# Experimental characterization of the thermophysical properties of some selected phase change materials for building applications: Critical input data for numerical simulations

Appolinaire Kaboré, J.V. Simo Tala, Zohir Younsi, Daniel Bougeard

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Appolinaire Kaboré, J.V. Simo Tala, Zohir Younsi, Daniel Bougeard. Experimental characterization of the thermophysical properties of some selected phase change materials for building applications: Critical input data for numerical simulations. Journal of Energy Storage, 2025, 111, pp.115463. 10.1016/j.est.2025.115463. hal-04925789

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Research Papers

# Experimental characterization of the thermophysical properties of some selected phase change materials for building applications: Critical input data for numerical simulations

Appolinaire Kaboré<sup>a,b,*</sup>, Jules Voguelin Simo Tala<sup>a</sup>, Zohir Younsi<sup>c</sup>, Daniel Bougeard<sup>a</sup>

<figure><img src="image_3.png" /></figure>

ARTICLE INFO

Keywords:

Experimental characterization

Thermophysical properties

Phase change materials

Building energy

Thermal energy storage

Energy efficiency

ABSTRACT

A precise characterization of the thermophysical properties of Phase Change Materials (PCMs) used for the Latent Heat Thermal Energy Storage (LHTES) is necessary for the development and manufacturing of LHTES technologies. The complete input data for Computational Fluid Dynamics (CFD) simulations of PCMs phase transition processes is very lacking in the literature, making it difficult to set up CFD simulations and specially to guarantee the accuracy of the results. The present study focuses on a comprehensive experimental characterization of the thermophysical properties of six PCMs in order to support the numerical studies. Several measurement techniques allowed the characterization of these PCMs. The Anton Paar MCR 102 rheometer was used to determine the viscosity of the six PCMs and their temperature dependency. A TPS 2200 model HotDisk allowed the measurements of the thermal conductivity of both solid and liquid phases of the PCMs, using a temperature-controlled bath. A high-precision in-house experimental setup was developed and validated, for measuring the liquid phase density of PCMs and its temperature dependency. Subsequently, it allowed the determination of the thermal expansion coefficient, which is rare in the literature. Finally, a Differential Scanning Calorimeter (DSC) was used to determine the necessary thermal data for modeling the phase change processes, including latent heat, transition temperatures, and specific heat capacity. Six paraffinic (RT18HC, RT21HC, RT24HC) and bio-based (PT20, PT23, PT25) PCMs, with high potential for buildings application were fully characterized using the aforementioned techniques. The obtained results allowed to establish correlations to consider and integrate the temperature dependence of the thermophysical properties of the analyzed materials in the numerical simulations. This will improve the accuracy of numerical studies using these materials.

Nomenclature

Principle notations

<table><tr><td>c<sub>p</sub></td><td>Specific heat capacity</td><td>J/g·°C</td></tr><tr><td>L</td><td>Latent heat</td><td>J/kg</td></tr><tr><td>m</td><td>Mass</td><td>kg, mg</td></tr><tr><td>N</td><td>Number of trials</td><td>–</td></tr><tr><td>T</td><td>Temperature</td><td>°C</td></tr><tr><td>V</td><td>Volume</td><td>m<sup>3</sup>, ml</td></tr></table>

Greek symbols

<table><tr><td>α</td><td>Thermal diffusivity</td><td>m<sup>2</sup>/s</td></tr><tr><td>β</td><td>Thermal expansion coefficient</td><td>1/K</td></tr><tr><td>λ</td><td>Thermal conductivity</td><td>W/m·°C</td></tr><tr><td>μ</td><td>Dynamic viscosity</td><td>Pa·s</td></tr><tr><td>ρ</td><td>Density</td><td>kg/m<sup>3</sup></td></tr><tr><td>σ</td><td>Uncertainty</td><td></td></tr></table>

<footnote><sup>a</sup> IMT Nord Europe, Institut Mines-Telecom, Univ. Lille, Centre for Energy and Environment, F-59000 Lille, France</footnote>

<footnote><sup>b</sup> French Environment and Energy Management Agency, 20, avenue du Grésillé, BP 90406, 49004 Angers Cedex 01, France</footnote>

<footnote><sup>c</sup> Univ. Lille, Institut Mines-Télécom, Univ. Artois, Junia, ULR 4515 – LGCgE, Civil Engineering and geo-Environment Laboratory, F-59000 Lille, France</footnote>

<footnote>* Corresponding author at: IMT Nord Europe, Institut Mines-Telecom, Univ. Lille, Centre for Energy and Environment, F-59000 Lille, France.
E-mail address: appolinaire.kabore@imt-nord-europe.fr (A. Kaboré).</footnote>
## Abbreviations

<table><tr><td>DSC</td><td>Differential Scanning Calorimetry</td></tr><tr><td>HVAC</td><td>Heating, ventilation and air conditioning</td></tr><tr><td>LHTES</td><td>Latent Heat Thermal Energy Storage</td></tr><tr><td>PCM</td><td>Phase change material</td></tr><tr><td>TES</td><td>Thermal energy storage</td></tr></table>

## Subscripts

<table><tr><td>0</td><td>Initial</td></tr><tr><td>a</td><td>Apparatus</td></tr><tr><td>av</td><td>Average</td></tr><tr><td>l</td><td>Liquidus, liquid</td></tr><tr><td>m</td><td>Melting</td></tr><tr><td>max</td><td>Maximum value</td></tr><tr><td>mean</td><td>Mean value</td></tr><tr><td>min</td><td>Minimum value</td></tr><tr><td>p</td><td>Peak</td></tr><tr><td>ref</td><td>Reference</td></tr><tr><td>s</td><td>Solidus, solid</td></tr><tr><td>t</td><td>Total</td></tr></table>

# 1. Introduction

The growing energy crises and the catastrophic consequences of climate change lead populations, policymakers, and researchers to question current energy systems. It is evident that the path to energy transition necessarily involves improving energy efficiency and innovating these systems, especially in the residential sector, which represents one of the most energy-consuming and polluting sectors in the world [1,2]. One highly interesting and extensively researched avenue focuses on the development of innovative systems for storing free and sustainable solar energy, as well as the utilization of domestic and industrial waste heat for deferred use. One of the most promising Thermal Energy Storage (TES) technologies is the Latent Heat Thermal Energy Storage (LHTES), using Phase Change Materials (PCMs). This LHTES can be done either passively [3–5] by directly integrating PCMs into the building envelope or actively [6–8] through the use of a ventilation and control systems. In both cases, several authors demonstrate the significant interest in the use of LHTES technologies, which enhance the thermal inertia of buildings, reduce their energy consumption for thermal comfort, and also decrease their carbon footprint. However, despite their enormous potential, such as the high volumetric energy density compared to sensible heat storage, LHTES technologies are still not fully mastered and are mostly at the laboratory scale and under development. The development of LHTES systems, like any energy system, relies on a fundamental understanding through numerical simulations that are based on real input data regarding the materials used, such as the thermophysical properties of PCMs. In fact, a significant number of studies conducted on LHTES systems are numerical in nature, requiring a mastery and precision of the thermophysical properties of PCMs used as input data.

Several authors have emphasized this need of mastering thermophysical properties through studies on the influence of these properties on the performance of LHTES systems. Iten et al. [9] experimentally and numerically analyzed the influence of the specific heat capacity ($c_p$) temperature-dependence curve on the melting kinetics of RT25. After experimentally characterizing $c_p$ values using a DSC at two heating rates, 10 °C/min and 0.2 °C/min, they conducted a numerical study on a LHTES system to assess the impact of the observed differences in the $c_p$ curves. The authors demonstrated that implementing the $c_p$ curve obtained at 10 °C/min resulted in an extended phase change range of the PCM (from 18 °C to 31 °C), deviating by 2 °C to 4 °C from experimental results. Using the $c_p$ values obtained at 0.2 °C/min led to a narrower

phase change range for the PCM, which was closer to experimental results. Ling et al. [10] went further by showing that thermophysical properties of PCMs, including the phase change temperature, specific heat capacity, and latent heat, undergo variations between melting and solidification. They emphasized that considering these variations was crucial for reducing uncertainties in numerical simulations. These above different authors thus highlight the necessity of mastering thermophysical properties for numerical simulations. Peng et al. [11] then conducted a numerical analysis of the influence of varying the thermophysical properties of PCM on the performance of a LHTES unit and the optimal dimensions of fins used for heat transfer enhancement. The geometry analyzed was rectangular with two orthogonal fins. The dimensions of the fins and thermophysical properties were independently varied. The authors demonstrated that increasing density, specific heat, and latent heat linearly increased the heat storage capacity of the system. Furthermore, with regard to the charging duration, the authors stated that it was significantly extended when density, specific heat, latent heat, and viscosity increased. However, it was reduced with an increase in thermal conductivity and the thermal expansion coefficient. The authors stated that the melting rate increased with the increase of all thermophysical properties except for viscosity. Thus, it is evident that the mastery and the accuracy of the thermophysical properties of PCMs are crucial for the numerical development of LHTES systems, regardless of the application domain. This allows for reducing uncertainties and calculation errors and can avoid a significant overestimation or underestimation of LHTES system performance.

In the application of PCMs and LHTES systems to buildings, some experimental studies on PCMs characterization are conducted on non-commercial PCMs, with only a minority of commercial PCMs. However, the characterization is often carried out at a single temperature in both the solid and liquid phases, as performed by suppliers [12,13]. Dhamodharan and Bakthavatsalam [14] experimentally characterized coconut oil and lauric acid as low-temperature PCMs, determining latent and specific heat capacity through DSC analysis, as well as thermal conductivity in both the solid and liquid phases. The temperature-dependence of $c_p$ was determined, but the thermal conductivity was assessed only at 10 °C and 30 °C for the solid and liquid phases, respectively. Viscosity and density were not characterized. Similarly, Toifane et al. [15] experimentally characterized the thermophysical properties of a coating called ETMV 8, composed by 70 % PCM (Inertek 23) and 30 % plaster. Only the density, the specific heat, and the thermal conductivity were determined, providing average values without information regarding the material's temperature-dependent behavior. Hayat et al. [16] developed and experimentally determined the thermophysical properties of a nano-PCM using DSC analysis and a HotDisk device for thermal conductivity. Only average values were determined for thermal conductivity, while other properties such as density, viscosity, and their temperature-dependence were not discussed. From the literature analysis, it appears that in many numerical studies, various authors primarily rely on data provided by suppliers, and the PCMs that have been experimentally characterized are typically those for which essential properties are unknown. In all cases, the data is often incomplete, covering aspects such as sensible and latent heat, thermal conductivity, viscosity, and thermal expansion coefficient, but more importantly, their temperature-dependence, which is crucial for accurate numerical simulations.

Faced with the unavailability of certain thermophysical PCM data and potential inaccuracies, some researchers have worked on characterizing potential PCMs to establish a database of reliable information. Among the few authors who have established the temperature-dependence of thermophysical properties of PCMs, Longo et al. [17] determined the thermophysical properties of 5 low-temperature materials (1 °C - 10 °C), only in the liquid phase. The targeted application was for refrigeration. The authors have used a densimeter, a HotDisk device, and a rheometer. However, as mentioned, the intended application was for refrigeration, and the characterization was not performed in the solid
phase, although it is known that thermophysical properties vary in this phase with temperature. DSC analysis was not conducted, preventing access to information about the latent and specific heat capacity of PCMs, as well as their transition temperatures. To our knowledge, three pertinent studies have actually established the temperature-dependence of physical properties of PCMs used in buildings. Soares et al. [18] characterized ten commercial paraffinic PCMs for building applications and established temperature dependencies for several thermophysical properties, including specific heat capacity using DSC, and thermal conductivity and diffusivity, using a HotDisk device. Furthermore, the melting and solidification temperatures, latent heats of melting and solidification, and the temperature-dependence of specific heat were determined using a modulated DSC. The authors, after providing significant data, noted a substantial lack of data for numerical simulations and that suppliers' data can sometimes be overly optimistic. In their study, the authors provided important thermophysical data and their temperature dependencies that can be useful for numerical simulations. However, some data, such as liquid PCM density and its temperature-dependence for determining the thermal expansion coefficient, and the temperature-dependence of viscosity, were not addressed. Kraiem et al. [19] also established the temperature-dependence of the thermophysical properties of four paraffinic PCMs from Rubitherm, namely RT21, RT27, RT35, and RT50, using various experimental methods. The first two of these PCMs are best suited for building applications in heating and cooling. The authors determined the latent heats, phase change temperatures, and the temperature-dependence of specific heat through DSC analysis, all of which are essential for improving the accuracy of numerical simulations. A HotDisk device was used to determine the thermal conductivity and thermal diffusivity of the PCMs and their temperature-dependence, while pycnometer provided information about the temperature-dependence of density and thermal expansion coefficient. The authors claimed to have obtained interesting results comparable to the literature. However, data on the viscosity of the PCMs were missing, and only two PCMs were found to be suitable for building applications. Finally, Duquesne et al. [20] manufactured two eutectic PCMs from combinations of Capric Acid, Myristic Acid, and Palmitic Acid. They conducted a nearly complete characterization, including transition temperatures, latent heat, temperature-dependence of specific heat in the solid phase, viscosity, and density. However, thermal conductivity was determined only in the solid phase at a single temperature, providing no information on its temperature-dependence. While this study is the most extensive in terms of characterizing the temperature-dependence of the thermophysical properties of PCMs, the thermal conductivity, which is particularly important for PCMs, was determined for the solid phase of the two PCMs, and its temperature-dependence was not established. Moreover, only two PCM were analyzed.

The analysis of open literature reveals a significant lack of reliable and reproducible thermophysical data to support numerical simulations, especially for materials used in buildings. The efforts made so far remain insufficient, and the present study brings some novelties by completing and supporting the previous studies. It essentially provides a complete characterization of all the necessary thermophysical properties for CFD simulations, including their temperature-dependence. With the advancements of 3D CFD simulations capable of integrating the complex fluid dynamics involved in phase change phenomena, precise thermal and dynamic characterization of PCMs becomes imperative. Thus, critical input data for CFD simulations such as phase change temperatures, latent heat, thermal expansion coefficient, temperature-dependence of specific heat, thermal conductivity, density, and viscosity have all been characterized. The selected materials including paraffin and biobased PCMs, while some may have been studied in the literature, had not been characterized, especially in a complete way. Suppliers' data are often incomplete and non-reliable. Moreover, it is very challenging to find data on viscosity and thermal expansion coefficients, both in the literature and from suppliers, and these data are mandatory for numerical modeling of natural convection. In the present study, these properties

have been determined for the six PCMs using reliable and validated methods. Another innovative aspect of this study lies in the determination of the temperature dependence of the thermophysical properties of the PCMs, with correlations, particularly for viscosity, thermal conductivity, and density. These properties are sometimes available in the literature for other PCMs but often for a single temperature, which does not allow for highly reliable numerical simulation results. Finally, well-estimated uncertainties were assessed and the experimental procedure was validated with reference data. The various properties have been determined for six bio-based (PT20, PT23, PT25) and paraffinic (RT18HC, RT21HC, RT24HC) PCMs with great potential for building applications. This study, therefore, constitutes the most complete PCMs database to date, aimed at supporting CFD simulations. It includes PCMs whose thermophysical properties have been minimally investigated, and it provides critical data such as the temperature-dependence of viscosity and thermal expansion coefficient, which are rarely found in the literature.

## 2. Materials and methods

### 2.1. Phase change materials selection

In this study, two groups of low-temperature PCMs suitable for building applications, each composed of three PCMs, were characterized. The first group consists of paraffinic compounds produced by Rubitherm GmbH [21], namely RT18HC, RT21HC, and RT24HC. These two first PCMs are commonly used in the literature (RT18HC [22–24], RT21HC [25–27]) with incomplete thermophysical properties, and mainly from suppliers. The PCM RT24HC is less frequently discussed despite its interesting thermophysical properties from the supplier data sheet. The phase change temperature range analyzed for this first group is from 18 °C to 24 °C, corresponding to a suitable building application. The second group of PCMs, namely PT20, PT23, and PT25, commercialized by PureTemp LLC [12], have been rarely addressed in the literature. They offer the advantage of being bio-based and possess interesting thermophysical properties referring to the supplier data sheet. They have been studied by a limited number of authors in the literature [28–32]. The above various materials were selected for their compatibility with the transition temperature required for building applications, as well as for their interesting thermophysical properties provided by the suppliers and summarized in Table 1 even incomplete. All the materials characterized in this study have never been completely characterized in previous research, in particular when considering the thermophysical properties.

### 2.2. Experimental procedures

#### 2.2.1. Dynamic viscosity measurements

The dynamic viscosity measurements of the PCMs were performed using the Anton Paar MCR 102 rheometer [33] piloted by the Rheo-Compass data acquisition software. The rheometer is composed by a sample crucible placed in a Peltier module thermostat system and a conical module mounted on a body with a rotary electric motor and the possibility of vertical translation. The PCM sample is placed into the crucible, which is then temperature-controlled above its melting point using the Peltier module. The cylindrical module is then immersed in the crucible to a distance of 1 mm from the bottom of the crucible, and the PCM volume is such that a 1 mm overflow above the cylinder is considered. The entire setup is maintained at a regulated temperature for a sufficiently long duration to ensure uniform temperature homogeneity of the PCM, crucible, and cylindrical module. The experimental apparatus is illustrated in Fig. 1.

The rheological study is then conducted over a range of shear rates from 20/s to 300/s. This range of shear rates is reasonable given the low stresses and shear rates in natural convection. For each temperature, using the software to control the test, the variation of the PCM viscosity
<table><caption>**Table 1**

Thermophysical properties of the phase change materials by suppliers [12,13].</caption><thead><tr><th rowspan="2"></th><th colspan="7">Thermophysical properties</th></tr><tr><th>T<sub>s</sub>/l (°C)</th><th>L (kJ/kg)</th><th>ρs/l (kg/m<sup>3</sup>)</th><th>β (1/K)</th><th>Cp<sub>s</sub>/l (J/g °C)</th><th>λs/l (W/m·°C)</th><th>μ (mPa·s)</th></tr></thead><tbody><tr><td>RT18HC</td><td>17/19</td><td>260</td><td>880/770</td><td>-</td><td>2</td><td>0.2</td><td>-</td></tr><tr><td>RT21HC</td><td>20/23</td><td>190</td><td>880/770</td><td>-</td><td>2</td><td>0.2</td><td>-</td></tr><tr><td>RT24HC</td><td>23/26</td><td>200</td><td>800/700</td><td>-</td><td>2</td><td>0.2</td><td>-</td></tr><tr><td>PT20</td><td>20</td><td>171</td><td>950/860</td><td>-</td><td>2.07/2.15</td><td>0.23/0.14</td><td>-</td></tr><tr><td>PT23</td><td>23</td><td>201</td><td>910/830</td><td>-</td><td>1.84/1.99</td><td>0.25/0.15</td><td>-</td></tr><tr><td>PT25</td><td>25</td><td>187</td><td>950/860</td><td>-</td><td>1.99/2.29</td><td>0.25/0.15</td><td>-</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Experimental apparatus for viscosity measurements.</figcaption></figure>

as a function of shear rate was recorded. The trials were performed at least three times to ensure repeatability. The temperature-dependence of the dynamic viscosity was established over 20 °C to 60 °C. The Anton Paar rheometers are very precise; however, measurement uncertainties were evaluated.

### 2.2.2. *Thermal conductivity measurements*

The measurement of the temperature-dependence of the thermal conductivity of the PCMs was carried out using the HotDisk transient TPS 2200 [34], equipped with a Kapton-insulated Hot Disk sensor of model 5465 defined by a diameter of 6.4 mm. The sensibility of the used apparatus was of 5 % on the thermal conductivity measurement. The

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Experimental apparatus for thermal conductivity measurements.</figcaption></figure>
equipment used for characterization includes the HotDisk device, the 5465 sensor, a JULABO HighTech F25-HL circulating cryostat with 0.01 °C temperature precision, a cylindrical stainless steel container, and a calibrated thermocouple. The thermocouple was maintained in the PCM during the trials, to capture the PCM temperature. The experimental protocol is summarized on Fig. 2. The measurement of the thermal conductivity by the HotDisk device is based on the Transient Plane Source (TPS) method, developed by Gustafsson [35,36], and certified according to ISO 22007-2. According to the supplier, the TPS method is absolute and does not require repeated calibrations or the use of standard samples, as is common with other approaches. Furthermore, there is no need for fixed sample geometries, which inherently distort contact agents or require cumbersome surface modifications. All the details about the measurement procedure, theories, and equations of the TPS method are presented in the HotDisk user manual [37].

The conductivity measurement was conducted in both the solid and liquid phases. Initially, the PCM was introduced in its liquid phase into the container, which was then immersed in the thermostatic bath. The Kapton sensor was vertically immersed in the container, with half of it submerged in the PCM, and it was held in place by a support. The calibrated thermocouple was also immersed in the PCM, positioned laterally near the sensor to determine the PCM's temperature surrounding the sensor. In the solid phase, the PCM solidifies directly around the sensor to ensure good thermal contact. The Thermal Conductants Analyzer software was used to simultaneously acquire thermal conductivity (λ), thermal diffusivity (a), and specific heat per unit volume (ρc_p). A temperature range from 10 °C to 50 °C was explored using the thermostatic bath. Power levels of 20 mW to 30 mW and measurement times ranging from 10 s to 40 s were used depending on the PCM and its phase. These power levels are recommended for materials with low conductivity [19], and the short measurement time helps inhibiting the influence of natural convection. This method for measuring conductivity in the liquid phase was also used by Kraiem et al. [19]. Several conditions must be met to ensure the validity of a measurement:

* D_p » R_p: The thickness or depth of the sample must be significantly greater than the radius of the sensor to ensure the theoretical assumption of a semi-infinite medium.

* 2 °C < ΔT < 5 °C: The temperature variation of the probed quantity of PCM must be between 2 °C and 5 °C.

* 0.33 < Δt < 1: The total characteristic time should range from 0.33 to 1 to ensure that the probing depth is significantly greater than the radius of the sensor in order to meet the assumption of a semi-infinite medium.

* Standard deviation <9 × 10⁻⁴.

For each temperature and each PCM, at least three tests were conducted to ensure repeatability, and the average of the values is considered.

### 2.2.3. Liquid phase density measurements

As explained in the introduction, the precise characterization of PCMs liquid phase density temperature dependence is crucial to accurately simulate natural convection movements in CFD simulations of LHTES. A laboratory-developed in-house technique was designed and used to ascertain the PCMs' liquid phase density's temperature-dependence. As seen in Fig. 3, the different elements used to develop the set-up are a water thermal bath with 0.01 °C regulation precision, volume graduated pipettes, a silicone stopper, a balance, and a glass flask with a flat bottom. Using a precise balance SAUTER RC 2022 with 0.1 g of accuracy, the masses of the apparatus elements m_a — flask, pipette, and stopper — were measured individually and after assembly to ensure a good accuracy. A known volume of the liquid PCM was introduced into the 250 ml glass flask, up to the flask's neck, using a 200 ml graduated beaker. The silicone stopper was used to seal the flask, and it had a hole drilled through the center for the insertion of a 25 ml graduated pipette. The amount of PCM in the flask was topped off with a second 3 ml graduated pipette until it spilled over into the firsts graduations of the 25 ml pipette. The initial volume of PCM - V₀ - was then precisely determined as well as the initial graduation. The total mass m_T including setup mass and PCM mass was determined using the precise balance. The PCM mass, m, was then calculated by the difference between the total mass and the setup mass m = m_T - m_a. After that, the assembly was embedded in a temperature-controlled bath and set point temperature of the bath was set to values from above the melting point, up to 60 °C with 5 °C increment. A reading of the PCM level in the 25 ml pipette was used to record the variation in the volume of the PCM V = V₀ + ΔV at each stabilized temperature, then using Eq. (1), the density ρ for each temperature was ascertained.

<figure><img src="image_6.png" /><figcaption>Fig. 3. Experimental apparatus for PCM liquid phase density measurements.</figcaption></figure>
$$ \rho = \frac{m}{V} \qquad (1) $$

Eq. (2) was used to obtain the thermal expansion coefficient, which is crucial for CFD modeling of natural convection. Various uncertainties associated with the measurement have been quantified and the precision of the technique was shown. To validate the experimental procedure and demonstrate its precision, a characterization was performed with distilled water, and the result was compared to data from the literature [38].

$$ \beta = - \frac{1}{\rho_0} \frac{\partial \rho}{\partial T} \qquad (2) $$

### 2.2.4. DSC analysis

The DSC (Differential Scanning Calorimetry) analysis of PCMs was performed using the NETZSCH 3500 Sirius Analyzer [39] with a precision of lower than 2 % in the phase change enthalpy and 0.1 °C in temperature. The results were post-processed using the Proteus Analyzer software. The equipment used is of the heat-flux DSC type [40], which allows the analysis of PCM samples weighing a few milligrams based on the measurement of the heat exchanged between the sample and its environment. In this method, two crucibles, one of which is a reference and the other containing the sample, are placed in the same environment (furnace) kept inert with nitrogen and at a controlled temperature, in the instrument's furnace. A temperature program was established to sweep a temperature range well before and after the phase change of the PCM. The instrument, using sensors, then measures the heat flow exchanged between each crucible and the environment, thus allowing the determination of the energy stored or released by the PCM during the temperature variation (sensible heat) or at constant temperature (latent heat) by the difference between the two heat flows. Since the method principle is well known from the literature [40–44], only the measurements processes were presented in this study.

For each measurement of L, a series of two test were conducted. Firstly, a baseline measurement was taken by acquiring the signal from two empty crucibles of nearly identical mass, one being the reference and the other to later hold the sample. Once the DSC signal was obtained, a few milligrams of the sample are placed into the second crucible, and the DSC signal was acquired again. The DSC signal used for

determining the latent heat and phase change temperatures will be the difference between the signal acquired with the sample and the baseline. This approach helps reduce uncertainties by eliminating the influence of potential differences in crucible masses. The measurement of $c_p$ is done in three steps: first, a baseline was established using two empty crucibles, followed by the acquisition of the DSC signal from a material with a known $c_p$ that serves as calibration, and finally, the acquisition of the DSC signal from the sample. The calibration material used in this study was sapphire, whose temperature-dependence of $c_p$ is precisely known. This method, based on these three measurements, follows ISO 11357-1 [42] standards and allows for the precise determination of the material's specific heat within the instrument's sensibility. So, the experimental procedure illustrated in Fig. 4 can be summarized in five steps as follows:

* The identification of a triplet of crucibles + lids with very similar total masses, using a high-precision balance from METTLER TOLEDO (0.01 mg).

* Preparation of the crucibles: the reference crucible is sealed empty, and the sample to be characterized, with its mass precisely determined, is introduced into the second crucible. For the $c_p$ measurements, a known mass of sapphire was placed into the third crucible.

* Placing the crucibles in the DSC instrument, taking care to center the sensors below, and handling them meticulously with the use of specially designed tweezers.

* Establishing a temperature program for acquiring the DSC signal.

* Post-processing and analyzing the results using the Proteus Analysis software.

At least two tests were conducted for the latent heat measurement to ensure repeatability, and the sensitivity of the apparatus was considered as main uncertainty source. The masses of the different PCMs samples

<table><caption>**Table 2**
PCMs sample masses for the DSC measurements.</caption><thead><tr><th rowspan="2"></th><th colspan="6">PCM</th></tr><tr><th>RT18HC</th><th>RT21HC</th><th>RT24HC</th><th>PT20</th><th>PT23</th><th>PT25</th></tr></thead><tbody><tr><th>Mass (mg)</th><td>24.20</td><td>24.78</td><td>26.45</td><td>27.78</td><td>23.00</td><td>30.40</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Experimental apparatus for DSC measurements.</figcaption></figure>
are summarized in Table 2.

## 2.3. Uncertainties analysis

In this section, the analysis of uncertainties related to measurements has been conducted. An uncertainty analysis was carried out in compliance with Recommendation INC-1 (1980) of the Working Group on the Expression of Uncertainties and Recommendation 1 (CI-1981) of the International Committee for Weights and Measures (CIPM) [45], and according to Moffat [46], in order to confirm the accuracy of the various experimental procedures and results as well as their relevance. According to these recommendations, two types of uncertainties can be identified based on the measurement procedure. Type A uncertainties characterize quantities estimated from repeated and independent tests, while type B uncertainties are associated with quantities estimated from a single test.

In the case of determining a given quantity X through N random and repeated tests, the best estimation of the quantity X is the arithmetic mean given by Eq. (3).

$$ \bar{X} = \frac{1}{N} \sum_{i=1}^{i=N} X_i \qquad (3) $$

The Type A uncertainty characterizing a series of multiple measurements is given by the experimental standard deviation of the mean, as designated by Eq. (4).

$$ \sigma = \sqrt{\frac{1}{N(N-1)} \sum_{i=1}^{i=N} (X_i - \bar{X})^2} \qquad (4) $$

In the case of Type B uncertainty associated with single measurements, the uncertainty considered for each measured quantities is linked to the precision of the measuring instrument. Considering e as the error associated with the precision of the measuring instrument, and assuming that all measurements are within the interval [X - e; X + e] with a probability of 1, and further assuming that the measured quantity is also equally distributed within the interval, according to ISO standard [45], the measurement uncertainty is given by relation (5).

$$ \sigma = \frac{e}{\sqrt{3}} \qquad (5) $$

When a quantity $X(x_i)$ is calculated from several other measured quantities, the total uncertainty $\sigma_T$ on the quantity is evaluated using Eq. (6) according to Moffat [46], which integrates the uncertainties $\delta x_i$ associated with each measured quantity.

$$ \sigma_t = \sqrt{\sum_{i=1}^{i=N} \left( \frac{\partial X(x_i)}{\partial x_i} \delta x_i \right)^2} \qquad (6) $$

### 2.3.1. Dynamic viscosity

The rheometer used in this study from Anton Paar [33] has a high precision in viscosity measurement. For each temperature and each PCM, at least three tests were conducted to ensure good precision of the results. Two types of uncertainties were considered in viscosity measurement. The first concerns uncertainty of “Type A” estimated by Eq. (4) related to conducting tests multiple times and considering the mean as the viscosity value. The second one concerns the precision of the hypothesis of Newtonian fluid considered for all PCMs. The viscosity value was considered as the average of the values of the viscosity over the shear rate range analyzed. The hypothesis is first confirmed by analyzing the quasi-constant viscosity with the shear rate. Then the precision of this hypothesis is determined by the calculation of an uncertainty. This uncertainty was considered to be the standard deviation associated to the previously determined average value of the viscosity. The uncertainties are represented in Section 3.1.

### 2.3.2. Thermal conductivity

The measurement of the thermal conductivity was carried out after several tests, allowing for considering an uncertainty of “Type A” for each temperature of each PCM. The average value of the different repeated tests was considered as the conductivity value at a given temperature. Furthermore, the HotDisk apparatus used, the TPS 2200 model [34], has a measurement sensitivity of 5 % on the thermal conductivity. The total uncertainty related to thermal conductivity measurement is considered as the sum of the uncertainty of Type A calculated by Eq. (4), and the uncertainty associated to the precision of the instrument. For the different PCMs, measurement uncertainties have been established in Section 3.2.

### 2.3.3. Liquid phase density

To guarantee result repeatability, density measurement experiments were run several times for the water example, then just once for each other PCM. As a result, type B uncertainties must be taken into account in these tests. The density uncertainty is a composite uncertainty that integrates the uncertainties of mass and volume. Eq. (7) thus yields the total uncertainty $\sigma_p$.

$$ \sigma_p = \sqrt{\left(\frac{1}{V}\sigma_m\right)^2 + \left(\frac{m}{V^2}\sigma_v\right)^2} \qquad (7) $$

The degree of uncertainty arising from the PCM mass, $\sigma_m$, is significantly associated with the balance's accuracy. The inaccuracy of the balance that was used is $e = 0.1$ g, then the uncertainty on the mass measurement was evaluated by Eq. (5). Five primary uncertainties can be identified from the PCM volume V determination:

* The uncertainty associated to the graduation of the supplier's flat-bottomed flask.

* The uncertainty related to the reading in the beaker when determining the initial PCM volume.

* The uncertainty associated with the pipette's graduation.

* The reading's uncertainty associated to the reading on the pipette during PCM volume expansion.

* The uncertainty associated to the pipette's and the flask's thermal expansion when rising the temperature, calculated by using a thermal expansion coefficient of $3.3 \times 10^{-6}/K$ for glass [47].

The uncertainties associated with density measurements are provided in Section 3.3.

### 2.3.4. DSC measurements

The balance used to determine the masses of the samples and crucibles is of very high precision, up to 0.01 mg. It is estimated that the uncertainty in the mass has negligible effect on the measurement data and can be neglected. The measurement uncertainties associated with the DSC analysis of the various PCMs are primarily related to the precision of the instrument, which has a measurement uncertainty of 2 % in the phase change enthalpy and 0.1 °C in temperature measurements. The results presented in Section 3.4 are associated with a 2 % uncertainty.

## 3. Results and discussions

In this section, the results of the various tests are presented and discussed with the aim of establishing the temperature-dependence of the complete thermophysical properties of the six PCMs.

### 3.1. Temperature-dependence of the liquid phase dynamic viscosity

The viscosity measurement was conducted by performing rheological analysis of the PCMs, i.e., observing the viscosity behavior as a function of the shear rate. In the case of PCMs melting or solidification,
shear is primarily due to the friction of the liquid PCM with the walls of the PCM container due to the development of the natural convection, and has low values. Low shear rates ranging from 20/s, limited by the capabilities of the rheometer, to 300/s were considered. For each PCM, the tests were conducted multiple times to ensure result repeatability. Fig. 5a presents the evolution of the viscosity of PT23 as a function of shear rate for 3 different tests at a temperature of 30 °C. A nearly linear evolution of viscosity is observed, indicating a quasi-independence of the viscosity on the shear rate, for the range of shear rates studied. This behavior observed for all PCMs allows them to be considered as Newtonian fluids with constant viscosity, which is the average value within the analyzed shear rate range. Additionally, a superposition of results is observed for all conducted tests, indicating an experimental procedure and test conditions that do not influence the results.

In addition to having a stable experimental procedure, the relevance of the results was verified by characterizing glycerol, whose temperature-dependent viscosity is known in the literature [48,49]. Glycerol with a purity >99 % from ThermoFisher was used as a validation case, and the results were compared to those of Slie and Madigosky [48]. Fig. 5b presents the evolution of the viscosity of glycerol determined in this study overlaid with the data from Slie and Madigosky [48]. A very high level of agreement is observed between the results of this study and those from the literature, with a maximum relative difference of 3.6 % observed at 20 °C. The rheometer and experimental procedure used enable the determination of viscosity with high precision as a function of temperature.

Once the experimental procedure was validated, the six PCMs, namely RT18HC, RT21HC, RT24HC, PT20, PT23, PT25, were characterized, and the temperature-dependence of the viscosity was determined and presented in Fig. 6. For the six PCMs studied, viscosity decreases as temperature increases, which is consistent with theory because increasing temperature increases the kinetic energy of the constituent molecules of PCMs, allowing them to overcome intramolecular attractive forces and thus move more freely. The trend of the temperature-dependence varies according to the PCM. By comparing the six PCMs, PureTemp products have higher viscosity values ranging from 2 mPas to 16 mPas than Rubitherm products, whose viscosity values, with fairly close values, vary from 1 mPas to 4 mPas depending on temperature. PT23 presents the highest viscosity values ranging from 16 mPas to 5 mPas as the temperature varies from 20 °C to 60 °C. These differences in viscosity values will impose different behaviors on the phase transition process of the PCMs studied: more viscous PCMs such as PureTemp products, will have limited movements due to high viscosity

forces that slow down natural convection compared to Rubitherm products. For the six PCMs studied, the temperature-dependence of viscosity can be fitted with an exponential function described in Eq. (8), with a coefficient of determination R² exceeding 0.99 in all cases. An exponential function is commonly used to interpolate the temperature dependence of a fluid's viscosity because it effectively captures the nonlinear variations in viscosity with temperature changes. Exponential models describe the rapid reduction in liquid viscosity as temperature increases, as intermolecular forces become less significant. This is supported by White and Majdalani [50], who state that the liquid's viscosity declines with an increasing temperature, and such declination is roughly exponential. This observation was confirmed during the analysis of our test results for all PCMs. The coefficients a and b of the fitting function as well as the coefficient of determination and the measurements uncertainties are given in Table 3 for all the six PCMs.

$$ \mu(T) = a \times e^{bT} \qquad (8) $$

## 3.2. Temperature-dependence of the thermal conductivity

Thermal conductivity is the intrinsic property of a material to propagate heat within itself. This property of the material is dependent on its temperature. In the present study, the thermal conductivity measurement was conducted using a HotDisk device and a thermostatic bath to regulate and control the temperature of the PCM sample. Multiple tests were performed for each target temperature of the PCM to ensure results repeatability and limit the uncertainties. In this regard, Fig. 7 depicts the distribution of PT23 and RT18HC thermal conductivity results for three different tests. A good superimposition of data is observed among the different trials for each given temperature and each PCM. These results indicate a well-controlled experimental procedure, with test conditions having minimal impact on the results, thereby also limiting uncertainties associated with measurements. The same experimental procedure was adopted for all the six PCMs studied. Fig. 8 illustrates the evolution of thermal conductivity for the six PCMs with temperature, ranging from 5 °C to 50 °C, encompassing both the solid and liquid phases. To facilitate the reading of the values on the figure, the data has been compiled in Table 4. Observing the trend of conductivity with temperature, as expected, the thermal conductivity of the six PCMs studied increases as temperature rises. Indeed, raising the material temperature increases the thermal agitation of molecules, causing them to vibrate and move more easily and rapidly, thereby facilitating heat transfer within the material. This increase in thermal conductivity with

<figure><img src="image_8.png" /><figcaption>Fig. 5. Validation of the experimental method: (a) measurements repeatability on PT23, (b) validation with data from literature using glycerol results by Slie and Madigosky [48].</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. Temperature-dependence of the dynamic viscosity of the six PCMs studied.</figcaption></figure>

<table><caption>**Table 3**
Fitting coefficients and uncertainties for the viscosity determination.</caption><thead><tr><th></th><th>a (mPa·s/°C)</th><th>b (mPa·s)</th><th>R<sup>2</sup> (-)</th><th>σ<sub>μ,min</sub> (mPa·s)</th><th>σ<sub>μ,max</sub> (mPa·s)</th></tr></thead><tbody><tr><td>RT18HC</td><td>5.7147</td><td>-0.02</td><td>0.9951</td><td>±0.08</td><td>±0.11</td></tr><tr><td>RT21HC</td><td>6.2538</td><td>-0.02</td><td>0.9983</td><td>±0.09</td><td>±0.1</td></tr><tr><td>RT24HC</td><td>15.1774</td><td>-0.024</td><td>0.9965</td><td>±0.09</td><td>±0.13</td></tr><tr><td>PT20</td><td>36.89</td><td>-0.034</td><td>0.9978</td><td>±0.08</td><td>±0.11</td></tr><tr><td>PT23</td><td>9.3533</td><td>-0.022</td><td>0.9964</td><td>±0.09</td><td>±0.12</td></tr><tr><td>PT25</td><td>4.7365</td><td>-0.018</td><td>0.9944</td><td>±0.09</td><td>±0.16</td></tr></tbody></table>

temperature is observed in the liquid phase for all the six PCMs studied, and in the solid phase for five PCMs except for RT24HC. This same trend observation has been made by authors such as Soares et al. [18] on PCMs such as Rubitherm's RT25HC and others like PCM18 and PCM28. The observation on the decrease trend in the thermal conductivity as the temperature increase can partly be attributed to the effect of thermal expansion and others specific properties of these PCMs. By comparing the solid and liquid phases, PCMs exhibit thermal conductivity values in the solid phase that are at least equal to those in the liquid phase, except for RT21HC. This trend observation, also noted by Kraiem et al. [19], can be explained by the crystalline and ordered structure of the solid phase of these PCMs, allowing for strong bonds between molecules, thus

favoring more efficient heat transfer. Additionally, there is the effect of density, as the density of the solid phase of PCMs is generally higher than that of the liquid phase, as seen in Table 1. This difference in density implies molecular compactness and better heat transfer.

By analyzing the various thermal conductivity values measured, they range from 0.17 W/m.°C to 0.34 W/m.°C, depending on the PCMs, phases, and temperatures. These relatively low values are consistent with thermal conductivity values observed in the literature for organic PCMs in general [18–20]. By comparing the PCMs, RT18HC exhibits the highest thermal conductivity values in the solid phase, reaching around 0.34 W/m.°C at 15 °C, followed by the RT24HC. At 10 °C, both RT24HC and RT18HC display thermal conductivity values of 0.32 W/m.°C. RT21HC shows the lowest thermal conductivity values in the solid phase, ranging from 0.17 W/m.°C to 0.2 W/m.°C. At 15 °C, the difference in thermal conductivity between RT18HC and RT21HC is 0.17 W/m.°C, representing a relative difference of 100 %. In the liquid phase, the disparity in values is reduced as all PCMs have thermal conductivity values between 0.2 W/m.°C and 0.26 W/m.°C. RT24HC exhibits the highest values, approaching 0.25 W/m.°C, closely followed by RT18HC, PT25, and PT20. Authors such as Kraiem et al. [19] and Soares et al. [18] present values of thermal conductivity very comparable to the data in the present study. The thermal conductivity values presented by the

<figure><img src="image_10.png" /><figcaption>Fig. 7. Measurements repeatability of the PT23 and RT18HC thermal conductivity.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 8. Temperature-dependence of the thermal conductivity of the six PCMs studied.</figcaption></figure>

**Table 4**

Summary of the temperature-dependence of the thermal conductivity of the six PCMs studied.

<table><thead><tr><th rowspan="2"></th><th colspan="7">Thermal conductivity values λ (W/m·°C)</th></tr><tr><th>5 °C</th><th>10 °C</th><th>15 °C</th><th>20 °C</th><th>25 °C</th><th>30 °C</th><th>40 °C</th><th>50 °C</th></tr></thead><tbody><tr><th>RT18HC</th><td>0.325</td><td>0.323</td><td>0.341</td><td>0.271</td><td>0.265</td><td>0.251</td><td>0.243</td><td>0.246</td></tr><tr><th>RT21HC</th><td></td><td>0.170</td><td>0.174</td><td>0.215</td><td>0.269</td><td>0.243</td><td>0.234</td><td>0.227</td></tr><tr><th>RT24HC</th><td></td><td>0.316</td><td>0.296</td><td>0.297</td><td>0.271</td><td>0.254</td><td>0.257</td><td>0.263</td></tr><tr><th>PT20</th><td></td><td>0.224</td><td>0.256</td><td>0.241</td><td>0.241</td><td>0.227</td><td>0.236</td><td>0.247</td></tr><tr><th>PT23</th><td></td><td>0.259</td><td>0.273</td><td>0.289</td><td>0.2</td><td>0.203</td><td>0.210</td><td>0.213</td></tr><tr><th>PT25</th><td></td><td>0.226</td><td>0.221</td><td>0.232</td><td>0.261</td><td>0.237</td><td>0.239</td><td>0.253</td></tr></tbody></table>

authors range from 0.18 W/m·°C to 0.35 W/m·°C for the solid phase of PCMs, and from 0.15 W/m·°C to 0.26 W/m·°C for the liquid phase [18]. The uncertainties associated to the thermal conductivity measurements are depicted in Table 5.

The thermal conductivity values will mainly influence the discharging process of the systems. Higher thermal conductivity implies accelerated solidification of the PCM during the discharge process. Table 6 presents the average thermal conductivity values of the PCMs, considering both the solid and liquid phases. The PCM RT18HC exhibits the highest thermal conductivity value, reaching 0.283 W/m·°C, thus having the highest potential of conductive heat transfer process. The PCMs PT20, PT23, and PT25 show similar average thermal conductivity values which are lower. RT24HC also demonstrates notable thermal conductivity value (λ = 0.279 W/m·°C), while RT21HC has the lowest thermal conductivity value (λ = 0.219 W/m·°C).

**Table 5**

Thermal conductivity measurements uncertainties.

<table><thead><tr><th></th><th>σλ, min (W/m·°C)</th><th>σλ, max (W/m·°C)</th></tr></thead><tbody><tr><th>RT18HC</th><td>±0.013</td><td>±0.019</td></tr><tr><th>RT21HC</th><td>±0.009</td><td>±0.019</td></tr><tr><th>RT24HC</th><td>±0.014</td><td>±0.021</td></tr><tr><th>PT20</th><td>±0.012</td><td>±0.015</td></tr><tr><th>PT23</th><td>±0.01</td><td>±0.016</td></tr><tr><th>PT25</th><td>±0.012</td><td>±0.015</td></tr></tbody></table>

**Table 6**

PCMs thermal conductivity mean values.

<table><thead><tr><th></th><th>RT18HC</th><th>RT21HC</th><th>RT24HC</th><th>PT20</th><th>PT23</th><th>PT25</th></tr></thead><tbody><tr><th>λ (W/m·°C)</th><td>0.283</td><td>0.219</td><td>0.279</td><td>0.239</td><td>0.235</td><td>0.238</td></tr></tbody></table>

### 3.3. *Temperature-dependence of the liquid phase density*

One of the particularities and novelties of the present study lies on the development of an in-house experimental method at the laboratory for characterizing the liquid density of PCMs. The experimental procedure described in Section 2.2.3 was validated using water as PCM. Tests were conducted multiple times to ensure result repeatability and mastery of the experimental procedure. Fig. 9a presents the two tests conducted on water with different target temperatures. This choice of different target temperatures between the two trials was intentionally done to further confirm the repeatability of the method. A superposition of the results from the two tests is observed, indicating repeatability of the experimental procedure and minimal influence from experimental conditions. To validate the device and experimental procedure, the results obtained on distilled water were compared to literature data. Additionally, characterization of the liquid density of RT21HC was performed using the D5 densimeter from METTLER TOLEDO which has a precision of 0.05 kg/m³ [51]. These results served as validation data for the measurements conducted on RT21HC. Fig. 9b presents the density data measured using the present method, compared to literature data for water [38] and the D5 densimeter data for RT21HC. The results
<figure><img src="image_12.png" /><figcaption>Fig. 9. Validation of the experimental method: (a) measurements repeatability for distilled water, (b) double validation with literature distilled water results [38] and results from D5 densimeter using the PCM RT21HC.</figcaption></figure>

show an overlap of the results for RT21HC and a near overlap for distilled water. The maximum relative deviation observed in the density values of this study compared to validation data is <0.5% for both water and RT21HC and the maximum measurement uncertainty is ±4 kg/m³.

After the double validation of the device and experimental procedure, the other 5 PCMs, namely RT18HC, RT24HC, PT20, PT23, and PT25, were characterized in order to determine the temperature-dependence of the density of the liquid phase and the thermal expansion coefficient. Fig. 10 shows the evolution of the density of the liquid phase as a function of temperature for the six PCMs characterized. For all these PCMs, the same trend is observed: an almost linear evolution, with a negative slope, due to the increase in the volume of the material induced by the thermal expansion. This linearity of density with temperature is common in many materials, even outside commonly used PCMs. Thus, the temperature-dependence of liquid density can be described by the linear regression polynomial defined by Eq. (9). While

the variation in density is nonlinear, within limited temperature ranges, density profiles as a function of temperature can be represented using polynomials. This approach allows to capture the main trends while keeping the model relatively simple. Several authors, such as Kraeim et al. [19] and Longo et al. [17], have used polynomial functions to interpolate the density values of the PCMs they characterized.

$$ \rho(T) = cT+d \quad (9) $$

The density values range from 750 kg/m³ to 800 kg/m³ for Rubi-therm's PCMs (RT18HC, RT21HC and RT24HC), which are lower than those of PureTemp's products (PT20, PT23 and PT25), which range from 820 kg/m³ to 880 kg/m³. This difference is due to the difference in molecular structure of the different materials. The PureTemp PCM PT25 has the highest density values, with a minimum of 860 kg/m³ at 60 °C, while RT21HC has the lowest values. This difference in density impacts the phase change kinetics of the material, among other factors such as

<figure><img src="image_13.png" /><figcaption>Fig. 10. Temperature-dependence of the liquid phase density of the six PCMs studied.</figcaption></figure>
natural convection and storage capacity.

By adopting the linear regression of the density variation with temperature from Eq. (9), the coefficients *c* and *d*, as well as the linear regression coefficient *R*², were determined and are indicated in Table 7 for the six PCMs. The thermal expansion coefficient *β*, which is highly important as considered as a critical data for modeling natural convection owing its lack in the open literature for a wide range of PCM, is determined using the relation given by Eq. (2). The reference density *ρ*₀ is taken at 30 °C for all PCMs, and the term *∂ρ/∂T* corresponds to the slope of the linear regression *ρ*(T) for the six PCMs, i.e., the coefficient *c*. The results of the thermal expansion coefficient *β* show relatively close values for all the six PCMs. Rubitherm's PCMs have slightly higher thermal expansion coefficients than PureTemp's, which have the highest density values. By comparing the six PCMs, the PCM RT18HC has the largest value of *β*, while PT20 has the smallest one, with values of 0.00093/°C and 0.00081/°C, respectively. The uncertainties, with a maximum value of ±4 kg/m³ for all the PCMs are depicted in Table 7. As a reminder, the buoyancy forces modeling natural convection are given, using the Boussinesq approximation for constant value of beta by Eq. (10).

$$F_b = \rho_{\text{ref}} \beta g (T - T_{\text{ref}}) \quad (10)$$

*ρ*<sub>ref</sub> is a defined reference temperature. When considering the average value of the density over a target range of operating temperature (25 °C - 60 °C) *ρ*<sub>av</sub>, the average density gradient, denoted by *ρ*<sub>avβ</sub>, is an intrinsic property of the PCM. This parameter can be used as a measure of its potential to be subject to buoyancy forces and therefore to natural convection. By Comparing the different PCMs, PT25 stands out as the PCM with the highest potential for natural convection, with an average density gradient of 0.7388 kg/m³°C, followed by RT18HC with a value of 0.7182 kg/m³°C. The PCM RT21HC has the lowest potential for natural convection with an average density gradient value of 0.6632 kg/m³°C.

The natural convection potential of the PCMs is compared by analyzing the values of the thermal expansion coefficient and viscosity. Using the Boussinesq approximation, buoyancy forces are proportional to the thermal expansion coefficient *β*. A high *β* value implies more intense natural convection. For viscosity, the opposite effect is observed: a high viscosity value inhibits natural convection. Therefore, a low viscosity combined with a high thermal expansion coefficient result in higher natural convection for the PCM, leading to an efficient melting process. The *β* values and the average of viscosity values of the PCMs between 25 °C and 60 °C are listed in Table 8. The results show that paraffinic PCMs exhibit higher natural convection potential compared to bio-based PCMs, with RT18HC demonstrating the highest potential (*μ* = 2.2 mPa·s, *β* = 0.00093/°C). This performance will particularly influence the charging speed of the latent storage systems in which these PCMs are used.

### 3.4. DSC analysis results

Thermal properties regarding latent and specific heats, as well as phase change temperatures, were determined using a DSC analyzer. These data are mainly used to model the phase transition and the mushy

<table><caption>**Table 8**
Mean values of viscosity and values of thermal expansion coefficient.</caption><thead><tr><th></th><th>RT18HC</th><th>RT21HC</th><th>RT24HC</th><th>PT20</th><th>PT23</th><th>PT25</th></tr></thead><tbody><tr><td>μ (mPa·s)</td><td>2.2</td><td>2.53</td><td>2.74</td><td>5.65</td><td>9.22</td><td>3.83</td></tr><tr><td>β (1/°C)</td><td>0.00093</td><td>0.00087</td><td>0.00088</td><td>0.00081</td><td>0.00083</td><td>0.00085</td></tr></tbody></table>

zone, which is the intermediate state between the solid and liquid phases. The latent heat of a material represents the energy absorbed or released when transitioning from one physical state to another. It constitutes the main interest of latent heat storage, as its value is often high, implying a large thermal energy storage capacity. Fig. 11 depicts the thermograms for the six PCMs at a heating and cooling rate of 1 °C/min. All curves exhibit a similar bell-shaped profile, with low values far upstream and downstream of the phase change temperatures, and higher values within the transition temperature range, featuring a distinct high peak. Additional details can be observed for specific PCMs, such as the RT21HC and RT24HC, which, in addition to the main peaks, secondary peaks can be observed between -10 °C and 0 °C for RT21HC for melting and solidification, between 0 °C and 10 °C for melting of RT24HC, and two prominent double peaks of equal amplitudes for the solidification of RT24HC. These observations have also been made by other researchers such as Kraiem et al. [19] on RT21, RT27, and RT50, and Soares et al. [18] on PCMs like MPCM18D, MPCM28D, PCM24, and RT25HC. The explanations provided in the literature suggest a solid-solid endothermic transition or a disordering of the monoclinic crystal to a pseudohexagonal crystal or even a supercooling behavior [52]. In the present study, the results on latent heat and specific heat capacity should be considered with 2 % of uncertainty due to the precision of the device.

The latent heat *L* of each PCM represents the area under the thermogram curve, weighted by the heating rate and the sample mass. Therefore, for the same heating rate, PCMs with higher latent heat have thermograms with greater and wider amplitudes. However, a wider thermogram indicates a larger temperature transition range, which impacts the phase change kinetics of the PCM. The thermograms of the different PCMs were post-processed using Proteus Analysis software, and the latent heat data are provided in Table 9. The latent heat was determined for PureTemp products by considering the area delimited by the DSC thermogram and the tangent to the curve starting far to the right of the melting peak [53]. For Rubitherm products, the method used by the supplier, which includes both sensible and latent heat within a temperature range [13], was adopted, knowing that the latent part remains predominant. The latent heat data determined in the present study are very comparable to the supplier data, with a maximum relative difference below 3 %, which is close to the device measurement uncertainty. The PCM RT18HC with *L* = 265 kJ/kg has the highest latent heat, and PT20 has the lowest latent heat value with *L* = 171 kJ/kg. Among PureTemp products (PT20, PT23 and PT25), PT23 has the greatest latent storage potential with a latent heat of *L* = 199 kJ/kg, higher than some of the Rubitherm products like RT21HC and RT24HC, whose latent heat values include a few sensible heat.

While the latent heat and the onset melting temperature, also known as solidus temperature *T*<sub>s</sub>, remain almost independent of the heating rate as indicated in Fig. 12a, the peak temperature is highly dependent on the

<table><caption>**Table 7**
Linear regression coefficients and uncertainties for the liquid phase density of the six PCMs studied.</caption><thead><tr><th rowspan="2"></th><th colspan="7">Parameters</th></tr><tr><th>β (1/°C)</th><th>ρ<sub>av</sub>β (kg/m<sup>3</sup> °C)</th><th>c (kg/m<sup>3</sup> °C)</th><th>d (kg/m<sup>3</sup>)</th><th>R<sup>2</sup> (-)</th><th>σρ<sub>min</sub> (kg/m<sup>3</sup>)</th><th>σρ<sub>max</sub> (kg/m<sup>3</sup>)</th></tr></thead><tbody><tr><td>RT18HC</td><td>0.00093</td><td>0.7182</td><td>-0.7267</td><td>799.95</td><td>0.9968</td><td>±3.07</td><td>±3.29</td></tr><tr><td>RT21HC</td><td>0.00087</td><td>0.6632</td><td>-0.6705</td><td>794.27</td><td>0.9985</td><td>±3.05</td><td>±3.25</td></tr><tr><td>RT24HC</td><td>0.00088</td><td>0.6849</td><td>-0.6945</td><td>810.65</td><td>0.9986</td><td>±3.14</td><td>±3.32</td></tr><tr><td>PT20</td><td>0.00081</td><td>0.6933</td><td>-0.7007</td><td>887.82</td><td>0.9991</td><td>±3.45</td><td>±3.66</td></tr><tr><td>PT23</td><td>0.00083</td><td>0.6954</td><td>-0.703</td><td>864.37</td><td>0.9993</td><td>±3.35</td><td>±3.56</td></tr><tr><td>PT25</td><td>0.00085</td><td>0.7388</td><td>-0.7472</td><td>896.36</td><td>0.9993</td><td>±3.45</td><td>±3.66</td></tr></tbody></table>
<figure><img src="image_14.png" /><figcaption>Fig. 11. DSC thermograms of the six PCMs studied.</figcaption></figure>

<table><caption>**Table 9**
Latent heat and phase transition temperatures of the six PCMs studied.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Thermal properties</th></tr><tr><th>L<sub>measured</sub> (kJ/kg)</th><th>L<sub>supplier</sub> (kJ/kg)</th><th>T<sub>s/t,measured</sub> (°C)</th><th>T<sub>s/t,supplier</sub> (°C)</th></tr></thead><tbody><tr><td>RT18HC</td><td>265 ± 5.3</td><td>260</td><td>17.1/21.7 ± 0.1</td><td>17–19</td></tr><tr><td>RT21HC</td><td>186 ± 3.7</td><td>190</td><td>17.6/22.2 ± 0.1</td><td>20–23</td></tr><tr><td>RT24HC</td><td>196 ± 3.9</td><td>200</td><td>19.2/25 ± 0.1</td><td>23–26</td></tr><tr><td>PT20</td><td>171 ± 3.4</td><td>171</td><td>19.1/22.3 ± 0.1</td><td>20</td></tr><tr><td>PT23</td><td>199 ± 4</td><td>201</td><td>20.2/24.1 ± 0.1</td><td>23</td></tr><tr><td>PT25</td><td>182 ± 3.6</td><td>187</td><td>22.7/26.2 ± 0.1</td><td>25</td></tr></tbody></table>

heating rate, as visible in Fig. 12b. Thus, the solidus temperature and latent heat can be determined from a test at a given heating rate. The end melting temperature, also known as liquidus temperature, corresponds to the peak temperature of the PCM at thermodynamic equilibrium, i.e., at a heating rate of 0 °C/min. To determine the liquidus temperature of each PCM, several tests were conducted at various heating rates, namely 1 °C/min, 5 °C/min, and 10 °C/min. To determine the peak temperature at zero heating rate, a linear extrapolation was performed on the three peaks obtained from the three heating rates. Fig. 12c shows the extrapolation results of the peak temperatures, which allowed for the determination of the liquidus temperature $T_l$. The solidus and liquidus temperatures are presented in Table 9, compared with supplier data. The present study notably allows for determining transition ranges and associated temperatures, extremely useful for CFD modeling, which are not provided by some suppliers who only provides the peak temperatures. Slight differences are observed between the measured transition temperatures and the Rubitherm data, which could be due to possible differences between the method used by the supplier and the present one, the precision of the measuring device, or the sample itself. The transition range of Rubitherm products is slightly wider in this study compared to the supplier data, but a significant overlap is observed between the two sets of data. The peak temperatures of PureTemp

products are 1 °C higher than the supplier data for PT25, PT23, and 2 °C for PT20.

The DSC analysis of the PCMs revealed that, overall, PureTemp PCMs exhibit narrower phase change temperature ranges compared to Rubitherm products. These differences can impact thermal performance depending on the intended application. According to Mehling and Cabeza [54], a narrow transition range offers advantages by enabling more efficient thermal management and maximizing latent energy storage at the expense of sensible heat. On the other hand, Sharma et al. [55] argue that a wider transition range allows for greater flexibility and adaptability to temperature fluctuations, particularly in building applications. Additionally, Loganathan et al. [56] note that a wide phase change temperature range slows the phase change kinetics. The literature suggests that for building applications, it may be advisable to use PCMs with narrow temperature ranges, such as PureTemp products, to maintain high storage density and achieve a more responsive system. However, depending on the climate, it might be preferable to opt for PCMs with broader temperature ranges to cover a wider operating temperature range, especially in environments with significant temperature fluctuations.

The heat storage in LHTES systems, although mostly latent, includes a non-negligible sensible part that must be well accounted for, through a good characterization of the specific heat capacity of the PCM. Fig. 13 shows the evolution of the specific heat capacity of different PCMs as a function of temperature. Specific heat capacity represents the energy stored or released during the temperature change of the PCM. The values considered are those upstream of the solidus temperature, which represent the specific heat capacity of the solid phase, and downstream of the liquidus temperature, which corresponds to the specific heat capacity of the liquid phase. In the solid phase, the specific heat varies from 1.4 J/g·°C to 4.5 J/g·°C depending on the temperature and the material. Due to the presence of double peaks as stated before, the RT21HC and RT24HC PCMs have specific heats that present a slight peak in the solid phase. The average specific heat value of the solid phase of RT24HC before the first peak is close to 2 J/g·°C, which
<figure><img src="image_15.png" /><figcaption>a</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>b</figcaption></figure>

<caption>c</caption>

<caption>Fig. 12. (a) Influence of the heating rate on the PCM latent heat, (a, b) solidus and peak temperatures: case of PT23 PCM, and (c) PCMs liquidus temperature determination.</caption>

corresponds to the supplier's data. For the RT18HC PCMs and PureTemp products (PT20, PT23 and PT25) with a monotone trend in the solid phase, the evolution of specific heat capacity as a function of temperature can be fitted with a second-degree polynomial function given by Eq. (11) in the temperature range [−10 °C 20 °C] according to the PCM. For RT21HC and RT24HC PCMs, the fitting was made in the temperature range after and before the first peak respectively, where regular evolutions of the specific heat capacity can be observed. In the liquid phase, the specific heat capacity values range from 1.5 J/g°C to 2.5 J/g°C depending on the PCM, with an almost quasi-constant evolution. Thus, an average value can be considered for the liquid phase for all the six PCMs. The PCMs PT20 and PT25 have the lowest specific heat, while the PCM PT23 has the highest values. For the six PCMs analyzed, the average value of $c_p$ for both solid and liquid phases are comparable and summarized in Table 10 and Table 11 with the corresponding temperature range for averaging. The uncertainties include both type “A” (due to the mean value consideration of the $c_p$) and the device uncertainties. The coefficients of the polynomials describing the temperature-dependence of the specific heat capacity in the solid phase are given in Table 10 for the different PCMs.

$$c_{p,s,l}(T) = eT^2 + fT + g \quad (11)$$

In order to compare the storage capacity of the PCMs, the values of the volumetric stored energy quantity $E = \rho L + \rho c_p \Delta T$ within a temperature range of 15 °C to 45 °C (ΔT = 30 °C) were evaluated, and the results were recorded in Table 12. The density was considered at 30 °C for all PCMs, and the heat capacity was taken as the average value between the solid and liquid phases. The results in Table 12 show that the PCM RT18HC has the highest volumetric energy density ($E = 255$ MJ/m³) and, therefore, the greatest storage capacity. PT23 also demonstrates a notable storage capacity, while PT20 has the lowest ($E = 196$ MJ/m³). Prioritizing storage capacity, RT18HC emerges as the best candidate.

The comparison of the characterized PCMs clearly shows that RT18HC is the most efficient in terms of storage capacity (255 MJ/m³), natural convection potential ($\mu = 2.2$ mPa.s, $\beta = 0.00093/°C$), and conductive heat transfer potential ($\lambda = 0.283$ W/m·°C). The PCM RT24HC also demonstrates interesting natural convection ($\mu = 2.53$ mPa.s, $\beta = 0.00087/°C$) and heat conduction ($\lambda = 0.279$ W/m·°C) potential but has a lower storage capacity (206 MJ/m³) compared to
<figure><img src="image_17.png" /><figcaption>Fig. 13. Temperature-dependence of the specific heat capacity of the six PCMs studied.</figcaption></figure>

<table><caption>**Table 10**

Fitting parameters of the specific heat capacity of the six PCMs in the solid phase.</caption><thead><tr><th></th><th>e (J/g °C³)</th><th>f (J/g °C²)</th><th>g (J/g °C)</th><th>R² (-)</th><th>cp,s,mean (J/g °C)</th><th>Temperature range (°C)</th></tr></thead><tbody><tr><td>RT18HC</td><td>0.004</td><td>0.0271</td><td>1.6669</td><td>0.8634</td><td>1.96 ± 0.16</td><td>[-10-14]</td></tr><tr><td>RT21HC</td><td>0.0088</td><td>-0.0148</td><td>2.5555</td><td>0.9937</td><td>2.92 ± 0.21</td><td>[0-12]</td></tr><tr><td>RT24HC</td><td>0.0023</td><td>0.0489</td><td>2.3505</td><td>0.9846</td><td>2.17 ± 0.08</td><td>[-10-0]</td></tr><tr><td>PT20</td><td>0.0034</td><td>0.035</td><td>1.6143</td><td>0.9076</td><td>1.89 ± 0.16</td><td>[-10-14]</td></tr><tr><td>PT23</td><td>0.0076</td><td>0.0429</td><td>1.5938</td><td>0.8918</td><td>2.29 ± 0.29</td><td>[-10-16]</td></tr><tr><td>PT25</td><td>0.002</td><td>0.0128</td><td>1.4533</td><td>0.8988</td><td>1.73 ± 0.12</td><td>[-10-20]</td></tr></tbody></table>

<table><caption>**Table 11**

Specific heat capacity data for the six PCMs liquid phase.</caption><thead><tr><th></th><th>c<sub>p,mean</sub> (J/g °C)</th><th>Temperature range (°C)</th></tr></thead><tbody><tr><td>RT18HC</td><td>2.19 ± 0.06</td><td>[22-50]</td></tr><tr><td>RT21HC</td><td>2.08 ± 0.04</td><td>[24-50]</td></tr><tr><td>RT24HC</td><td>2.15 ± 0.04</td><td>[28-50]</td></tr><tr><td>PT20</td><td>1.84 ± 0.04</td><td>[26-50]</td></tr><tr><td>PT23</td><td>2.30 ± 0.05</td><td>[28-50]</td></tr><tr><td>PT25</td><td>1.87 ± 0.04</td><td>[30-50]</td></tr></tbody></table>

<table><caption>**Table 12**

PCMs volumetric energy density.</caption><thead><tr><th></th><th>RT18HC</th><th>RT21HC</th><th>RT24HC</th><th>PT20</th><th>PT23</th><th>PT25</th></tr></thead><tbody><tr><td>E (MJ/m³)</td><td>255</td><td>203</td><td>206</td><td>196</td><td>225</td><td>208</td></tr></tbody></table>

RT18HC and PT23. The PCMs PT20, PT23, and PT25 globally exhibit the least favorable natural convection and heat conduction potential, although PT23 has a high storage capacity (225 MJ/m³). A more relevant comparison of the PCMs would involve analyzing them under identical operating conditions during the melting and solidification processes to assess the overall contribution of their combined

thermophysical properties.

## 4. Conclusion

The objective of the present study was to experimentally characterize the relevant thermophysical properties and their temperature-dependence of several PCMs, with the aim of supplying critical input data for the CFD modeling of phase change processes. Six paraffinic and bio-based PCMs namely RT18HC, RT21HC, RT24HC, PT20, PT23 and PT25, from different suppliers, with great potential for improving seasonal thermal comfort in building, were analyzed. Data concerning phase change properties, dynamic viscosity, thermal conductivity, liquid density, and thermal expansion coefficient were established, as well as their temperature dependence when concerned.

Dynamic viscosity was measured in the PCM liquid phase using a high-precision rheometer. The results showed a relatively low viscosity values - but higher than that of water - for paraffinic PCMs (1 to 4 times more viscous than water) and higher for bio-based PCMs (2 to 16 times more viscous than water). PCM PT23 has been found to be the most viscous, reaching up to 16 mPas, and RT18HC has been found to be the less viscous among the six PCMs analyzed. The temperature-dependence of the dynamic viscosity was described by an exponential function.

Thermal conductivity was measured in both solid and liquid phases, and the temperature-dependence was established. For most PCMs, the
solid phase was found to be more conductive than the liquid phase. In the solid phase, a significant disparity in thermal conductivity among the PCMs was observed, with RT18HC being the most conductive (λ > 0.3 W/m·°C) and RT21HC being the least conductive (λ < 0.2 W/m·°C). In the liquid phase, RT24HC has the highest thermal conductivity and PT23 has the lowest one.

An in-house experimental setup was developed to determine the liquid density of PCMs as well as the thermal expansion coefficient. The experimental setup and method were validated using reference data from water and RT21HC. An accuracy of over 99 % with an uncertainty of ±4 kg/m³ was observed. All the PCMs were found to have a lower density than water. PCMs from PureTemp were found to have a higher liquid density (820 kg/m³ - 880 kg/m³) than those from Rubitherm (750 kg/m³ - 800 kg/m³). The PCM RT18HC was found to have the highest thermal expansion coefficient β = 0.00093/°C, and PT25 to have the greatest potential for natural convection with an average density gradient of 0.7388 kg/m³°C.

Finally, a DSC analysis allowed for the evaluation of phase change properties of PCMs, including latent heat and transition temperatures, as well as specific heat capacity. The measured data were compared to supplier data, and very close similarity was observed. PCM RT18HC was found to have the highest latent heat of melting equals to 265 kJ/kg, and PT20 was found to have the lowest one equals to 171 kJ/kg, while both exhibiting high storage density. PCMs from PureTemp were found to have narrower transition ranges of 3–4 °C compared to those from Rubitherm, which are wider by about 5–6 °C. A temperature-dependence of specific heat capacity was established and described by polynomials in solid phase.

The present study provides the main thermophysical properties of six PCMs, that are extremely useful for proper CFD modeling of LHTES systems. Based on these results, numerical and experimental studies will be conducted on these PCMs under the same operating conditions to determine the most efficient PCM for improving thermal comfort in buildings.

## CRediT authorship contribution statement

**Appolinaire Kaboré:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Jules Voguelin Simo Tala:** Writing – review & editing, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization. **Zohir Younsi:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. **Daniel Bougeard:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This study was performed with the financial support of IMT Nord Europe, the French Environment and Energy Management Agency (ADEME), Haut-De-France Region, and Junia HEI to whom we express our sincere thanks.

## Data availability

Data will be made available on request.

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