas-separation system based on temperature
swing adsorption. Owing to the heavy global reliance on fossil fuels for energy,
CO2 has become the most copious greenhouse gas. Such a substantial increase in
atmospheric CO2 emissions has unprecedentedly changed the climate system,
causing large increases in surface temperature in recent decades. Carbon capture
and storage (CCS) technology promises to cut CO2 emissions and preserve the existing industrial assets.3 However, the energy-intensive nature of the carbon capture
process has bottlenecked the advancement of this technology. For example, the energy consumption of the amine-scrubbing CO2 capture process can account for half
the annual processing cost.35 Temperature swing adsorption can potentially enable
cyclic CO2 capture within adsorptive materials36 and can be readily integrated into
TEcR systems. Thus, we propose that a TEcR system can reduce energy consumption
and quicken the cyclic period of CCS.
Figure 4A is a structural diagram of the proposed gas-separation system based on
the TEcR (see Note S2 and Figure S9 for more details). The temperature control
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core of the system is a TE device (55 3 55 3 4.75 mm) sandwiched between both
sides of a mini-type fixed bed. The cycling temperature in the TEcR system is
enlarged using a heat exchanger. The convective heat-transfer coefficient was
measured as around 29.14 W m2 K1 (Figure S10). The mini-type fixed bed is cyclically cooled and heated. The mini-type fixed bed adsorbs CO2 from mixed gas during the cooling process and desorbs it during the heating process, thereby separating the CO2 at high concentration from the mixed gas (see Figure 4B).
Because the system is intended to reduce the energy consumption of CO2 capture,
the efficiency index COP is selected as the primary indicator of system performance.
The thermal performance of the gas-separation system was compared with that of a
mathematical model. The modeled COP follows the same trend as the experimental
values but with a noticeable systematic error (Figure 4C). The smaller measured COP
than the predicted COP is attributable to overrating the high temperature during the
temperature cycling, caused by a systematic error in the model, such as misestimating the specific heat capacity or thermal conductivity of the system. The model also
ignores various phenomena, such as the enthalpy change during gas adsorption and
desorption. Moreover, the system COP is less than one at high currents because the
system consumes a large amount of power to maintain the high temperature of the
fixed bed, leading to a high heat loss that sharply reduces the COP. Thermoregulation power, another crucial evaluative metric in most contexts, is less important in
gas-separation applications. Augmenting the electrical current enhances the heattransfer rate within the system (Figure S11).
Figure 4D compares the energy consumption of the TEcR-based mini-type fixed bed
and a conventional electric heating system. For the same temperature change, the
electrical heating system consumes 42% more electrical energy than the TEcR system. Moreover, the natural cooling period of the electrical heating system is 2.3
times that of the TEcR system. The cooling time of the electrical heating system
can be reduced to that of the TEcR system by introducing additional cooling systems, which further increase the energy consumption. In diverse CCS application
contexts, the energy consumption of CO2 capture is observed to increase with
decreasing CO2 concentration.37 In this study, the CO2 concentration was 10%,
but the advantages of TEcR over traditional electric heating systems are expected
to amplify in scenarios with lower CO2 concentrations, such as natural gas-fired power plants (4% CO2)38 and ambient air (0.04% CO2).39 Besides reducing the energy
consumption of CCS, the TEcR offers a versatile solution to electrical swing adsorption of CO2 from various environments, especially from direct air40 or enclosed
spaces, to restore a natural living environment. Therefore, it can potentially
sequester CO2 from humans living in polluted surroundings, scientific research stations during long-term underwater exploration, space stations for extraterrestrial
missions, and potential settlements on the Moon and Mars. By managing different
CO2 concentrations in distinct regions, the TEcR system can potentially provide
low-concentration areas for human activities and high-concentration areas for promoting plant growth through the CO2 fertilization effect.41
The TEcR system is also potentially applicable to thermal cycling processes with minimal temperature variation, such as small, rapid, and efficient PCR systems widely
utilized in molecular biology and other life sciences.42 PCR subjects DNA to thermal
cycles of high-temperature denaturation, annealing, and low-temperature extension. TEcR systems might also be incorporated with thermal-response materials in
thermally driven mini soft robots that expand at high temperatures and contract at
low temperatures.43 Such a robot could crawl and perform tasks such as
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microenvironment detection under cyclic-thermal stimulation. Besides these initial
concepts, we anticipate numerous unexplored application scenarios of TEcR.
Perspectives on material optimization for TEcR systems
After manipulating their current and convective heat-transfer coefficients and determining their structural parameters (F, L), different TE materials in a TEcR system can
achieve the same temperature cycle (i.e., the same Th*, Tc*, and tp), but cannot
achieve the same energy consumption and system efficiency. Therefore, selecting
the appropriate TE material and optimizing its material strategies are critical for
enhancing system performance. In this section, we evaluate the effectiveness of
traditional optimization strategies based on the conventional figure of merit (ZT =
S2sT/k) for TEGs and TECs and explore new optimization strategies for the TEcR
system.
When optimizing the TE material for a gas-separation system, we assume that the
optimal adsorption and desorption temperatures of the adsorbent material are
90 C and 120 C, respectively. Here, the material is a solid amine adsorbent.44,45
The cycle period and ambient temperature are 10 min and 20 C, respectively.
Although the TEcR model can calculate the COP of a given TE material, the intricate
calculation lengthens the time of finding a superior TE material. To overcome this
challenge, we adjust a particular physical property within a specific range based
on the current TE material and hence establish the potential relationship between
the physical properties and COP. Our findings indicate that increasing the Seebeck
coefficient or electrical conductivity induces a rapid initial rise in COP followed by a
gradual slowdown. Conversely, increasing the thermal conductivity rapidly decreases the COP (Figure S12). These trends in physical properties are consistent
with those of the maximum generation efficiency (hmax) of a TEG and maximum
COP (COPmax) of a TEC (Figure S13). Moreover, the specific heat capacity dominantly influences the transient behavior but does not affect the COP (Figure S14A),
possibly because the TE material possesses a much lower internal energy than the
object. When the specific heat capacity increases exponentially, its influence on
the COP is expected to emerge (Figure S14B). Therefore, the TE material in the
TEcR system should be optimized following the current optimization strategies
but with different proportional weights during the optimization. We standardize
the physical properties of TE materials using the dimensionless sensitivity function
SF, defined as the partial derivative of an evaluation index with respect to a physical
property of the TE material. For the TEcR system, the SF is calculated as46
SFX =
vCOP X
$
vX COP
(Equation 5)
where X = {S, s, k}.
To assess the effectiveness of optimizing the physical properties of TE materials and,
hence, enhancing the system performance, we compared the dimensionless SFs of
S, s, and k of six materials.47–50 The dimensionless SF quantifies the degree of influence of a parameter on the system’s performance, where a larger value indicates a
higher potential for improvement through optimization.
Our analysis revealed that the Seebeck coefficient most significantly influences the
performance of traditional TEC systems, while electrical conductivity and thermal
conductivity exert almost equal influences (Figure 5A). The SF of the Seebeck coefficient is twice that of the electrical and thermal conductivities. This observation is
attributed to the quadratic relationship between ZT and the Seebeck coefficient
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Figure 5. TE material optimization strategies for the TEcR system
(A and B) Radar plots of dimensionless sensitivity functions of the physical properties for (A) COP max in TECs and (B) COP in TEcRs using different
materials.
(C and D) COP versus (C) traditional figure of merit (ZT) and (D) new figure of merit (Z R T) in TEcR systems with different TE materials (16 materials) 47–58
under the same size and operating conditions. In all calculations of the TEcR system, the parameter settings are T h * = 120 C, T c * = 90 C, T a = 20 C, t p =
10 min, F = 0.04, A obj = 25 mm 2 , and L = 2 mm. In all calculations of the TEC system, the parameter settings are Th = 120 C, T c = 90 C, F = 0.04, A obj =
25 mm 2 , and L = 2 mm.
versus the first-order relationship between ZT and the electrical and thermal conductivities. A similar pattern is observed in TEG systems (Figure S15). In the TEcR, TEC,
and TEG systems, the SF of the Seebeck coefficient is twice as sensitive as the SF of
the electrical conductivity, indicating that the order of the Seebeck coefficient is
double that of the electrical conductivity (Figure 5B). Optimizing the power factor
(PF = S2s) of the TE material is a traditional optimization approach for enhancing
the system performance, but the effect of thermal-conductivity optimization notably
differs from the conventional perception of ZT. In some materials, the order of thermal conductivity is much higher than first-order and sometimes surpasses that of the
Seebeck coefficient. Thermal conductivity and PF have equivalent significance in
material optimizations of TECs and TEGs, but in the TEcR context, thermal conductivity is markedly more important than PF. This distinction highlights that the fundamentals and important material properties in TEcR systems differ from those in TECs
and TEGs.
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Further calculations based on additional data gathered from other TE materials47–58
confirmed our previous findings. Assuming that a new figure of merit is a first-order
function of electrical conductivity and a second-order function of the Seebeck coefficient, the order of thermal conductivity varied from 1.8 to 3.5 (Figure S16). Accordingly, we suggest this new empirical figure of merit (ZR) for TE materials utilized in the
TEcR system. The ZR is calculated similarly to the conventional TE figure of merit for
TEG and TEC systems as follows:
ZR =
S2 s
k2:3
(Equation 6)
The order of thermal conductivity in Equation 6 depends on the maximum residual
error (R2) of the linear fitting. In the following discussion, we adopt ZRT = ZRT for convenience. Note that ZRT is not dimensionless but shares an engineering concise.
The effectiveness of the new ZRT was evaluated through comparisons with the traditional ZT in TEcR systems with 16 different TE materials.47–58 Although the overall
efficiency of the TEcR system increases with increasing ZT, the results are widely
dispersed (Figure 5C), indicating that the traditional ZT might not accurately optimize the efficiency of a TEcR system. Conversely, the relationship between COP
and ZRT is nearly monotonically linear, enabling quick prediction of the performance
of a TE material in TEcR systems (Figure 5D). Accordingly, this measure can easily
guide the optimization direction of TE materials. Furthermore, the thermal conductivity of the TE material more significantly affects the performance in a TEcR system
than in traditional TEG and TEC systems. Thus, materials with lower thermal conductivity should be preferred in TEcR systems. The ZRT is also effective across a wide
range of boundary conditions, as demonstrated in Figure S17. That is, the optimal
TE material for a TEcR is also determined by the thermal boundary conditions,
emphasizing the importance of systems-level engineering when exploring new applications of TE materials.
Conclusions
The TEcR system is a novel operating mode for TE devices operating under periodically fluctuating temperature conditions. Besides actively regulating the heat flow,
this innovative technology achieves precise temperature variation within a limited
space while consuming low amounts of energy. When tested in a gas-separation system, the TEcR system substantially improved the energy efficiency from that of a
conventional heating system, saving electricity consumption by 42% and increasing
the cycle speed by 2.3 times. This system is easily applicable to other scenarios that
would benefit from reduced power consumption and miniaturization of system size,
such as PCR systems in the biomedical field and thermal-response materials created
by 4D printing. Furthermore, an empirical figure of merit for the TE material design
was proposed, which promises to realize the final implementation from systemslevel design to material-level design. This study provides a paradigm for developing
applications and optimizing the materials of TEcR systems with different thermal
boundaries and device operating modes.
RESOURCE AVAILABILITY
Lead contact
Requests for additional information, and for resources and materials should be directed to and will be
fulfilled by the lead contact, Weishu Liu (liuws@sustech.edu.cn).
Materials availability
This study did not generate new unique materials.
Joule 8, 3201–3216, November 20, 2024 3213
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Data and code availability
The published article includes all data generated or analyzed during this study.
ACKNOWLEDGMENTS
This work was supported by the Guangdong Major Project of Basic and Applied Basic Research
(no. 2023B0303000024), the Shenzhen Key Program for Long-Term Academic Support Plan
(no. 20200925164021002), the Shenzhen Innovation Program for Distinguished Young Scholars (no.
RCJC20210706091949018), and also partially by the Guangdong Provincial Key Laboratory Program
(2021B1212040001) from the Department of Science and Technology of Guangdong Province. Z.Z.
also acknowledges the support from The National Science Fund for Distinguished Young Scholars
(52225407).
AUTHOR CONTRIBUTIONS
Methodology, Y.W., X.W., M.Y., X.S., S.W., H.L., and W.L.; validation, Y.W. and W.L.; investigation,
Y.W.; simulation, Y.W.; data curation, Y.W.; writing – original draft, Y.W.; writing – review and editing,
X.W., M.Y., X.S., S.W., H.L., and W.L.; conceptualization discussion, Z.Z.; funding acquisition, Z.Z. and
W.L.; conceptualization, W.L.; supervision, W.L.
DECLARATION OF INTERESTS
The authors declare no competing interests.
SUPPLEMENTAL INFORMATION
Supplemental information can be found online at https://doi.org/10.1016/j.joule.2024.08.002.
Received: May 14, 2024
Revised: July 16, 2024
Accepted: August 6, 2024
Published: August 30, 2024
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