Applied Energy 292 (2021) 116843

Contents lists available at ScienceDirect

Applied Energy
journal homepage: www.elsevier.com/locate/apenergy

Design and performance evaluation of a dual-circuit thermal energy storage

module for air conditioners
Anurag Goyal a, *, Eric Kozubal a, Jason Woods a, *, Malek Nofal b, Said Al-Hallaj b
a
Building Energy Science Group, National Renewable Energy Laboratory, Golden, CO 80401 USA
b
Department of Chemical Engineering, University of Illinois at Chicago, Chicago, IL 60608 USA

H I G H L I G H T S

• A dual-circuit thermal storage module (~3.5 kWh) is presented for HVAC systems.
• Dual-circuit design can improve system integration and operational flexibility.
• High thermal conductivity achieved by using porous graphite foams with n-C14H30.
• Thermal contact resistance between tubes and material identified as bottleneck.
• Different control scenarios show operational flexibility of dual-circuit design.

A R T I C L E I N F O A B S T R A C T

Keywords: We present experimental results and a validated numerical model of a dual-circuit phase-change thermal energy
Thermal energy storage storage module for air conditioners. The module incorporates a phase-change material encapsulated in com­
Composite phase-change material pressed expanded natural graphite foam. We used n-tetradecane as the PCM with a transition temperature (~4.5
Compressed expanded natural graphite ◦
C) suitable for air-conditioning applications. Heat exchange to and from the module is accomplished through
Simulation
Heat exchanger
two fluid loops operating as a heat source and sink embedded inside multiple slabs of the composite material.
This dual-circuit design enables easier integration with air-conditioning equipment and provides enhanced
flexibility in system operation as compared to the state-of-the-art thermal storage systems. When integrated with
an air-conditioner, this design will enable peak-load shaving and enhances operational efficiency. The thermal
storage device was designed for a nominal storage capacity of ~ 3.5 kWh. We evaluated the heat transfer and
energy storage performance of this device using standalone heat transfer experiments to estimate key thermal
resistances and identify design improvements before integration with an air conditioner. The numerical model of
the heat exchanger uses a combination of discretized and lumped parameter approaches to maintain a balance
between accuracy and computational expense. Our analyses show that the geometric features and integration of
fluid tubes are key contributors to the thermal contact resistance between the fluid and the thermal storage
material, and consequently, to the overall performance of the thermal storage module. Our standalone experi­
ments also identified important operating scenarios in which this thermal storage module can be used for air-
conditioning in buildings.

by 2050. Carbon dioxide (CO2) emissions resulting from electricity

generation using fossil fuels to meet the space-cooling requirements
1. Introduction
amount to ~ 1,100 million tonnes and ~12% of total carbon emissions
from buildings [1]. In the United States, the electricity consumption for
Energy consumption for heating, ventilating, and air conditioning
space cooling in residential and commercial buildings amounts to
(HVAC) and thermal comfort in buildings amounts to approximately
~1,240 billion kWh and $141 billion annually [2,3].
10% of total electricity consumption in the world and 20% of electricity
Daytime space-cooling loads cause a peak in electricity demand. If
use in buildings. With increasing demands for air-conditioning systems,
the electric utility operators implement time-of-use (TOU) energy
the electrical energy required for HVAC is projected to more than triple

* Corresponding authors at: 15013 Denver West Parkway, Golden, CO 80401, USA.
E-mail addresses: Anurag.Goyal@nrel.gov (A. Goyal), Jason.Woods@nrel.gov (J. Woods).

https://doi.org/10.1016/j.apenergy.2021.116843
Received 7 August 2020; Received in revised form 26 February 2021; Accepted 16 March 2021
Available online 2 April 2021
0306-2619/© 2021 Elsevier Ltd. All rights reserved.
A. Goyal et al. Applied Energy 292 (2021) 116843

Nomenclature t time (s)

△t time step (s)
Abbreviations U heat transfer coefficient (W⋅m− 2⋅K− 1]
CAD computer-aided design UA heat transfer conductance (W⋅K− 1)
CENG compressed expanded natural graphite V volume (m3)
COP coefficient of performance W width of control volume (m)
CV control volume Ẇ work input (W)
DSC differential scanning calorimetry z axial/flow direction
HVAC heating, ventilating, and air conditioning
PCC phase-change composite Subscripts/Superscripts
PCM phase-change material Avg average value
SOC state of charge ambient ambient conditions
TES thermal energy storage c charge/cold fluid
TOU time-of-use comp compressor
cond conduction heat transfer
Variables conv convection heat transfer
A area (m2) cs cross-section
Cp specific heat capacity (kJ⋅kg− 1⋅K− 1) eff effective value
E energy stored (J) End end of charge/discharge duration
η isentropic efficiency (-) evap evaporator
H height of control volume (m) f fluid
h enthalpy (kJ⋅kg− 1) h discharge/hot fluid
ID inner diameter (m) hor horizontal neighboring node
k thermal conductivity (W⋅m− 1⋅K− 1) i,j nodal indices
L length of control volume (m) in inlet
M mass (kg) LM logarithmic mean
ṁ mass flow rate (kg⋅s− 1) o previous time step
OD outer diameter (m) out outlet
ρ density (kg⋅m− 3) PCC phase-change composite
Pe Péclet number (=Reynolds number × Prandtl number) TC-PCC thermal contact between adjacent PCC elements
Per perimeter of flow channel (m) TC-t thermal contact between tubes and PCC
Q̇ heat transfer rate (W) t-PCC tube-to-PCC conduction
q‘‘ heat flux (W⋅m− 2) ver vertical neighboring node
R thermal resistance (K⋅W− 1) ‘ current time step
r specific thermal contact resistance (K⋅m2⋅W− 1) || in-plane (perpendicular to heat transfer direction)
T temperature (◦ C) ⊥ perpendicular (parallel to heat transfer direction)
△T temperature difference (K)

pricing or peak-power demand charges, these loads can lead to signifi­ they use densely packed tubes or fins within the TES heat exchanger to
cant operating expenses for consumers. However, TOU pricing is also an overcome the low PCM thermal conductivity, adding cost and weight to
incentive for consumers to implement technologies to shift the demand the system, and (3) the evaporator temperature to generate ice is much
from peak durations to off-peak durations [4]. This can lead to signifi­ lower than standard air conditioner operation, reducing efficiency. Past
cant savings in the operating cost due to lower electricity prices. research has largely overlooked component design for ease of integra­
Moreover, the efficiency of an air conditioner in cooling mode is tion and operational flexibility. Integrating TES into widely used pack­
generally higher during cooler outdoor conditions at night. Therefore, aged rooftop systems will expand the load shifting benefits of thermal
the consumers and the utility operators can benefit from energy savings storage into this untapped cooling market. This is also crucial for deeper
from improved efficiency of air conditioners. penetration of renewable sources of energy in buildings in the future.
Thermal energy storage (TES) is a promising solution to store energy Several researchers have studied enhancement in thermal conduc­
during off-peak periods and dispatch energy during peak periods [5]. tivity of PCMs using various types of additives and some have studied
Sensible (liquid and solid materials – water, concrete, bricks, etc.) [6,7] components and systems for integration with buildings, existing tech­
and latent (phase change materials – organic and inorganic) [8] TES nologies on TES systems for buildings. Baby and Balaji [11] used a
methods have been proposed in many applications for building thermal porous copper and aluminum matrix to increase the thermal conduc­
management. Phase-change materials (PCMs) can provide high energy tivity of organic PCM (n-eicosane) used as a heat sink for electronics
densities (>150 kJ kg− 1), leading to compact storage systems that can thermal management. They showed significant enhancement in heat
apply to residential and commercial buildings [8]. transfer performance due to the addition of these metal structures.
Most commercially available PCM-based systems are large ice tanks However, these types of metal structures can become expensive for
that are integrated with central chillers [6,9,10]. However, central larger components needed for HVAC systems. Cabeza et al. [12] used
chiller plants are a small fraction of the total cooling market. Instead, dispersed metal particles (stainless steel and copper) and also a porous
packaged rooftop units and split air-conditioning systems provide space graphite structure to improve the thermal conductivity of water when
cooling for >75% of the US commercial floorspace [3]. But there are used as a PCM. They noticed that the addition of metallic pieces is
several constraints preventing these ice-based approaches from being helpful only when high thermal conductivity meals are used, such as
adapted for smaller packaged HVAC systems: (1) They require custom copper. Stritih [13] used finned structures to enhance the heat transfer
engineering and installation and are not economical at small scales, (2) in paraffin waxes and reported an increase in the melting heat transfer

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A. Goyal et al. Applied Energy 292 (2021) 116843

rate (discharge) due to the effect of fins. Other mechanism of enhancing They studied the effect of graphite-foam on thermal conductivity
the thermal conductivity of PCMs is to use carbon fiber networks enhancement for salt-based PCMs. Aljehani et al. [23] presented results
[14,15]. They can provide a significant increase in the thermal con­ using a similar single-fluid TES module using graphite-n-tetradecane
ductivity but tend to be expensive, and the orientation and length of composite for integration with an air-conditioner. However, in both
fibers have to be carefully investigated. cases, the PCM heat exchanger required diverting valves and separate
Porous graphite structures and their composites with PCMs have pumps to switch between charging and discharging. A single-fluid cir­
been of significant interest to many researchers [16–23]. They are an cuit coupled to the TES module severely limits the flexibility in system
attractive solution due to their high thermal conductivity, light weight, operation and increases the complexity of the system, and is difficult to
and manufacturability. Composites of porous graphite and PCMs also integrate directly with refrigerant as the working fluid.
enable ease of integration with conventional heat exchanger geometries Considering these limitations in the state-of-the-art TES components
such as round tubes, flat plates, and finned geometries. Py et al. [16] and systems, we present the design of a dual-fluid TES module and re­
used various mass fractions of porous graphite composites with paraffin sults from heat transfer simulations and experiments. Fig. 1 shows the
wax and observed the thermal conductivity to increase by ~ 16–290 integration of our design with a roof top air-conditioning unit. The
times as compared to the pure PCM. They observed stabilization of heat proposed module utilizes a high-conductivity matrix of CENG with n-
transfer rate with the addition of the graphite matrix and recommended tetradecane as an organic PCM. This provides the desired high thermal
optimization of graphite fraction for different applications. Mills et al. conductivity for enhanced heat transfer rates. The dual-circuited design
[17] showed almost two orders of magnitude increase in the thermal of the TES module allows for a drop-in replacement for the conventional
conductivity of paraffin wax by adding compressed expanded natural refrigerant-to-coolant evaporator, simplifying integration with an air
graphite (CENG). They also reported anisotropy in thermal conductivity conditioner. As shown in Fig. 1, the secondary loop can contain pumped
due to the manufacturing process of the CENG foams. They demon­ refrigerant, eliminating the need for glycol loops and pumps, heat ex­
strated the performance of this composite in a passive thermal man­ changers, separate storage vessels for the PCM, thereby making it easy to
agement solution for lithium-ion batteries. Zhang and Fang [18] integrate with existing HVAC systems and also reduce the capital and
demonstrated the use of CENG foams with paraffin wax and noted no installation cost.
liquid leakage during phase transition, and higher heat transfer rate than This configuration of the TES system also provides several other
pure paraffin. benefits. It decouples charging and discharging processes, such that it
Few experimental studies on the component design using composites can operate independently (at the same or different times). The dual-
of phase-change materials exist in the literature [19–23]. Mallow et al. circuit design enables simultaneous charging and discharging of the
[19] presented results from different graphite fractions and heat fluxes TES module, therefore making the integrated HVAC system to better
as applied to charging a composite phase-change material. Their results respond to dynamic air-conditioning loads. Moreover, this system allows
show an opportunity to optimize the graphite loading for different ap­ variable-capacity operation by only modulating the airflow rate in the
plications, and suggested that the anisotropy in high thermal conduc­ conditioned space, therefore eliminating the need for a variable-speed
tivity, especially at high graphite fractions, comes at the cost of reduced compressor.
energy storage capacity. Mallow et al. [20] presented the optimization This dual-circuit design has not been studied before and requires the
of a porous graphite substrate for organic PCMs. The authors presented a characterization of heat transfer performance and the development of
numerical model for optimization of power and energy densities using a simulation tools for design optimization. Key research objectives of this
simplified geometry of a short tube containing a heat transfer fluid paper are to:
surrounded by the composite PCM material. Such a simplified geometry
limits the understanding of heat transfer phenomena under isolated • Design and fabricate a dual circuit TES module and evaluate its
charging or discharging conditions only. performance using standalone heat transfer experiments,
Kim et al. [21] and Zhao et al. [22] developed numerical simulation • Develop a detailed numerical model to predict the energy storage
methods and experimentally evaluated the performance of a high- and heat transfer performance of the module and validate it with
temperature TES module for concentrated solar power applications. experiments,

Fig. 1. TES-integrated air conditioner using compressed expanded natural graphite with n-tetradecane.

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A. Goyal et al. Applied Energy 292 (2021) 116843

• Estimate the key thermal resistances and potential for design 3. Methods
optimization,
• And, demonstrate charging and discharging capabilities of the 3.1. Experimental setup
module, as well as a hybrid mode of simultaneous charge/discharge,
that simulates the performance in an actual air conditioner Fig. 3 shows a schematic of the experimental setup, which can con­
installation. dition the temperature of the two fluid circuits. Although the actual
system (Fig. 1) will use a refrigerant as the charge and discharge fluids, a
In this study, we achieve these goals with two glycol loops, avoiding mixture of propylene glycol and water is used in this prototype. The lab
the complexity of refrigerants at this stage. This understanding is critical chiller and boiler, connected to the glycol circuits, serve as the ambient
for the design of a refrigerant-coupled TES module (Fig. 1) for imple­ heat sink and the building load, respectively. This setup allows us to
mentation in a packaged air-conditioning system. easily condition the glycol circuits to the operating conditions encoun­
tered in an air-conditioner. Using this experimental setup, we can
2. Material and design of thermal energy storage module rapidly evaluate and optimize the design of these modules before inte­
gration with a complete HVAC system. These experiments also allow us
2.1. Phase-change composite (PCC) material to simulate different modes of operation which can enhance the flexi­
bility of storage systems in buildings. These aspects will be discussed in
We used a composite of n-tetradecane (C14H30) as the PCM and CENG the following sections.
as the high thermal conductivity matrix for encapsulation [23] (Fig. 1). The discharge fluid circuit (19 wt% propylene glycol–water mixture)
We manufactured this material using intercalated and acid-treated flake was connected to a heat exchanger to ultimately exchange heat with the
graphite, which forms expanded graphite upon heat treatment. The lab boiler. The charge circuit (16 wt% propylene glycol–water mixture)
expanded graphite is compressed to form a high-porosity foam matrix, exchanged heat with the lab chiller in a similar manner. Electronic flow
which is then soaked in liquid n-tetradecane to form the final energy control valves on the chiller and the boiler enabled precise regulation of
storage material. We measured the thermophysical properties (enthalpy the supply temperature of fluids to the module using temperature
of phase change and thermal conductivity) of the composite using dif­ feedback. The pumps provided variable flow rates of both the fluids
ferential scanning calorimetry (DSC) and a steady-state heat transfer using a variable-frequency drive. A bypass line in both fluid circuits
measurement. Table 1 summarizes the key properties of this material enabled preconditioning of the fluids to the desired temperature set
and Fig. 1 (lower-right plot) shows the relationship between the specific point before being introduced into the module.
enthalpy and temperature of this composite. This relationship is used in
numerical simulations of the phase-change process. 3.2. Instrumentation

2.2. Design of thermal energy storage module We installed type-T thermocouples to measure fluid temperatures
entering and leaving the module, embedded thermocouples to measure
We designed and fabricated a prototype TES module for experi­ the temperature in the composite slabs, and surface-mounted thermo­
mental evaluation. Fig. 2 (left) shows a 3D computer-aided design (CAD) couples on the copper tubes to estimate flow maldistribution between
drawing of the module. The module consists of 10 slabs of graphite- different rows. To ensure low measurement uncertainties in fluid tem­
tetradecane composite material with alternating discharge (hot) and perature differences, we calibrated them using a thermocouple bath. We
charge (cold) fluid circuits. Fluid circuits can be easily connected to the measured the flow rates of fluids using an electro-optical flow sensor.
refrigerant (charge fluid) and chilled water (discharge fluid) side of an Table 2 contains the uncertainties and relevant information about these
air conditioner. The dimensions of an individual slab are 0.559 m × sensors.
0.460 m × 0.035 m (L × W × H). Copper tube of outer diameter 0.0095
m (3/8 in.) was used for both fluid circuits. The fluid circuits formed a 3.3. Numerical model
22-pass serpentine path in each row. A total of nine fluid circuits (five
parallel discharge-side and four parallel charge-side) were used. The We developed a numerical model of the heat transfer process within
flow configuration through the module maintained overall counterflow the TES module. This model serves two important purposes. First, the
between the charge and discharge fluids. Fig. 2 (right) shows the steady-state heat transfer experiments are used to determine the thermal
packaged prototype module for laboratory experiments. We used a contact resistance between the tubes and the PCC and between different
plastic case with insulation around the module to minimize thermal slabs of the PCC material. Thermal contact resistance is an important
losses with ambient. Fluid distribution headers on both fluid circuits parameter for these modules and will be discussed later in the paper.
allowed uniform distribution through each pass. This prototype module Second, the model with calibrated thermal contact resistance values is
was installed on the experimental setup to characterize its performance used to simulate the charging/discharging experiments and compared
over a range of operating conditions. with data that we collected. This validated model can then be used for
evaluation of different TES materials using high thermal conductivity
matrices (e.g., CENG-slat hydrates), and also help rapidly valuate
different heat exchanger geometries ((flat tubes, microchannels).
We used a discretization approach using the finite volume method.
Fig. 4 shows the computational domain and geometrical details of a
single control volume (CV). Each CV consists of the PCC material along
Table 1 the pass of the tube over the total depth dimension of the module and
Thermophysical properties of tetradecane-graphite composite for TES. exchanges heat with the fluid flowing in the copper tubing. As thermal
Property Value storage is an inherently unsteady phenomenon, the conservation laws in
their unsteady form are used to model the process.
Transition temperature ~4.5 ◦ C
Density 836.1 kg⋅m− 3
Porosity ~90% 3.3.1. Model assumptions
Enthalpy of phase change ~168 kJ⋅kg− 1 We assumed the following to simplify the governing equations:
Thermal conductivity (in-plane direction) 18 W⋅m− 1⋅K− 1
Thermal conductivity (heat-transfer direction) 10 W⋅m− 1⋅K− 1
• Fluid flow is assumed to be one-dimensional and incompressible

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A. Goyal et al. Applied Energy 292 (2021) 116843

Fig. 2. Module CAD rendering (left) and the prototype (right).

Fig. 3. Schematic of the experimental setup. The experiment uses glycol–water mixture as the charge and discharge fluid to simulate different operating conditions
that would be encountered in an integrated air-conditioner (Fig. 1). In a prototype full system, the charge circuit would contain refrigerant with the potential of using
refrigerant in the discharge circuit too for ease of integration.

• The graphite-tetradecane composite is modeled as a single material

Table 2
with one set of material properties
Details of instrumentation and sensors.
• Lumped capacitance is used for the PCC element (Biot number ~ 0.2)
Sensor Description Measurement Uncertainty • Heat transfer from curved tube surface to the PCC is modeled using
Thermocouple: fluid Omega Type- ±0.1 ◦ C temperature an empirical shape factor for heat conduction
temperature difference T difference • Finite thermal contact resistance is used at the interface between the
Thermocouple: surface-mounted Omega Type- ±0.5 ◦ C absolute temperature
tube and the PCC element and between PCC elements.
and embedded T measurement
Volumetric flow sensor Omega FTB- ±1% of reading
603 3.3.2. Governing equations
The previous assumptions simplify the conservation laws and the
energy conservation equations for the two fluids and the PCC material,
• Viscous dissipation and body forces are neglected and the static pressure drop equation is used per node to formulate the
• Dynamic variations in pressure are neglected and a static formula­ system of discretized equations. The partial differential equations are
tion of pressure loss is used over each control volume during every below:
time step Fluid Energy Conservation
• Effects of axial conduction are neglected in the fluid as the Péclet (Pe)
number is typically large ρf Cpf Acs,f
∂Tf ∂(ṁf Cpf Tf )
+ − Uf Perf (TPCC − Tf ) = 0 (1)
• Constant cross-sectional area of fluid flow ∂t ∂z
• Uniform heat transfer coefficient assumed in the control volume for PCC Energy Conservation (using enthalpy method [6])
both fluids
• Heat transfer in the PCC is modeled as two-dimensional conduction
from the adjacent nodes

5
A. Goyal et al. Applied Energy 292 (2021) 116843

Fig. 4. Computational domain (left) and thermal resistance network (right) implemented in the numerical model.

∂hPCC
ρPCC VPCC − Uf ,h Perf ,h (TPCC − Tf ,h ) + Uf ,c Perf ,c (TPCC − Tf ,c ) + ∇⋅q‘‘cond 1 ln(ODt /IDt )
∂t Roc,i,j = o
+ + Rt− PCC + RTC− t (10)
Uc,i,j Ac πkt L
=0
(2) In these equations, Roc,i,j and Roh,i,j account for thermal resistances
Integrating these partial differential equations over the length of CV from the cold and hot fluid nodes, respectively, to the PCC node: con­
results in ordinary differential equations describing the heat transfer vection, tube-wall conduction, tube-to-PCC conduction (Rt-PCC), and
response of a single control volume. We use a thermal resistance thermal contact resistance between the tube and PCC (RTC-t). For
network formulation to resolve different convective and conductive heat conductive thermal resistance from the curved surface of the tube to the
transfer media. Fig. 4 also shows a single CV with both fluid tubes and PCC material, we simplify the computation by using the shape-factor
the PCC volume. The heat transfer path from the hot fluid to the cold formulation described by Janna [24] and shown below:
fluid through various materials and interfaces accounts for different ln[4(H − ODt )/ODt ]
thermal resistance terms discussed below. Rt− PCC = (11)
kPCC,eff πL
Fluid Energy Conservation
We validated this calculation using finite element simulations over a
• Discharge Fluid single control volume representative of the geometry of the tubes and
the PCC in COMSOL®. Thermal contact resistance between the tube and
PCC is calculated using:
′
dTh,i,j
(3)
o
o
Mh,i,j Cpoh,i,j = ṁoh Cpoh,i,j (Th,i,j,in
o o
− Th,i,j,out ) − Q̇conv,h,i,j
dt rTC− t
RTC− t = (12)
′ ′
o 0.5π ODt L
dTh,i,j Th,i,j − Th,i,j
= (4) where rTC-t is the specific thermal contact resistance expressed as
dt Δt
K⋅m2⋅W− 1.
The heat transfer coefficients Uoc,i,j and Uoh,i,j for the cold and hot
o o
Th,i,j − TPCC,i,j
(5)
o
Q̇conv,h,i,j =
fluid, respectively, are calculated using single-phase convective heat
o
Rh,i,j
transfer relations developed by Gnielinski [25] and Shah and London
Roh,i,j =
1
+
ln(ODt /IDt )
+ Rt− + RTC− (6) [26].
PCC t
PCC Energy Conservation
o
Uh,i,j Ah πkt L
The energy conservation equation for the PCC is formulated as:
• Charge Fluid ′
dhPCC,i,j
(13)
o o o o
MPCC,i,j = Q̇conv,h,i,j − Q̇conv,c,i,j + Q̇cond,hor,i,j + Q̇cond,ver,i,j
′
dTc,i,j dt
(7)
o
o
Mc,i,j Cpoc,i,j = ṁoc Cpoc,i,j (Tc,i,j,in
o o
− Tc,i,j,out ) + Q̇conv,c,i,j
dt ′ ′
dhPCC,i,j hPCC,i,j − hoPCC,i,j
= (14)
′ ′
o
dTc,i,j Tc,i,j − Tc,i,j dt Δt
= (8)
dt Δt o
TPCC,i,j− o o
1 − 2TPCC,i,j + TPCC,i,j+1
(15)
o
Q̇cond,hor,i,j = kPCC,|| LH
o
TPCC,i,j o
− Tc,i,j W
(9)
o
Q̇conv,c,i,j = o
Rc,i,j o
TPCC,i− o
− 2TPCCi,j o
+ TPCCi+1,j
(16)
o 1,j
Q̇cond,ver,i,j = H
kPCC,⊥ APCC,ver
+ RTC− PCC

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A. Goyal et al. Applied Energy 292 (2021) 116843

o o
Here, Q̇cond,hor,i,j and Q̇cond,ver,i,j are the conductive heat transfer rates 4.1. Heat transfer performance
between adjacent PCC nodes in horizontal and vertical directions,
respectively. kPCC,|| and kPCC,⊥ represent the thermal conductivity of the We performed these experiments with both fluids above the phase-
PCC material in the in-plane (perpendicular to heat transfer direction) transition temperature of the PCC material. These helped us charac­
and perpendicular (parallel to heat transfer direction) directions, terize the average heat transfer conductance (UA) of the TES module.
respectively. In addition, RTC-PCC represents thermal contact resistance This is an important parameter as it provides an estimate of the overall
between the slabs, as the module consists of slabs stacked on top of each heat transfer performance of the module. We conducted experiments
other. over a range of fluid flow rates. The experimental conditions are listed in
Table 3. For the counterflow configuration, we used Eq. (19–21) to
rTC− PCC
RTC− PCC = calculate the overall heat transfer conductance values for the module at
APCC,ver (17) varying flow rates.
APCC,ver = L(W − ODt )
Q̇c,avg = ṁc Cpc,avg (Tc,out,avg − Tc,in,avg ) (19)
For pressure-drop calculation on the fluid side, we account for major
and minor losses using previously established literature [26–29]. Q̇h,avg = ṁh Cph,avg (Th,in,avg − Th,out,avg ) (20)
We developed the numerical model using MATLAB [30] with a time-
explicit solution scheme for the system of coupled algebraic solutions Q̇c,avg + Q̇h,avg
and solved for pertinent fluid and PCC temperatures and enthalpy. Q̇avg = = UA(ΔTLM ) (21)
2
Finally, the enthalpy-temperature relationship shown in Fig. 1 is used to
solve for nodal PCC temperatures: Here, the average heat transfer rate is calculated at steady-state
operation using the heat transfer rate of both fluid streams, and △TLM
(18) is the logarithmic mean temperature difference for a counterflow heat
′ ′
TPCC,i,j = f (hPCC,i,j )
exchanger [32].
3.3.3. Solution method Fig. 5 shows the results of these experiments at different fluid flow
The model initiates with an initial condition of module and fluid rates. With this variation, we can disaggregate different heat transfer
temperatures at thermal equilibrium and uses time-dependent boundary conductance values (conduction, convection, thermal contact) and
conditions of fluid inlet temperatures and flow rates as inputs. The identify potential for design improvements. The average heat transfer
system of discretized equations is solved at each time step to predict conductance values varied between 0.18 and 0.24 kW⋅K− 1 ± 0.006
fluid outlet temperatures, nodal fluid and PCC temperatures, and the kW⋅K− 1. We also observed that the average heat transfer conductance
heat transfer rate through each fluid circuit. The approach presented increased with the flow rate of either fluid. This is expected, as the
here using the thermal resistance network can be readily modified to convective heat transfer coefficient increases with the fluid flow rate.
predict only charging or discharging performance of the module. In As the contact surfaces in our module are nonconventional, we used
those cases, the convective heat transfer to or from one of the fluids our numerical model to perform simulations of the heat transfer
reduces to zero and the conduction path through the PCC becomes twice response of the module at the experimental operating conditions. This
as long due to alternating fluid circuits. We use experiments on charging allowed us to estimate the specific thermal contact resistance between
and discharging the module to compare with model predictions. Several fluid tubes and PCC (rTC− t ) and between the PCC slabs (rTC− PCC ). This
operating scenarios are discussed in the following sections. analysis showed that the thermal contact resistance at various interfaces
This modeling approach of conjugate heat transfer is adapted from a contributed significantly to the total thermal resistance in the module.
previously validated method published by Woods et al. [31]. Their We estimated the magnitude of specific thermal contact resistances as
method involves several computational nodes within the PCC along the rTC− t = 0.0013 K⋅m2⋅W− 1 andrTC− PCC = 0.0068 K⋅m2⋅W− 1.
vertical and horizontal directions, however other assumptions and the Fig. 6 shows the relative magnitudes of thermal resistances and
physics of the process are the same here as well. shows that the thermal contact resistance accounts for > 50% of the total
thermal resistance in the module. The convective resistance is calculated
4. Results and discussion at charge and discharge fluid flow rates of 1.33 × 10− 4 m3⋅s− 1 and 1.67
× 10− 4 m3⋅s− 1, respectively. This is primarily due to difficulty in
We conducted several experiments to characterize the heat transfer machining accurate slots for fluid tubes in the brittle PCC material,
and energy storage performance of the energy storage module, which we leading to uneven contact surfaces and suboptimal thermal contact be­
compared to the predictions of our model. A summary of key experi­ tween PCC slabs. It shows that in future designs, the tube geometry can
ments is below with details in the subsequent sections. be selected appropriately to minimize this contact resistance. A high
value of total thermal resistance does not affect the energy storage ca­
• Heat transfer performance: The first set of experiments charac­ pacity of the module, but it decreases the heat transfer rate (charge/
terized the heat transfer performance with both fluids exchanging discharge rate) for a given driving temperature difference. This leads to
heat through the PCC matrix. These experiments provided estimates lower refrigerant charging temperature to achieve the same heat
of (1) the steady-state heat transfer conductance at different fluid transfer rate as a system with lower or negligible contact resistance,
flow rates, (2) individual resistances of the thermal resistance requiring higher compressor power and a lower overall system effi­
network, and (3) the value of thermal contact resistance between the ciency. Based on simplified Carnot efficiency of an air-conditioning
fluid tubes and the PCC layers. system, (coefficient of performance, COP = Tambient/(Tambient - Tevap)),
• Energy storage performance: We characterized the energy storage
capacity of the module by freezing and melting it using only one fluid
Table 3
circuit. We conducted these experiments by maintaining a constant
Experimental conditions to characterize the heat transfer performance of the
fluid flow rate and varying the inlet temperature to simulate different TES module.
cases.
Fluid Variation Properties Charge Fluid Discharge Fluid

Charge Fluid Inlet Temperature (◦ C) 7 20

Flow Rate (m3⋅s− 1) 0.33 – 1.5 × 10− 4
1.67 × 10− 4
Discharge Fluid Inlet Temperature (◦ C) 7 20
Flow Rate (m3⋅s− 1) 1.33 × 10− 4 0.33 – 2 × 10− 4

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A. Goyal et al. Applied Energy 292 (2021) 116843

resistance increases the temperature difference between the coolant and

the TES material and renders the coolant temperature hotter than the
desired value for a fixed heat transfer rate.

4.2. Energy storage performance

The second set of experiments allowed us to characterize the energy

storage performance of the module under different conditions. In these
experiments, we estimated the heat transfer rate to or from the active
fluid circuit and integrated it throughout the experiment to estimate the
total amount of energy stored or discharged.
∫ t=tend
Estore = Q̇c/h dt (22)
t=o

We evaluated the performance of the module under two modes of

operation. In the first mode, we supplied the module with a constant
temperature at the inlet of the charge or discharge fluid during the
freezing and melting processes, respectively. This allowed us to estimate
the total energy content of the module during these processes. In the
second mode, we kept the rate of heat transfer constant during dis­
charging (melting) of the module. We accomplished this by varying the
discharge fluid inlet temperature and keeping the fluid flow rate con­
stant. This mode allowed us to simulate expected load profiles for peak
load shaving where a constant discharge rate is demanded from the
energy storage system for a certain duration of time.
We define the state of charge (SOC) of the thermal storage module as
a metric of its energy storage capacity between a specified temperature
range of the PCC material:
hPCC (T = 15◦ C) − hPCC (T = T)
SOC(T) = (23)
hPCC (T = 15◦ C) − hPCC (T = 0◦ C)
Here, we specified it to be nominally 100% (fully charged state) at 0
Fig. 5. Overall heat transfer conductance of the module with variation in fluid
◦
C and 0% (fully discharged state) at 15 ◦ C. It is analogous to the SOC of
flow rates. an electrochemical battery. This definition of SOC also includes the
storage of sensible thermal energy beyond the transition temperature of
the PCC. Based on this definition, the specific energy stored by the PCC
between 0% and 100% SOC is ~ 196.2 kJ⋅kg− 1.

4.2.1. Charge/Discharge at constant fluid inlet temperature

We conducted these experiments starting from completely dis­
charged (for charging) or charged (for discharging) state of the module
to estimate the full potential of energy storage capacity. These experi­
ments also simulate how this module would operate within an HVAC
system, and provides insight into the expected outlet temperatures, heat
transfer rates, and energy storage capacities. We varied fluid inlet
temperatures to understand charging or discharging performance at
different driving temperatures. We discuss one representative case of
charging and discharging at constant fluid inlet temperature and
compare our results to the model. Additional results are presented in the
Supplementary Information.
Fig. 7 shows results from discharging the module by providing it with
Fig. 6. Relative magnitude of different thermal resistances in the TES module. constant inlet temperature and flow conditions of the discharge fluid
(18 ◦ C at the inlet and a flow rate of 1.67 × 10− 4 m3⋅s− 1). To conduct a
complete discharge experiment on the TES module, we first charged it
we can observe that for a fixed ambient temperature, a lower evaporator
and then let it equilibrate to achieve near-isothermal initial conditions
temperature reduces the system efficiency. If the evaporator tempera­
within the module. Before starting the discharge experiment, we use the
ture decreases by a degree while keeping the ambient conditions and the
fluid conditioning loop to achieve the desired set point temperature at
cooling load at the same levels, the compressor work would increase by
the inlet of the discharge fluid. As the module is discharged, the fluid
0.03 kW per kW of cooling, leading to an increase in the total energy
temperature decreases from the inlet to the outlet. The lab boiler pro­
required for charging the TES module. Our objective behind using a
vides the required heat input to maintain the fluid temperature at its set
higher transition temperature material instead of ice is to keep the
point. The results show that during the bulk of the phase-change process,
charging refrigerant temperature as high as possible and minimize the
the module provides an approximately constant fluid temperature of
decrease in the system efficiency. A high contact resistance acts against
11.8 ◦ C and a discharge power of ~ 4.1 kW. This is attributed to a near-
that objective, and emphasizes the value of an effective heat transfer
isothermal phase-change process that provides a constant driving tem­
design. This also applies during discharge a high thermal contact
perature difference between the PCC and the fluid. As most of the

8
A. Goyal et al. Applied Energy 292 (2021) 116843

Fig. 7. Discharge performance of the module and comparison to simulations at Fig. 8. Fluid outlet temperature as a function of the SOC (discharge fluid inlet
constant discharge fluid inlet temperature of 18 ◦ C: fluid and module temper­ temperature 18 ◦ C).
atures (top), and discharge power and capacity (bottom) (uncertainties in re­
ported experimental quantities (not shown on the plot to maintain clarity): temperature and the SOC can inform the control designer about when
temperatures ± 0.5 ◦ C, discharge power: ±2.5% at nominal value). and for how long the TES system can be discharged.
Fig. 9 shows similar variations in the temperature of the charge fluid,
material within the module is melted (at ~ 40 min into discharge), the average module temperature, heat transfer rate, and energy storage
fluid outlet temperature starts to increase gradually, and the heat capacity during the charging of the module at a constant inlet temper­
transfer rate starts to decrease. This is due to a lower driving tempera­ ature of the charge fluid at − 2 ◦ C and a flow rate of 1.33 × 10− 4 m3⋅s− 1.
ture difference between the fluid and the PCC material. The total energy As the module is charged, the fluid outlet temperature decreases grad­
discharged during this process is ~ 3.46 ± 0.087 kWh. ually. The time required to completely charge the module is longer in
Fig. 7 also shows the variation in the average PCC temperature comparison to the discharge experiment because of fewer tubes in the
(arithmetic mean of eight embedded temperature measurements) with charging circuit and a lower driving temperature difference between the
time. The module starts at a near-isothermal condition at 2 ◦ C and is charging fluid and the phase-transition temperature of the material. The
discharged until it achieves an average temperature of 15 ◦ C. During total energy stored during this process is ~ 3.79 ± 0.18 kWh. As shown
discharge, the average module temperature does not show a distinct in Fig. 9, the discrepancies between the model and the experiment are
phase-change temperature, an observation consistent with separate more pronounced for the charge experiment. This might be due to
melting experiments in an environmental chamber. In these experi­ hysteresis between melting and solidification, and the unified property
ments, the average temperature is not an accurate predictor of the state data for the material might need to be adjusted to account for that.
of charge of the module but provides a qualitative indication of the Fig. 10 shows the variation in the charge fluid outlet temperature
performance of the module. Many factors can contribute to the uncer­ with SOC. The module starts charging at a near-isothermal condition at
tainty in measuring internal PCC temperature, including poor thermal 15 ◦ C and is charged until it achieves an average temperature of 0 ◦ C, as
contact between the tip of the probe and the material, inherent uncer­ shown in Fig. 9. In this experiment, we started with the module at 0%
tainty in the position of the probe, thermal hysteresis between melting
and solidification, and nonuniform distribution of the PCM within the
graphite matrix. To maintain the simplicity of a component-level model,
these effects are not captured in our numerical model.
As shown in Fig. 7, our calibrated numerical model predicts the
overall module performance well, and the fluid temperature at the outlet
of the module agreed with the experimental values. During the initial
phase of the discharge process, there is a discrepancy between the model
and the experiment because our model neglects the effects of fluid
storage in the tubes. The temperature decreases sharply in the experi­
ments because the cold liquid stored inside the tubes requires a finite
duration of time to be pushed out of the module as the pump begins
circulation. Minor discrepancies between simulations and experiments
are attributed to the assumption of uniform thermal contact resistance,
which could vary spatially within the module.
Fig. 8 shows the variation in the discharge fluid outlet temperature as
a function of the SOC for this case. In this experiment, we started with
the module at ~ 97.5% SOC (average module temperature 2 ◦ C) and
discharged it to 0% SOC (average module temperature 15 ◦ C). Regions
of the plot at both ends show a higher rate of change in the outlet
temperature of the discharge fluid due to the sensible heating of the Fig. 9. Charge performance of the module and comparison with simulations at
module. This profile of SOC with fluid outlet temperature is important in constant charge fluid inlet temperature of − 2 ◦ C (uncertainties in reported
developing active controls for using these TES modules with an HVAC experimental quantities (not shown on the plot to maintain clarity): tempera­
system. For different demand response scenarios, correlating the fluid tures ± 0.5 ◦ C, charge power: ±5% at nominal value).

9
A. Goyal et al. Applied Energy 292 (2021) 116843

Fig. 11. Discharging the module at constant heat transfer rate; outlet temper­
Fig. 10. Fluid outlet temperature as a function of the SOC (charge fluid inlet
ature of the discharge fluid (top) and discharge rate and total discharged energy
temperature − 2 ◦ C).
(bottom) (uncertainties in reported experimental quantities (not shown on the
plot to maintain clarity): temperatures ± 0.5 ◦ C, discharge power: ±3%).
SOC (average module temperature 15 ◦ C) and charged it to 100% SOC
(average module temperature 0 ◦ C). The outlet temperature of the
heat transfer rate, the module can sustain it for ~ 95 mins and pro­
charge fluid shows the corresponding variation, with steeper rates of
vide a total energy of 3.29 ± 0.03 kWh. Similarly, for the cases of 3.6-kW
change during the sensible cooling of the module and relatively constant
and 5.3-kW discharge rates, the module can sustain these heat transfer
temperature during the bulk of the phase-change process.
rates for ~ 49 and ~ 23 min and provide total energy of 3.04 ± 0.06
We observe that the total energy stored and discharged during these
kWh and 1.97 ± 0.35 kWh, respectively.
experiments (including the data presented in Supplementary Informa­
These experiments showed that starting at a fully charged condition,
tion) shows a gradual decrease over several cycles for the same depth of
a TES system for HVAC applications operates similar to electrochemical
discharge or state-of-charge variation. We attribute this to some leakage
batteries. The total usable energy that can be obtained from the module
from the PCC in the liquid state. As the PCC material undergoes repeated
depends on the discharge rate, which can vary with different operating
freezing and melting, there is some release of liquid phase during
scenarios. This behavior is also observed in electrochemical batteries, in
melting as it expands. In the next prototype system, we will employ
which the total energy extracted from a battery depends on the rate
methods to better seal the PCC and prevent this loss in capacity.
(electric current) at which it is discharged [33].
4.2.2. Discharge at constant heat transfer rate
In many load-shaving and load-shifting applications, the TES system
4.3. Hybrid operation with simultaneous charge and discharge
will be required to deliver a constant heat transfer rate to the building
for a desired duration of time. Therefore, we characterized the discharge
In many electric-grid scenarios, it is most valuable to shave the peak
performance of the TES module under different heat transfer rates. This load rather than shift it entirely [34]. The proposed system, with its dual
technique also allows for a comparison of TES systems in an analogous
fluid circuit configuration, enables the unique capability to simulta­
manner to electrochemical systems [31]. We conducted three experi­ neously charge and discharge the TES system to provide peak load
ments at varying heat transfer rates. The heat transfer rate in the system
shaving, which is not possible with conventional TES systems. For
was controlled by maintaining a constant flow rate of the discharge fluid instance, once fully charged during off-peak hours, the system can then
(1.67 × 10− 4 m3⋅s− 1) and modulating the inlet temperature to always
be discharged at a lower heat transfer rate to shave the peak load and the
maintain a constant temperature difference from the inlet to the outlet of remaining cooling capacity can be provided by operating the
the discharge fluid. For these experiments, we selected a cutoff tem­
compressor at a reduced capacity. This mode of operation will enable a
perature for the discharge fluid leaving the module (going to the longer discharge period using a smaller energy storage capacity and
conditioned space). This temperature is representative of the highest
reduced electricity consumption during peak-load hours.
fluid temperature that can be used by the building for space-cooling We performed an experiment to demonstrate this capability. We
applications. We then calculate the total discharged energy by the
initialized the experiment at a completely charged state. Fig. 12 shows
module in each experiment. the results from the experiment to provide a total heat transfer rate to
Fig. 11 shows the results of these experiments. The top plot shows the
the conditioned space of 3.75 kW while discharging the TES module at
variation in the discharge fluid temperature at the outlet of the module 1.75 kW over a period of ~ 90 min. This required simultaneous charging
(supplied to the conditioned space). As the heat transfer rate is
of the module at 2 kW. Therefore, this module design provides the
increased, the cutoff outlet temperature is achieved earlier. This is due to capability to shave the peak because of decoupled charge/discharge
a higher temperature difference required between the fluid and the PCC
processes and can be used for discharging over longer periods. As dis­
for a constant fluid flow rate. As the inlet temperature of the fluid is cussed earlier, oscillations during the early phase of the experiment are
increased to provide a higher heat transfer rate, the outlet temperature
attributed to the stored fluid inside the heat exchanger. Another brief
exceeds the cutoff temperature sooner compared to a case with a lower deviation in the temperature and heat transfer rate of the charge fluid is
heat transfer rate.
observed at ~ 20 min due to partial freezing of the glycol mixture and a
The bottom plot in Fig. 11 shows the variation of the heat transfer consequent decrease in its flow rate. Nonetheless, this experiment shows
rate and the total energy discharged from the module for the three
the potential of the versatile operation of this TES design. It should be
different heat transfer rates. As discussed above, at a high heat transfer noted that when coupled to an air conditioner, the charging fluid will be
rate the cutoff temperature is achieved sooner. For the case of a 2-kW
the refrigerant. As the refrigerant evaporates within the TES module, the

10
A. Goyal et al. Applied Energy 292 (2021) 116843

conductivity while maintaining the required energy density. This ma­

terial is readily available and inexpensive, making it viable for
manufacturing at commercial scales for integration with HVAC equip­
ment. We demonstrate that a finite volume approach of modeling this
system accurately predicts the performance of the system, as observed in
experiments. This modeling framework can be used as a design tool by
researchers and commercial manufacturers. Standalone experiments
using water-glycol in both circuits of the energy storage module helped
us uncover important aspects of the design and operation of these
systems.

• We identified that the thermal contact resistance between the fluid

tubes and the PCC material in the module accounted for a significant
fraction (>50%) of the total thermal resistance. Future designs will
aim at improving thermal contact at various interfaces in the module
by using flat tubes.
• We showed interesting operating principles for thermal batteries.
The heat transfer rate through these devices affects the total amount
Fig. 12. Simultaneous charging and discharging to enable hybrid mode oper­
ation for peak load shaving; fluid temperatures (top) and heat transfer rates of energy that can be utilized for a given use case. This information,
(bottom) (uncertainties in reported experimental quantities (not shown on the and the model developed here, can be used to better design thermal
plot to maintain clarity): temperatures ± 0.5 ◦ C, discharge power: ±2.5%, batteries to ensure access to all the PCC for the required discharge
charge power: ±5%). rate.
• Moreover, our heat transfer experiments show that this TES module
temperature of the fluid will remain nearly constant, with a significantly design can potentially be operated with both circuits using refrig­
higher heat transfer coefficient compared to the configuration presented erant, with the discharge side being a pumped liquid refrigerant
here. Therefore, we anticipate the performance of the system to improve loop. This feature would enable seamless integration with existing
during charging in an actual system. building HVAC systems. This would require more experimental evi­
Here, we evaluate the amount of peak load shaving from reducing dence in the future.
the compressor power as compared to a conventional air-conditioner
without TES. Using the Carnot COP definition (Section 4.1), we calcu­ Our ongoing research is focused on prototype development and
late the ideal compressor work input using Ẇcomp = Q̇evap /(COP × ηcomp ). experimental evaluation of a 21-kWh TES system integrated with an air
conditioner, using multiple modules like the design presented above.
We assume an ambient temperature during the peak load duration is 35
This system can shave peak energy demand and improve the demand
◦
C and the isentropic efficiency of the compressor (ηcomp) is 65%. For a
flexibility in caparison to an air conditioner without thermal storage.
conventional air-conditioner, we assume an evaporator temperature of
This can lead to significant energy and cost savings in locations with
10 ◦ C, which leads to a Carnot COP of 12.33. Therefore, for an air
time-of-use pricing of electricity.
conditioner providing 17.5 kW of cooling capacity, the electrical power
input required by the compressor is 2.18 kW.
CRediT authorship contribution statement
With the hybrid operation presented above, the total cooling pro­
vided to the conditioned space is 3.75 kW with 2 kW supplied from
Anurag Goyal: Software, Methodology, Investigation, Validation,
operating the charge-circuit compressor (46.7% of cooling comes from
Visualization, Writing - original draft. Eric Kozubal: Methodology,
the TES). Therefore, using the same ratio for a 17.5 kW capacity system,
Supervision, Validation, Conceptualization. Jason Woods: Supervision,
the compressor will provide 9.33 kW of cooling and the rest of the
Conceptualization, Funding acquisition, Project administration, Writing
cooling would be supplied by discharging the TES module during the
- review & editing. Malek Nofal: Resources. Said Al-Hallaj: Resources,
peak period. But, the integrated system operates at a lower evaporator
Conceptualization.
temperature due to the PCM transition temperature. Assuming an
average evaporator temperature of − 4◦ C from Fig. 12, the Carnot COP
Declaration of Competing Interest
during the peak period is 7.90. Using this and the 9.33 kW load for the
charge circuit, the electrical power input to the compressor is 1.82 kW.
The authors declare that they have no known competing financial
This translates to ~ 16% less power consumption for the compressor
interests or personal relationships that could have appeared to influence
during the peak period and can provide significant financial savings to
the work reported in this paper.
end-users.
This analysis also highlights the importance of the heat transfer
Acknowledgments
design of the TES module and the transition temperature of the PCM. For
a hybrid system operating with an evaporator temperature of 4 ◦ C, the
This work was authored by the National Renewable Energy Labo­
compressor power can be reduced to 1.45 kW (~33% less than a con­
ratory, operated by Alliance for Sustainable Energy, LLC, for the U.S.
ventional system). A higher evaporator temperature can be achieved by
Department of Energy (DOE) under Contract No. DE-AC36-08GO28308.
minimizing the contact resistance between the charge circuit and the
Funding provided by the U.S. Department of Energy Office of Energy
PCC and by using a PCM with a higher transition temperature (~8–10
Efficiency and Renewable Energy Building Technologies Office. The
◦
C).
views expressed in the article do not necessarily represent the views of
the DOE or the U.S. Government. The U.S. Government retains and the
5. Conclusions
publisher, by accepting the article for publication, acknowledges that
the U.S. Government retains a nonexclusive, paid-up, irrevocable,
We present results from the numerical modeling and experiments on
worldwide license to publish or reproduce the published form of this
a TES system for integration with building air conditioners. A PCC ma­
work, or allow others to do so, for U.S. Government purposes.
terial using n-tetradecane and graphite is used to provide high thermal
The authors also appreciate the financial and technical support for

11
A. Goyal et al. Applied Energy 292 (2021) 116843

this research by the U.S. Department of Energy Technology Commer­ [16] Py X, Olives R, Mauran S. Paraffin/porous-graphite-matrix composite as a high and
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