Thermal properties and performance of
glycerol-water-NaCl phase change material for cold
chain applications

Zakaria Ouaouja, Michel Havet, Olivier Rouaud, Cyril Toublanc, Abdellah Ousegui

► To cite this version:

Zakaria Ouaouja, Michel Havet, Olivier Rouaud, Cyril Toublanc, Abdellah Ousegui. Thermal proper-
ties and performance of glycerol-water-NaCl phase change material for cold chain applications. Journal
of Energy Storage, 2025, 126, pp.117045. 10.1016/j.est.2025.117045. hal-05076022

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Research papers

# Thermal properties and performance of glycerol-water-NaCl phase change material for cold chain applications

Zakaria Ouaouja<sup>a,b,*</sup>, Michel Havet<sup>a</sup>, Olivier Rouaud<sup>a</sup>, Cyril Toublanc<sup>a</sup>, Abdellah Ousegui<sup>b</sup>

## ARTICLE INFO

**Keywords:**

- Phase change materials
- Cold thermal energy storage
- Cold chain
- Latent heat
- Thermophysical characterization
- Glycerol
- Numerical model

## ABSTRACT

This study investigates the thermal properties of glycerol-water mixtures and their potential as Phase Change Materials (PCM) for Cold Thermal Energy Storage (CTES) in cold chain applications. The study characterizes key thermal properties, including Phase Change Temperature (PCT), latent heat, density, thermal conductivity, and specific heat. Results indicated that increasing glycerol concentration decreased the PCT of the mixture, reaching -7.76 °C to -21.82 °C, at glycerol concentrations ranging between 25 wt% to 45 wt%, respectively. However, this decrease in PCT is accompanied by a reduction in latent heat, $147.5 \text{ kJ·kg}^{-1}$ to $73.6 \text{ kJ·kg}^{-1}$ for the respective concentrations.

To enhance the PCM properties and achieve optimal thermal performance, NaCl was added as an additive to the glycerol-water mixture. The Response Surface Methodology (RSM) was employed to optimize the concentrations of PCM components, aiming to achieve a desired PCT of -20 °C and maximize latent heat capacity. The developed model demonstrated high predictability, with an $R^2$ of 99.20 %, and good statistical significance, as indicated by an overall model *F*-value of 98.68 and a *P*-value of 0.0003. Based on this optimization, three mixtures were selected for further characterization, exhibiting suitable PCT values of around -20 °C to -18 °C and latent heat capacities ranging from $97 \text{ kJ·kg}^{-1}$ (PCM-M1) to $280 \text{ kJ·kg}^{-1}$ (PCM-M3).

A one-dimensional model was developed to assess the impact of optimized PCM-M3 on the temperature stability of frozen food products. Incorporating the PCM layers significantly improved the thermal control of the perishable product. During standard freezer operation, the product temperature was maintained at -20 °C ± 0.065 °C compared to the reference case (without PCM) at -20 ± 0.81 °C. During defrost cycles, and using PCM-M3, the maximum product temperature reached -19.42 °C, compared to -16.98 °C without PCM.

## 1. Introduction

The cold chain represents a critical infrastructure in modern food logistics, covering a continuous sequence of temperature-controlled systems that facilitate transporting and storing perishable food products from production to consumption (Fig. 1) [1-4]. This sophisticated logistical framework should be designed to maintain the quality and safety of refrigerated goods throughout their journey in the supply chain, effectively mitigating spoilage risks and preserving nutritional value for long periods. The cold chain's temperature regulation is adapted to specific product requirements, with five main temperature zones: deep-frozen (–30 °C to –28 °C), frozen (–20 °C to –16 °C), cold-chilled (0 °C to 1 °C), medium-chilled (2 °C to 5 °C), and exotic-chilled (10 °C to 15 °C) [5,6].

Cold chain systems, while essential for preserving products, are a significant contributor to greenhouse gas emissions. These emissions can be categorized into two main types: indirect emissions, resulting from electricity consumption, and direct emissions, due to refrigerant leakage and transportation. Studies have shown that indirect emissions account for the largest share of CO₂ emissions at 60 %, while direct emissions from refrigerant leakage and transport contribute 22 % and 18 %, respectively [1,7].

To prevent these environmental impacts, PCM as a sustainable CTES system presents a promising solution, due to their ability to absorb and release thermal energy through latent heat processes. PCM s have been successfully implemented in various fields, including buildings [8,9], solar energy [10], electronics [11], and photovoltaic panels [12]. Furthermore, this technique has been integrated into various cold chain infrastructure systems, from refrigerated warehouses [13,14] to

<footnote><sup>a</sup> Oniris, Nantes Université, CNRS, GEPEA, UMR 6144, F-44000, Nantes, France</footnote>

<footnote><sup>b</sup> RIPA, Département de Physique, Faculté des Sciences, Université Moulay Ismaïl, Meknès, Morocco</footnote>

<footnote>* Corresponding author at: Oniris, Nantes Université, CNRS, GEPEA, UMR 6144, F-44000 Nantes, France. E-mail addresses: zakaria.ouaouja@oniris-nantes.fr, zakaria.ouaouja@edu.umi.ac.ma (Z. Ouaouja).</footnote>
## Acronyms and Abbreviations

<table><tr><td>ANOVA</td><td>Analysis Of Variance</td></tr><tr><td>CCD</td><td>Central Composite Design</td></tr><tr><td>CTES</td><td>Cold Thermal Energy Storage</td></tr><tr><td>DOE</td><td>Design of Experiment</td></tr><tr><td>DSC</td><td>Differential Scanning Calorimetry</td></tr><tr><td>FFA</td><td>Free Fatty Acid</td></tr><tr><td>MDSC</td><td>Modulated Differential Scanning Calorimetry</td></tr><tr><td>PCM</td><td>Phase Change Materials</td></tr><tr><td>PCT</td><td>Phase Change Temperature</td></tr><tr><td>RMSE</td><td>Root Mean Square Error</td></tr><tr><td>RSM</td><td>Response Surface Methodology</td></tr><tr><td>RPD</td><td>Relative Percentage Difference</td></tr><tr><td>SE</td><td>Standard Error</td></tr><tr><td>SSC</td><td>Soluble Solid Content</td></tr></table>

## Symbols and variables

A RSM independent variable (NaCl)

<table><tr><td>B</td><td>RSM independent variable (Glycerol)</td></tr><tr><td>Bi</td><td>Biot Number</td></tr><tr><td>C<sub>p</sub></td><td>Specific Heat (kJ·kg<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>F-value</td><td>Fisher's test value</td></tr><tr><td>h<sub>air</sub></td><td>Air Heat Transfer Coefficient (W·m<sup>-2</sup>·K<sup>-1</sup>)</td></tr><tr><td>P-value</td><td>Probability value</td></tr><tr><td>R<sup>2</sup></td><td>Coefficient of Determination</td></tr><tr><td>R<sup>2</sup>(adj)</td><td>Adjusted Coefficient of Determination</td></tr><tr><td>R<sup>2</sup>(pred)</td><td>Predicted Coefficient of Determination</td></tr><tr><td>T</td><td>Temperature (°C)</td></tr><tr><td>Y</td><td>Response</td></tr></table>

## Greek symbols

<table><tr><td>α</td><td>The significance value = 5 %</td></tr><tr><td>β</td><td>Regression Coefficient</td></tr><tr><td>κ</td><td>Thermal Conductivity (W·m<sup>-1</sup>·K<sup>-1</sup>)</td></tr><tr><td>ρ</td><td>Density (g·cm<sup>-3</sup>)</td></tr><tr><td>ξ</td><td>Predicted Property</td></tr><tr><td>χ</td><td>Mass/Volume Fraction</td></tr></table>

<figure><img src="image_3.png" /><figcaption>Fig. 1. Illustration of the cold chain logistical infrastructure showing different cold chain stages.</figcaption></figure>

domestic refrigerators [15]. The integration of PCMs has proven to be an effective approach in enhancing the efficiency of refrigeration systems [16,17] and maintaining the quality of stored products [18,19], thereby contributing to the sustainability of cold chain operations [19–21].

Rahimi et al. [22] conducted an experimental evaluation to investigate the thermal and energy performance of a domestic refrigerator integrated with PCM. The results demonstrated that incorporating a PCM slab provides continuous cooling energy during the compressors off cycles, thereby reducing its run time ratio and energy consumption by 2.86–7.33 %. The researchers also assessed the impact of adding copper fins to the PCM container, examining three different configurations. Experimental results indicated that the addition of fins further decreased compressor energy usage by 4.37–9.56 %. This enhancement can be attributed to the improved heat transfer rate within the PCM facilitated by the copper fins, which consequently reduced the PCM’s charging and discharging period. Similarly, Principi et al. [23] placed a PCM container next to the evaporator of a walk-in freezer. This setup aims to maximize the use of cold energy provided by the refrigeration unit and charge the PCM efficiently. This setup also takes advantage of natural convection, which helps distribute the cold air more evenly throughout the space, promoting a uniform temperature. The results showed that the PCM container acts as an additional evaporator, stabilizing the temperature and absorbing heat gain due to infiltration. Consequently, the compressor’s on-off cycles were reduced, leading to a 16 % decrease in daily energy consumption. Numerical studies have also been conducted to assess the impact of PCM on system energy consumption. Gado et al. [17] developed a model of a cold storage room integrated with PCM. The model predicted that PCMs could stabilize the storage case’s air temperature more effectively than a reference case without PCM.

This stabilization significantly extended the compressor-off time period, reducing the daily on-off cycles from 256 to 46 cycles, resulting in a 10.53 % energy savings.

Furthermore, PCMs have demonstrated significant potential to preserve product quality. Multiple studies have shown that PCM integration in cold chain systems can effectively mitigate temperature fluctuations, reducing weight loss and degradation of perishable goods compared to conventional methods [19,24,25]. For instance, Liu et al. [25] reported that PCM-integrated scenarios maintained air temperatures between 0.45 and 3 °C for 22.83 h under ambient conditions. This thermal stability significantly affected product quality, resulting in lower weight loss (0.74 %) and rotting rates (7.69 %) compared to reference cases (36.8 % and 58.14 %, respectively). Similarly, Tong et al. [19] investigated the effectiveness of PCM-equipped containers in maintaining the quality of fruits and vegetables during long-distance transportation, covering approximately 2500 km over 96.4 h under fluctuating outdoor temperatures. This study evaluated the Soluble Solid Content (SSC), a key parameter for assessing ripeness and flavor quality [26–29]. The SSC tends to increase in low-maturity products during storage as they ripen, followed by a decline once peak ripeness is reached [30,31]. The experimental results demonstrated that PCM implementation minimized post-transportation quality degradation across various types of products, including lettuce, strawberries, and mangos. Specifically, SSC measurements showed modest increases in lettuce (3.47 % to 3.67 %) and strawberries (10.05 % to 10.50 %), while mangos exhibited a slight decrease (15.3 % to 14.3 %). Additionally, pH measurements demonstrated limited variations, with changes of 1.22 %, 2.75 %, and – 6.68 % observed in lettuce, strawberries, and mangos, respectively. These observations underscore the crucial role of PCMs in maintaining the
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** A performance evaluation chart displaying the relative strengths and limitations of different PCM types across multiple criteria. Each performance attribute is rated on a scale from 0 (poorest performance) to 3 (excellent performance) [32].</figcaption></figure>

quality of perishable products throughout the cold chain.

PCMs are any materials that undergo phase transitions, such as solid-to-liquid or liquid-to-solid, at specific temperature ranges. These transitions enable PCMs to store and release significant amounts of thermal energy in the form of latent heat. During the charging phase, the PCMs release heat as they transition from liquid to solid, while during discharging, the material absorbs heat as it turns liquid, thereby facilitating thermal energy storage and regulation. The PCMs are classified into

three main categories: organic, inorganic, and eutectic [32,33]. The radar chart in Fig. 2 presents a comparative analysis of the three distinct categories. This visualization illustrates the material's relative performance across various physicochemical properties crucial for thermal energy storage applications. Organic PCMs are subdivided into petroleum-based paraffin and bio-based (fatty acid, sugar alcohol). These materials are known for their compatibility with encapsulation materials, absence of supercooling and phase segregation effect, and

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Scatter plot showing the melting temperature vs. latent heat for the three PCM categories commonly found in the market: hydrated salts (yellow markers) are dominant, followed by petroleum paraffin waxes (orange markers), and bio-based (green markers) [32]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
degradability [34,35]. Inorganic PCMs include hydrated salts and metals [36,37]. In particular, inorganic hydrated salts are commonly used for CTES applications due to their suitable freezing temperatures ranging from -86 °C to -1.6 °C, high latent heat capacity, and relatively good thermal conductivity [38-40]. However, inorganic PCMs (hydrated salts) are known to be corrosive to encapsulation materials and exhibit a high degree of supercooling [41]. Supercooling is defined as the phenomenon where a liquid persists in a metastable state below its freezing temperature without undergoing crystallization [32]. This phenomenon is particularly relevant to the performance of PCMs, as it can significantly affect their thermal behavior. Specifically, research has demonstrated that the delayed onset of freezing due to supercooling results in a less efficient release of latent heat [42]. When nucleation occurs in a supercooled PCM, a portion of the latent heat is absorbed by the material, causing its temperature to rise to the melting point, thereby reducing the effective release of latent heat. Moreover, the degree of supercooling is inversely correlated with the amount of latent heat that is effectively released [43]. Finally, eutectic PCMs represent a hybrid approach that aims to combine the advantages of both organic and inorganic materials [44,45].

A comprehensive review study has revealed that hydrated salts and paraffin-based materials are the most commonly used PCMs for CTES [32]. As shown in Fig. 3, which compares the melting temperature and latent heat properties of various commercial PCMs, hydrated salts (yellow markers) are dominant as they deliver very high latent heat (up to ~400 kJ/kg) at moderate melting temperatures (-115 °C to +10 °C). Whereas paraffin (orange markers) come in second place covering a melting-point range (-30 °C to +10 °C) but with somewhat lower energy densities (~120-280 kJ/kg). However, despite their favorable thermal properties, hydrated salts and paraffins often face limitations such as corrosion, supercooling, and environmental concerns. To address these drawbacks, research has shifted focus toward more sustainable alternatives, particularly bio-based PCMs.

Among these, aqueous solutions of organic compounds and sugar alcohols (polyols) have emerged as promising candidates for CTES applications. These materials have attracted significant attention due to their sustainability and favorable characteristics, such as non-toxicity, reduced flammability, and biodegradability [32].

Glycol-based solutions, including ethylene, diethylene, triethylene, and propylene variants, have been extensively explored for CTES applications [46-49]. Studies have revealed that the PCT of glycol solutions decreases to approximately -40 °C for 55 wt% concentration [50,51]. Similarly, PCT and sugar alcohol concentrations are inversely related [40].

Mulawarman et al. [52] investigate the PCT and supercooling degree of propylene glycol and glycerol solutions at various concentrations. The results showed that both additives effectively reduced the freezing point of water, indicating their suitability for CTES applications. Specifically, 10%, 20%, and 30% propylene glycol solutions decreased the freezing point to -4.5 °C, -12 °C, and -17 °C, respectively. While 10% and 20% glycerol solutions lowered it to -5 °C and -10 °C. Furthermore, the study demonstrated that the propylene glycol solutions significantly reduced the supercooling degree, with measurements of 7 K, 3.5 K, and 1.5 K for the 10%, 20%, and 30% solutions, respectively. On the other hand, the glycerol solutions exhibited varying supercooling degrees, with the 10% solution showing a relatively small supercooling degree of 3 K and the 20% solution displaying a larger supercooling degree of 10 K. These results highlight the potential of these mixtures as low-temperature PCMs, as they have a good PCT while addressing water limitations, such as high supercooling degree.

The study mentioned above [25] reported the melting point of three different aqueous sugar alcohols, including mannitol, sucrose, and glycerol. Four mixtures were studied with concentrations ranging from 3% to 12%. The results confirmed that the melting temperature of the mixtures decreases with polyols concentrations. Compared to pure water, mannitol has the smallest temperature drops to -1.5 °C for 3%

<table><caption>**Table 1**

Thermal properties of salt-additives-water PCMs [39,54,56].</caption><thead><tr><th>Mixture</th><th>Concentration (%)</th><th>PCT (°C)</th><th>Latent Heat (kJ·kg<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Ethylene Glycol/H<sub>2</sub>O</td><td>12:88</td><td>-4.9</td><td>281</td></tr><tr><td>Ethylene Glycol/H<sub>2</sub>O</td><td>50:50</td><td>-37.1</td><td>41.59</td></tr><tr><td>Ethylene Glycol/Sodium Lactate/H<sub>2</sub>O</td><td>10:10:80</td><td>-12</td><td>157.4</td></tr><tr><td>Ethylene Glycol/Sodium Propionate/H<sub>2</sub>O</td><td>10:10:80</td><td>-15</td><td>127.8</td></tr><tr><td>Ethylene Glycol/Sodium Acetate/H<sub>2</sub>O</td><td>10:10:80</td><td>-19</td><td>118.5</td></tr><tr><td>Ethylene Glycol/Sodium Formate/H<sub>2</sub>O</td><td>10:10:80</td><td>-25</td><td>173.1</td></tr><tr><td>Glycerol/Sodium Lactate H<sub>2</sub>O</td><td>10:10:80</td><td>-10</td><td>159.3</td></tr><tr><td>Glycerol/Sodium Acetate/H<sub>2</sub>O</td><td>10:10:80</td><td>-14</td><td>156</td></tr><tr><td>Glycerol/Sodium Propionate/ H<sub>2</sub>O</td><td>10:10:80</td><td>-14</td><td>123.2</td></tr></tbody></table>

and -2.1 °C for 12%. Then followed by sucrose with -1.3 °C for 3% and -3 °C for 12%. On the other hand, glycerol has the biggest temperature drop reaching -2.5 °C for 3% and -7.1 °C for 12%.

These findings provide valuable insights into the thermal behavior of organic and sugar alcohol solutions and their potential to decrease the freezing temperatures and reach appropriate PCT for cold chain applications. However, it is important to note that this advantage is accompanied by a decrease in the mixture's latent heat capacity [25,53,54]. This drawback has prompted researchers to improve PCM properties by incorporating salts to achieve an optimal balance between latent heat and PCT [39,54-56].

Zhan et al. [55] investigated the thermal properties of two novel organic PCMs by incorporating glucose and sorbitol at various mass fractions (5 wt%-15 wt%) into a 1 % NaCl solution. The results showed that both the PCT and the latent heat of the mixtures decreased as the concentration of the sugar alcohol increased. The 5% solutions exhibited the most promising results regarding good latent heat capacity. This sample was 23% (sorbitol) and 24.6% (glucose) higher than that of 15 wt% solution. Furthermore, the PCT decreased from -4.3 °C to -6.7 °C as the concentration of both additives increased from 5% to 15%. Multiple review studies [39,54,56] have indicated that adding salt to organic/sugar alcohol solutions significantly enhances the mixture's properties. Salt effectively lowers the PCT while maintaining a satisfactory latent heat capacity. This combination of Salt-Additive-Water makes the resulting eutectic mixture a promising candidate for CTES applications. Table 1 summarizes the thermal properties of various salt-additive solutions as reported in the literature [39,54,56].

The selection of appropriate PCMs for CTES involves evaluating five key criteria. A good PCM must exhibit appropriate thermal properties, including a PCT that aligns with the specific application, along with high latent and specific heat capacities to optimize energy storage capacity. Additionally, high thermal conductivity is essential for efficient heat transfer. Regarding physical properties, the PCM should exhibit minimal density changes during phase transitions to reduce storage volume and encapsulation size. Chemical criteria are also important, with low phase hysteresis effect requirements, strong cyclic thermal stability with minimal degradation of latent heat capacity, and PCT over time [57,58]. The material should also be compatible with encapsulation materials and non-hazardous to ensure safe implementation. Finally, practical considerations include economic and environmental factors. The PCM must be available to support reliable supply chains, cost-effective to enable commercial feasibility, and designed for recyclability to minimize environmental impact and ensure sustainable disposal.

Glycerol ($C_3H_8O_3$) has the potential to be used as a PCM for cold chain applications. It drops the freezing temperature of water-based mixture as a function of its concentration, reaching freezing points between -43 °C and -50 °C for concentrations ranging from 64 wt% to 70 wt% [59-61]. In addition, glycerol is a readily available by-product
<figure><img src="image_6.png" /><figcaption>Fig. 4. (a)- Flowchart of the transesterification procedure used in biodiesel production, depicting the key components involved. (b)- Photograph showing the crude biodiesel and glycerol layers formed after the transesterification process. Creative Commons license [63].</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Global biodiesel demand and potential generated crude glycerol, assuming 10 wt% of glycerol is produced during biodiesel manufacturing. Data converted to graph [76].</figcaption></figure>

of biodiesel production, which is generated through the transesterification of biomass sources such as animal fat [62], cooking oil waste [63–65], and olive pomace oil [66–68]. The transesterification process–illustrated in Fig. 4(a)–involves the reaction between fat or oil with alcohol (typically methanol) in the presence of a catalyst (commonly sodium hydroxide, NaOH). This reaction yields two distinct phases: crude biodiesel in the upper layer and crude glycerol, denser and darker, in the lower layer (Fig. 4(b)) [69]. Crude glycerol typically has a high pH, making it too essential for direct use as a PCM in cold chains. Therefore, neutralization is an essential step to ensure both safety and functionality. This process involves using acids such as hydrochloric (HCl), sulfuric (H₂SO₄), and phosphoric (H₃PO₄) acids. This causes the mixture to separate into three distinct phases: fatty acids, glycerol, and salt residue [69,70]. Despite this, the neutralized glycerol (pre-treated glycerol) may still contain soluble salts like NaCl, Na₂SO₄, and Na₃PO₄, which are residuals from the catalyst used in the production process [71].

Studies indicate that biodiesel production results in approximately 10 wt% of glycerol as a byproduct [72–75]. Given the scale of global

biodiesel production, this proportion represents a considerable volume of waste that requires valorization. Fig. 5 presents data on biodiesel demand and the potential glycerol generation from 2016 to 2028, with forecasts beyond 2023 [76]. The data indicates a steady increase in biodiesel demand, with a prediction of 68 billion liters by 2028, potentially generating around 8.5 billion kilograms of crude glycerol.

This study presents an integrative approach, which combines the selection of a sustainable, bio-based PCM, its optimal formulation using the response surface methodology, comprehensive measurement of thermophysical properties, and numerical evaluation of the PCM performance. Unlike most existing studies, which typically focus on only one or two of these aspects, our comprehensive methodology provides a multifaceted assessment of the developed PCM.

For this purpose, glycerol is investigated as a promising sustainable alternative to conventional hydrated salts and petroleum-based phase change materials. The primary focus lies in establishing the fundamental thermal properties of pure glycerol-water mixtures as a baseline, thereby opening doors for future studies of crude glycerol.

First, we conducted a systematic series of experiments to investigate
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Schematic illustration of the sample preparation process for salt-additive-water mixtures. Water and glycerol are first weighed and mixed using a magnetic stirrer. The additive is weighed separately and gradually introduced into the solution, followed by thorough mixing until fully dissolved. The prepared solution is then portioned into containers to create uniform test samples.</figcaption></figure>

glycerol-water mixtures at concentrations ranging from 25 wt% to 45 wt %, analyzing their thermal properties. This was done by employing various characterization techniques. These include the T-history method for determining melting/freezing temperatures, Differential Scanning Calorimetry for measuring specific heat and latent heat, and the hot-wire technique for assessing thermal conductivity.

Furthermore, this study explores how sodium chloride (*NaCl*)—an additive present in crude glycerol—affects the thermal performance of glycerol-based PCMs. This investigation seeks to determine whether such inherent impurities are beneficial or detrimental to thermal energy storage performance, thereby assessing the viability of crude glycerol as a sustainable PCM option. To optimize the PCM formulation, we employed the Response Surface Methodology to precisely identify ideal compositions that effectively balance the competing properties of phase change temperature and latent heat capacity.

The practical significance of our findings was assessed through a one-

dimensional model that simulates the performance of the studied PCMs in maintaining stable temperature conditions for perishable food products. This model allowed us to compare different configurations, including scenarios with and without PCM, under challenging and realistic cold chain conditions, such as ambient temperature fluctuations and defrost cycles.

Through this integrated experimental-numerical approach, we provide valuable insights into the potential of glycerol-based PCMs as sustainable solutions for cold thermal energy storage applications.

## 2. Materials and characterization methods

### 2.1. Materials

The phase change materials investigated in this study were eutectic mixtures prepared using deionized water, high-purity glycerol (≥99 %, Honeywell Inc.), sodium chloride (*NaCl*, 90–100.5 %, Pan-ReacAppliChem GmbH.), sodium hydroxide (*NaOH*, ≥98 %, Sigma Aldrich Co.), and sodium sulfate (*Na₂SO₄*, 99.7 %, VWR Prolabo Chemicals). All chemicals were used without further purification. The eutectic PCMs were synthesized by combining the components in precise ratios to achieve the desired composition, as detailed in the Section 2.2.

### 2.2. Preparation of the mixtures

The preparation of the salt-additive-water mixtures was conducted using a systematic procedure to ensure accuracy and homogeneity. Initially, precise quantities of deionized water and glycerol were measured using a Denver Instrument TB-124A weighing balance with a precision of ±0.01 mg and combined in a glass beaker. The mixture was stirred using a magnetic stirrer at 500 rpm for 15 min to ensure thorough

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Experimental setups and instruments used for PCM properties measurements. (a) Experimental setup for temperature measurement, featuring sample tubes equipped with thermocouples and placed in a freezer. The thermocouples are connected to a data logger and computer for real-time temperature monitoring. (b.1) Schematic of the DSC instrument, illustrating the arrangement of reference and sample crucibles, (b.2) The components used in DSC measurements: an aluminum pan, a lid, and the closed pan assembly, (b.3)- Photograph of the DSC machine employed in the study. (c) Illustration of the thermal conductivity analyzer, showing the hot-wire device connected to the PCM sample container within a thermostatic chamber. (d) Setup for density measurement, featuring graduated cylinders for volume determination and a balance for mass measurement to calculate density.</figcaption></figure>
<table><caption>**Table 2**
Experimental results for pure glycerol-water mixtures with different concentrations of pure glycerol (Pure G).</caption><thead><tr><th rowspan="2">Mixture</th><th colspan="3">Phase Change Temperature (°C)</th><th rowspan="2">Supercooling Temperature (°C)</th><th rowspan="2">Latent Heat (kJ·kg<sup>-1</sup>)</th></tr><tr><th>Freezing</th><th>Melting</th><th>Literature</th></tr></thead><tbody><tr><td>25 wt% Pure G</td><td>-7.76 ± 0.58</td><td>-7.90 ± 0.54</td><td>-7.00 [77]</td><td>-10.44 ± 0.98</td><td>147.53 ± 8.57</td></tr><tr><td>35 wt% Pure G</td><td>-12.63 ± 0.61</td><td>-11.20 ± 0.42</td><td>-12.40 [78]</td><td>-13.19 ± 0.80</td><td>110.87 ± 1.37</td></tr><tr><td>45 wt% Pure G</td><td>-21.82 ± 0.45</td><td>-20.39 ± 0.48</td><td>-19.90 [78]</td><td>-23.02 ± 0.49</td><td>73.55 ± 0.62</td></tr></tbody></table>

mixing. A predetermined amount of additive (NaCl, NaOH, or Na₂SO₄) was weighed separately using the same balance and gradually added to the glycerol-water mixture, with continuous stirring for an additional 30 min to achieve full dissolution and homogeneity. The stirring process was carried out in a tap water bath to prevent heat generation from exothermic reactions and maintain a stable temperature during mixing. The preparation process is illustrated in Fig. 6.

All experimental studies, including sample preparation and

characterization, were conducted in a controlled laboratory environment to ensure consistent and reproducible results. The laboratory was controlled by an air conditioning system at an ambient temperature of 22 ± 1 °C.

## 2.3. Characterization methods & experimental procedures

The PCMs were characterized using multiple experimental

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Impact of varying pure glycerol concentration on the properties of the mixture. (a)- Plot of Phase Change Temperature (PCT) as a function of glycerol concentration, with data compiled from references [77–79]. (b)- Graph showing the latent heat of the mixture at different glycerol concentrations, compared to data from [77].</figcaption></figure>
methodologies to determine their thermal and physical properties. To ensure statistical reliability and experimental validity, measurements for each property were conducted on three-four PCM samples, with each measurement repeated a minimum of three times to establish reproducibility and minimize experimental uncertainty. The procedures for each method are described below.

### 2.3.1. Phase Change Temperature (PCT)

The T-history method was employed to measure the PCT of PCM mixtures. This method involves tracking the temperature of samples over time, as they change from liquid to solid phase during freezing, and vice versa. Fig. 7(a) shows the experimental setup for the PCT measurements, where the PCM mixture was divided into three identical samples, each weighing 40 g, and placed in test tubes. These samples were then placed inside a freezer set to -40 °C, where they froze under natural convection conditions. To monitor temperature changes, a thermocouple was inserted at the center of each test tube, and an additional thermocouple measured the air temperature inside the freezer. All thermocouples were connected to a data logger (AOIP DATALOG 20-90-140), which recorded temperature data every 30 s and transmitted it to a computer for storage and analysis. After the samples were fully frozen, they were removed from the freezer and placed at room temperature (22 ± 1 °C) to melt, with the data logger continuing to record temperatures throughout the entire experiment. This continuous monitoring captured both the freezing and melting behavior of the PCMs. By analyzing the resulting temperature history curves, the PCTs of the mixtures were determined.

### 2.3.2. Latent heat and specific heat capacity

The latent heat and specific heat of the PCMs were determined using Modulated Differential Scanning Calorimetry (MDSC) with a Q100 TA Instruments device. Nitrogen served as the purge gas, maintained at a flow rate of 50 ml·min⁻¹, to ensure an inert atmosphere during the analysis. The measurements spanned a temperature range of -80 °C to 40 °C, employing a heating rate of 2 °C/min and a modulation amplitude of ±0.318 °C every 60 s. These measurements generated heat flux curves, which were analyzed to determine the latent heat and specific heat of each sample. Notably, only the DSC endothermic (melting) curves were used in this analysis for each sample, while the exothermic (freezing) curves were not included due to the supercooling effect exhibited by the PCMs, which resulted in loops in the heat flux curves, making them unreliable for accurate property determination. Before testing, the instrument was calibrated with sapphire as a reference material to guarantee accurate specific heat results. A schematic diagram of the DSC setup is shown in Fig. 7(b.1). The PCM samples, each weighing approximately 13 mg, were precisely measured using a Denver Instrument TB-124A balance (precision: 0.01 mg) and sealed in aluminum hermetic pans to prevent environmental interactions, as depicted in Fig. 7(b.2). These sealed pans were subsequently loaded into the DSC Q100 for analysis, as illustrated in Fig. 7(b.3).

### 2.3.3. Thermal conductivity measurements

The solid and liquid thermal conductivities of PCMs were measured using the Transient Hot-Wire method with a TEMPOS Thermal Properties Analyzer (METER Group), which has an accuracy of 0.0001

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Experimental results for the eutectic mixture composed of 40 wt% glycerol. (a)- T-history curve showing the temperature evolution over time during the phase change process. (b)- DSC analysis, presenting the heat flow as a function of temperature. (c)- Measured thermal conductivity of the mixture at various temperatures. (d)- Specific heat capacity of the mixture as a function of temperature.</figcaption></figure>
W·m⁻¹·K⁻¹. To ensure reliability and repeatability, the thermal conductivity of each of the three samples was assessed at least three times, with 15–20 min between each measurement to ensure that the sample reached thermal equilibrium. Before measurements, the analyzer was calibrated using glycerol as a reference material. Samples were placed in cylindrical tubes (50 mm diameter, 100 mm height) and positioned inside a thermostatic chamber (VC 7018–80/180 °C, Vötsch Industriechnik). The solid phase measurements were conducted at –50 °C to ensure that the PCM sample was fully solidified, while the liquid phase measurements were performed at 5 °C. Fig. 7(c) shows the experimental setup for the thermal conductivity measurement.

### 2.3.4. Density measurements

The density of the mixture was determined through a systematic gravimetric method, which involves measuring the mass and volume of a sample to calculate its density. This technique was employed for both the liquid and solid states of the mixture. The experimental apparatus used for these measurements is illustrated in Fig. 7(d). The procedure began with the weighing of empty graduated tubes to establish a baseline mass. Subsequently, the mixture was carefully transferred into each graduated tube, where both its volume and mass were measured. The density was then computed using the standard formula $ρ = m/V$, where $ρ$ denotes the density, $m$ represents the mass of the sample, and $V$ indicates its volume. For the solid-state measurements, the graduated tubes containing the mixture were placed in a freezer maintained at –40 °C–under natural convection conditions–until the mixture achieved complete solidification. Following this, the same measurement protocol was applied to ascertain the mass and volume of the solidified sample.

## 3. Experimental results

### 3.1. Thermal properties of pure glycerol-water mixtures

Previous studies [25,77–79] reported an inverse relationship between the concentration of pure glycerol in glycerol-water mixtures and their freezing temperatures. A comprehensive analysis of Table 2 reveals similar trends with previously published results.

As glycerol concentration increases from 25 wt% to 45 wt%, the freezing temperature decreases substantially from –7.76 ± 0.58 °C to –21.82 ± 0.45 °C, demonstrating glycerol’s effective freezing point depression properties (Fig. 8(a)). The melting temperatures follow a similar pattern, decreasing from –7.90 ± 0.54 °C to –20.39 ± 0.48 °C as glycerol concentration increases. Notably, there exists a small hysteresis between freezing and melting temperatures across all concentrations, with melting points being slightly higher than freezing points for the 35 wt% and 45 wt% samples. Supercooling temperature, a critical parameter for PCMs, also shows a clear concentration dependence. The 25 wt% mixture reaches a supercooling temperature of –10.44 ± 0.98 °C, while the 45 wt% mixture extends to –23.02 ± 0.49 °C. The supercooling degree (difference between freezing and supercooling temperatures) remains relatively consistent across concentrations. Fig. 8 (b) presents a comparative analysis between the experimentally measured average latent heat values and those reported in previous literature [77]. The results are consistent with prior findings [25,77], showing a decrease in latent heat with increasing glycerol concentration. The 25 wt% mixture exhibits a latent heat of 147.53 ± 8.57 kJ·kg⁻¹, which drops by approximately 50 % to 73.55 ± 0.62 kJ·kg⁻¹ for the 45 wt% mixture (see Table 2).

The changes in the mixtures’ PCT and latent heat are mainly due to glycerol’s ability to modify the structure of pure water, weakening intermolecular forces. In pure water, strong hydrogen bonds between water molecules create a stable network that supports ice formation. When glycerol is added, it interacts with water molecules, disrupting the network. Specifically, glycerol forms new hydrogen bonds with water, replacing some of the water-water and glycerol-glycerol bonds [80,81]. As a result, the modified structure of the mixture is less likely to form ice

<table><caption>**Table 3**

Summary of the thermal properties of 40 wt% glycerol-water mixture.</caption><thead><tr><th>Property</th><th></th><th>Mean</th><th>Literature</th><th></th></tr></thead><tbody><tr><td rowspan="3">Phase Change<br>Temperature (°C)</td><td>Freezing</td><td>-17.83 ±<br>0.15</td><td>-21; -16</td><td>[51,77]</td></tr><tr><td>Melting</td><td>-17.50 ±<br>0.10</td><td></td><td></td></tr><tr><td>Supercooling Temperature (°C)</td><td>-21.17 ±<br>1.95</td><td>-</td><td>-</td></tr><tr><td>Latent Heat (kJ·kg⁻¹)</td><td></td><td>87.69 ±<br>1.47</td><td>86.19</td><td>[77]</td></tr><tr><td>κ<sub>liquid</sub> (W·m⁻¹·K⁻¹) @ 5 °C</td><td></td><td>0.484 ±<br>0.06</td><td>0.461<sup>a</sup></td><td></td></tr><tr><td>κ<sub>solid</sub> (W·m⁻¹·K⁻¹) @ -50 °C</td><td></td><td>1.138 ±<br>0.09</td><td>1.800<sup>a</sup></td><td></td></tr><tr><td>ρ<sub>liquid</sub> (×10³ kg·m⁻³) @ 22 °C</td><td></td><td>1.096 ±<br>0.01</td><td>1.096/1.097/<br>1.100</td><td>[61,78,84]</td></tr><tr><td>ρ<sub>solid</sub> (×10³ kg·m⁻³) @ -35 °C</td><td></td><td>1.071 ±<br>0.01</td><td>1.059<sup>a</sup></td><td></td></tr><tr><td>c<sub>p-liquid</sub> (kJ·kg⁻¹·K⁻¹) @ 25 °C</td><td></td><td>3.179 ±<br>0.04</td><td>3.417<sup>a</sup></td><td></td></tr><tr><td>c<sub>p-solid</sub> (kJ·kg⁻¹·K⁻¹) @ -72 °C</td><td></td><td>2.381 ±<br>0.04</td><td>-</td><td>-</td></tr></tbody></table>

crystals, contributing to the decrease in the phase change temperature [82]. This water-glycerol bond formation further contributes to the decrease reduction in the latent heat capacity of the mixture [25,83].

The main objective of this study is to develop a low-temperature PCM suitable for storing frozen products, with a PCT around –20 °C to –18 °C. The experimental curve in Fig. 8(a) shows that a glycerol concentration of 40 wt% closely aligns with this target temperature range. Therefore, this concentration was selected for the characterization of the thermal properties.

Fig. 9(a) illustrates the temperature profiles of three samples (40 wt % glycerol mixture) during the freezing/melting cycle. All samples display similar trends: a sharp decline in temperature indicating a supercooling effect (–21 °C), followed by stabilization around –18 °C, which represents the freezing temperature. The average freezing temperature was observed at –17.8 °C while the average melting temperature was around –17.5 °C. The PCMs exhibit supercooling effects at different degrees, with an average of 3.33 K.

Fig. 9(b) shows the heat flow curves for the three samples as a function of temperature. All the curves show similar patterns with endothermic peaks, corresponding to the melting process occurring consistently at around –18 °C. The latent heat of fusion for the samples was also comparable, with an average of 87.69 kJ·kg⁻¹. This value aligns closely with the latent heat reported in previous research [77] which was 86.19 kJ·kg⁻¹.

The thermal properties of an ideal solution mixture can be estimated using the linear mixing rule, represented by the eq. (1):

$$ \xi_{\text{pred}} = \sum_{i=1}^{n} \chi_{i} \xi_{i} \qquad (1) $$

where $\xi_{pred}$ represents the predicted property of the mixture, $\xi_i$ denotes the property of each pure component, $\chi_i$ represents the mass fraction (for heat capacity) and the volume fraction (for density). This equation assumes ideal mixing behavior. The properties of individual pure components were obtained from [77,84–86].

Other thermal properties of the 40 wt% glycerol-water mixture are also investigated and summarized in Table 3. Thermal conductivity ($k_{solid}$) measurements reveal that the solid phase at –50 °C exhibits a value of 1.137 W·m⁻¹·K⁻¹, while liquid thermal conductivity ($k_{liquid}$) at 5 °C was 0.482 W·m⁻¹·K⁻¹ (as illustrated in Fig. 9(c)). The density ($\rho_{liquid}$) for the liquid state was 1.094 × 10³ kg·m⁻³ at 22 °C (room temperature). This value aligns with those reported in the literature, specifically 1.097 × 10³ kg·m⁻³ and 1.1 × 10³ kg·m⁻³ as reported in [78,84], respectively. In contrast, the solid-state density ($\rho_{solid}$) was

<footnote>a Approximated using linear mixing rule of the pure components.</footnote>
<caption>**Table 4**</caption>

Comparison of measured specific heat of 40 wt% glycerol-water mixture with literature values.

<table><thead><tr><th rowspan="2">Temperature (°C)</th><th colspan="2">c<sub>p</sub> (kJ·kg<sup>-1</sup>·K<sup>-1</sup>)</th><th rowspan="2">Difference (%)</th></tr><tr><th>Measured</th><th>[78]</th></tr></thead><tbody><tr><td>35</td><td>3.21</td><td>3.52</td><td>8.71</td></tr><tr><td>30</td><td>3.20</td><td>3.48</td><td>7.96</td></tr><tr><td>-20<sup>a</sup></td><td>8.47</td><td>8.37</td><td>1.09</td></tr><tr><td>-31.7<sup>a</sup></td><td>4.79</td><td>5.02</td><td>4.65</td></tr></tbody></table>

a Represents apparent specific heat.

determined to be $1.07 \times 10^3$ kg·m⁻³ at -35 °C, which is lower than the liquid-state density. This behavior is consistent with expectations, given that the mixture contains a significant proportion of ice, which is, as known, less dense than its liquid form (water).

Specific heat capacity values for both liquid and solid states are reported in Fig. 9(d); Table 3. The liquid phase at 25 °C shows a higher average value ($c_{p-liquid}$ = 3.179 kJ·kg⁻¹·K⁻¹) compared to the solid phase at -72 °C ($c_{p-solid}$ = 2.381 kJ·kg⁻¹·K⁻¹). Furthermore, Table 4 provides a comparison of the measured and literature values of specific heat for the mixture across four distinct temperatures: 35 °C, 30 °C, -20 °C, and -31.7 °C. The results reveal a strong overall agreement, with deviations ranging from 1.09 % to 8.71 %. The largest observed discrepancy occurs at 35 °C, where the measured $c_p$ (3.21 kJ·kg⁻¹·K⁻¹) is 8.71 % lower than the literature value (3.52 kJ·kg⁻¹·K⁻¹) [78].

The experimental findings offer significant insights into the thermal characteristics of the glycerol-water mixture. The results indicate consistent thermal behavior across samples, with uniform freezing and melting temperatures around -20 °C/-18 °C. This consistency highlights the mixture's potential as PCM for applications requiring phase transitions within this temperature range. However, the relatively low latent heat capacity of the glycerol-water mixture, compared to alternative PCMs such as hydrated salts, may restrict its practical applications. This limitation emphasizes the need for further research to enhance the latent heat capacity of the glycerol-water system. Such improvements are crucial for developing an optimized PCM that achieves an ideal balance between the desired phase change temperature and sufficient latent heat capacity.

## 3.2. PCM enhancement with additives

PCT and latent heat capacity are critical parameters for PCMs in cold chain applications. PCT ensures that products are maintained at their desired temperatures, while latent heat capacity provides sustained cooling. The above results have shown that glycerol-water mixtures can achieve sub-zero PCTs suitable for cold chain use. However, increasing glycerol concentration, while lowering PCT, significantly reduces latent heat capacity. For example, a mixture with a PCT of -18 °C exhibits up to a 74 % reduction in latent heat capacity. Therefore, to develop an appropriate PCM for cold chain applications, it is necessary to enhance the latent heat capacity of the mixture.

Three additives were primarily studied for their effect on the PCT of the glycerol-based mixtures. Sodium hydroxide (NaOH), Sodium chloride (NaCl), and sodium sulfate ($Na_2SO_4$) were selected due to their presence in crude glycerol derived from biodiesel production [70,71,87]. The results showed that $Na_2SO_4$ has a minimal effect on the mixture's PCT, limiting its utility. On the other hand, NaOH and NaCl showed a significant effect, decreasing the PCT to -15 °C and -12 °C, respectively, for 10 wt% NaOH and NaCl. However, NaOH is hazardous for food preservation applications and corrosive to the aluminum pans used in DSC analysis. Consequently, NaCl was selected as the most suitable additive for further study.

<caption>**Table 5**</caption>

Levels of the independent variables used in the CCD design.

<table><caption>**Table 6**</caption><thead><tr><th rowspan="2">Independent variables</th><th rowspan="2">Symbol</th><th colspan="3">Variables Level</th></tr><tr><th>-1</th><th>0</th><th>1</th></tr></thead><tbody><tr><td>NaCl</td><td>A</td><td>0</td><td>0.075</td><td>0.15</td></tr><tr><td>Glycerol</td><td>B</td><td>0.02</td><td>0.21</td><td>0.4</td></tr></tbody></table>

Matrix of Design Of Experiment (DOE) used during the optimization.

<table><caption>**Table 7**</caption><thead><tr><th rowspan="2">Runs</th><th colspan="2">Independent variables</th><th colspan="2">Temperature (°C)</th><th rowspan="2">Residual (°C)</th></tr><tr><th>A (NaCl)</th><th>B (Glycerol)</th><th>Measured</th><th>Predicted</th></tr></thead><tbody><tr><td>1</td><td>0.075</td><td>0.21</td><td>-13.30</td><td>-13.86</td><td>0.56</td></tr><tr><td>2</td><td>0.15</td><td>0.02</td><td>-12.10</td><td>-12.38</td><td>0.28</td></tr><tr><td>3</td><td>0.15</td><td>0.4</td><td>-35.8</td><td>-37.37</td><td>1.37</td></tr><tr><td>4</td><td>0</td><td>0.4</td><td>-18.30</td><td>-18.58</td><td>0.28</td></tr><tr><td>5</td><td>0.075</td><td>0.4</td><td>-29.40</td><td>-27.75</td><td>1.65</td></tr><tr><td>6</td><td>0.15</td><td>0.21</td><td>-23.70</td><td>-22.05</td><td>1.65</td></tr><tr><td>7</td><td>0</td><td>0.02</td><td>-0.10</td><td>0.70</td><td>0.8</td></tr><tr><td>8</td><td>0.075</td><td>0.21</td><td>-13.30</td><td>-13.86</td><td>0.56</td></tr><tr><td>9</td><td>0.075</td><td>0.02</td><td>-5.10</td><td>-5.62</td><td>0.52</td></tr><tr><td>10</td><td>0</td><td>0.21</td><td>-5.60</td><td>-6.12</td><td>0.52</td></tr></tbody></table>

Summary of the model's practical significance.

<table><caption>**Table 8**</caption><thead><tr><th>SE</th><th>R<sup>2</sup></th><th>R<sup>2</sup>(adj)</th><th>R<sup>2</sup>(pred)</th><th>F-value</th><th>P-value</th></tr></thead><tbody><tr><td>1.52</td><td>99.20 %</td><td>98.19 %</td><td>91.94 %</td><td>98.68</td><td>0.0003</td></tr></tbody></table>

Analysis of variance (ANOVA) results of the quadratic model.

<table><thead><tr><th>Source</th><th>DF</th><th>Adj SS</th><th>Adj MS</th><th>F-Value</th><th>P-Value</th></tr></thead><tbody><tr><td>Model</td><td>5</td><td>1143.478</td><td>228.696</td><td>98.68</td><td>0.0003</td></tr><tr><td>Linear</td><td>2</td><td>1115.633</td><td>557.817</td><td>240.68</td><td>0.0001</td></tr><tr><td>NaCl</td><td>1</td><td>380.807</td><td>380.807</td><td>164.31</td><td>0.0002</td></tr><tr><td>Glycerol</td><td>1</td><td>734.827</td><td>734.827</td><td>317.06</td><td>0.0001</td></tr><tr><td>Square</td><td>2</td><td>19.723</td><td>9.861</td><td>4.25</td><td>0.1022</td></tr><tr><td>NaCl×NaCl</td><td>1</td><td>0.114</td><td>0.114</td><td>0.05</td><td>0.8351</td></tr><tr><td>Glycerol×Glycerol</td><td>1</td><td>18.574</td><td>18.574</td><td>8.01</td><td>0.0473</td></tr><tr><td>2-Way Interaction</td><td>1</td><td>8.123</td><td>8.123</td><td>3.50</td><td>0.1345</td></tr><tr><td>NaCl×Glycerol</td><td>1</td><td>8.123</td><td>8.123</td><td>3.50</td><td>0.1345</td></tr><tr><td>Error</td><td>4</td><td>9.271</td><td>2.318</td><td></td><td></td></tr><tr><td>Lack-of-Fit</td><td>3</td><td>9.271</td><td>3.090</td><td></td><td></td></tr><tr><td>Pure Error</td><td>1</td><td>0.000</td><td>0.000</td><td></td><td></td></tr><tr><td>Total</td><td>9</td><td>1152.749</td><td></td><td></td><td></td></tr></tbody></table>

## 3.3. Response Surface Method optimization (RSM)

To determine the optimal formulation for our study, we used the Central Composite Design (CCD) method to investigate the effects of two independent variables—NaCl and Glycerol Concentration—on the response phase change temperature. These factors and their three levels are shown in Table 5.

The experimental design matrix, presented in Table 6, consists of 10 distinct runs to determine the response on the phase change temperature of the mixtures. The table also presents the measured and expected values. The resulting data were subjected to regression analysis using Statgraphics Centurion 19 software and Matlab MathWorks. The experimental results were fitted using a quadratic polynomial model as formulated in the Eq. (2) below:

$$Y(°C) = \beta_0 + \beta_1 A + \beta_2 B + \beta_3 A^2 + \beta_4 B^2 + \beta_5 A \times B \quad (2)$$

where $Y(°C)$ is the predicted phase change temperature, A and B are representatives of the independent variables of NaCl and Glycerol, while $\beta_i$, ($i$ = 0...1) are the regression coefficients.
<figure><img src="image_12.png" /><figcaption>Fig. 10. (a)- Normal plot of the standardized effects, (b)- Pareto chart illustrating the standardized effects of the factors, (c)- Effect of the variables' main factors NaCl and Glycerol concentration, on the response variable PCT, (d)- Normal probability plot of residuals.</figcaption></figure>

The results show that the CCD predicted values are in good agreement with experimental data. The model's accuracy is further assessed using the coefficient of determination ($R^2$). Additionally, the Analysis of Variance (ANOVA) results were evaluated through the Probability value ($P$-value) and Fisher's test ($F$-value).

### 3.4. RSM analysis

The practical and statistical significance of the model are checked using the model summary and ANOVA results presented in Table 7 and Table 8, respectively. The model demonstrates a remarkably high $R^2$ of 99.20 %, indicating a robust correlation between experimental and predicted values. The ANOVA results provide additional support for the

model's significance. The overall model $F$-value of 98.68, coupled with a $P$-value of 0.0003—which is well below the significance value $\alpha = 0.05$—provide strong evidence that the model is statistically significant and that the independent variables have a significant effect on the response temperature [88,89]. The $P$-values for both linear terms, A (NaCl) and B (Glycerol), show a high statistical significance, as they are both lower than $\alpha$ (0.0002 for NaCl and 0.0001 for Glycerol). This suggests that these factors strongly influence the response, as also shown in Fig. 10(a, b). The quadratic term for Glycerol ($B^2$) is also significant with a $P$-value of 0.0473, suggesting a non-linear relationship with the response variable (Fig. 10(c)). On the other hand, the quadratic term for NaCl ($A^2$) has a $P$-value higher than the significance value at 0.8351, indicating a linear relation between NaCl concentration and the response temperature

<table><caption>**Table 9**
Regression coefficients of the model.</caption><thead><tr><th>Regression Coefficient</th><th>β<sub>0</sub></th><th>β<sub>1</sub></th><th>β<sub>2</sub></th><th>β<sub>3</sub></th><th>β<sub>4</sub></th><th>β<sub>5</sub></th></tr></thead><tbody><tr><td></td><td>1.091</td><td>-79.318</td><td>-17.920</td><td>-39.365</td><td>-78.156</td><td>-100.000</td></tr></tbody></table>
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Results from Response Surface Methodology (RSM) analysis. (a) Contour plots displaying temperature variations as a function of NaCl and glycerol concentrations, with contours representing different temperature levels to visualize interaction effects. (b) Three-dimensional surface plots illustrating the combined influence of NaCl and glycerol concentrations on the freezing temperature of the mixture, showing how it changes across the tested concentration range.</figcaption></figure>

(Fig. 10(c)). The interaction term (NaCl×Glycerol), does not reach the statistical significance level, meaning that the factor does not significantly affect the response.

The normal probability plot of the standardized residuals for the temperature response–Fig. 10(d)–was analyzed to assess the validity of the normality assumption in the RSM model. The residuals exhibited a close alignment with the theoretical reference line, indicating that the distribution of the model errors approximates a normal distribution. These results support the robustness of the quadratic model in capturing the relationship between the independent variables and the temperature response, ensuring reliable predictions within the experimental domain.

The regression coefficients and the response equation are provided in Table 9 below.

The contour plot–Fig. 11(a)–illustrates the relationships between the independent variables and the responses of the PCT of the mixture. These plots visually demonstrate how variations in the independent variables influence the PCT response. The x and y axes represent the independent variables NaCl and glycerol concentration, respectively, while the colour gradient indicates different levels of the PCT. The second-order model is plotted as a three-dimensional surface –as presented in Fig. 11(b)– describing the relationship between glycerol

<table><caption>**Table 10**
Comparison of predicted and measured temperatures.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Independent Variables</th><th colspan="2">Phase Change Temperature (°C)</th><th rowspan="2">Residual (°C)</th></tr><tr><th>A</th><th>B</th><th>Measured</th><th>Predicted</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0.25</td><td>-7.4</td><td>-8.27</td><td>0.87</td></tr><tr><td>2</td><td>0.05</td><td>0.1</td><td>-5.9</td><td>-6.05</td><td>0.15</td></tr><tr><td>3</td><td>0.1</td><td>0.1</td><td>-10.4</td><td>-10.81</td><td>0.41</td></tr><tr><td>4</td><td>0.1</td><td>0.05</td><td>-8.6</td><td>-8.83</td><td>0.23</td></tr><tr><td>5</td><td>0.1</td><td>0.15</td><td>-12.6</td><td>-13.18</td><td>0.58</td></tr><tr><td>6</td><td>0.1</td><td>0.2</td><td>-15.6</td><td>-15.94</td><td>0.34</td></tr><tr><td>7</td><td>0.15</td><td>0.1</td><td>-16.4</td><td>-15.77</td><td>-0.63</td></tr><tr><td>8</td><td>0.15</td><td>0.15</td><td>-19.7</td><td>-18.39</td><td>-1.31</td></tr><tr><td>9</td><td>0.06</td><td>0.35</td><td>-21.3</td><td>-21.76</td><td>0.46</td></tr><tr><td>10</td><td>0.03</td><td>0.05</td><td>-2.7</td><td>-2.57</td><td>-0.13</td></tr><tr><td>11</td><td>0.14</td><td>0.08</td><td>-13.9</td><td>-13.84</td><td>-0.06</td></tr><tr><td>12</td><td>0.15</td><td>0.03</td><td>-12.5</td><td>-12.75</td><td>0.25</td></tr></tbody></table>

concentration, NaCl concentration, and the PCT of the mixtures. The temperature is represented by colour variation, with yellow indicating higher temperatures and blue denoting lower temperatures. Red points on the surface denote the DOE points used to construct the model, while blue points represent the validation points (further discussed in the validation section below). The plot reveals a nonlinear relationship between the independent variables and temperature response. It appears that the glycerol concentration has a pronounced effect on temperature compared to NaCl concentration.

### 3.5. Model validation

The RSM model was validated by comparing predicted temperatures with experimentally measured values across 12 distinct experimental trials, as presented in Table 10. The predicted temperatures ranged from -21.76 °C to -2.57 °C, while the measured temperatures spanned from -21.3 °C to -2.7 °C. To quantitatively assess the model's accuracy, residuals were calculated as the difference between predicted and measured values. These residuals varied from -1.31 °C to 0.87 °C, with most values below 0.6 °C, demonstrating substantial agreement between model predictions and experimental measurements.

Fig. 12 further illustrates this correlation through a linear regression analysis of predicted versus measured temperatures. The regression yielded a slope of 0.963 ± 0.031 and an intercept of -0.544 ± 0.415. The R² coefficient of 0.9897 and RMSE of 0.574 °C confirm the model's strong predictive capability. The proximity of data points to the ideal case reference line (y = x) provides visual confirmation that the developed RSM model effectively predicts the relationship between the independent variables and phase change temperature of the mixtures under the specified experimental conditions.

### 3.6. Characterization of thermal properties for optimized PCM compositions

Based on the RSM, three PCM mixtures with PCTs suitable for frozen food storage (-20 °C to -18 °C) were selected for further characterization. The primary objective was to identify an optimal mixture that combines the target PCT with high latent heat capacity for efficient thermal energy storage applications. As presented in Table 11 and visualized in Fig. 13, the predicted PCT values showed good agreement with the measured values across all three mixtures. Predicted PCTs ranged from -19.06 °C to -18.05 °C, while measured values spanned from -20.97 °C to -17.43 °C. Research indicates that the PCT decrease can be attributed to the bonding properties of dissolved NaCl ions and glycerol molecules with water molecules. As the concentration of these solutes increases, Na⁺ and Cl⁻ ions form hydration shells, while glycerol forms direct hydrogen bonds with water molecules, disrupting the characteristic of the ice lattice [80,81,90]. This molecular disruption results in a shift of the PCT to lower values, proportional to solute
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Linear regression analysis between predicted and measured temperatures, showing strong agreement (R² = 0.9897). The dashed orange line represents the ideal 1:1 or y = x relationship.</figcaption></figure>

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

Thermal properties for optimal potential PCM.</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Mixtures</th></tr><tr><th>PCM-M1</th><th>PCM-M2</th><th>PCM-M3</th></tr></thead><tbody><tr><td>NaCl (wt%)</td><td></td><td>2.20</td><td>7.70</td><td>14.00</td></tr><tr><td>Glycerol (wt%)</td><td></td><td>36.00</td><td>28.00</td><td>18.00</td></tr><tr><td>Phase Change</td><td>Predicted</td><td>-18.05</td><td>-18.55</td><td>-19.06</td></tr><tr><td>Temperature (°C)</td><td>Measured</td><td>-17.43 ± 0.21</td><td>-18.60 ± 0.84</td><td>-20.97 ± 0.77</td></tr><tr><td>Supercooling</td><td></td><td>-22.8 ± 0.35</td><td>-22.07 ± 2.60</td><td>-22.77 ± 1.55</td></tr><tr><td>Temperature (°C)</td><td></td><td>97.58 ± 1.53</td><td>99.75 ± 1.83</td><td>281.81 ± 5.17</td></tr><tr><td>Latent Heat (kJ·kg<sup>-1</sup>)</td><td></td><td>97.58 ± 1.53</td><td>99.75 ± 1.83</td><td>281.81 ± 5.17</td></tr><tr><td rowspan="3">Specific Heat (kJ·kg<sup>-1</sup>·K<sup>-1</sup>)</td><td>Liquid @ 25 °C</td><td>3.56 ± 0.33</td><td>3.29 ± 0.26</td><td>3.22 ± 0.30</td></tr><tr><td>Solid @ -74 °C</td><td>1.92 ± 0.06</td><td>1.96 ± 0.07</td><td>1.91 ± 0.19</td></tr></tbody></table>

concentration—a phenomenon known as freezing-point depression [91]. The supercooling temperatures were also consistent across all mixtures, ranging from -22.07 ± 2.60 °C to -22.84 ± 0.35 °C, suggesting similar nucleation behavior despite compositional differences.

The observed differences in latent heat capacity are similarly related to the influence of solutes on ice formation, resulting in decreased latent heat values for the mixtures [90–92]. The relationship between latent heat capacity reduction and PCT varies between NaCl and glycerol solutions. Experimental data show that NaCl maintains a relatively stable latent heat capacity while achieving a considerably lower PCT. In contrast, glycerol markedly reduces the latent heat capacity, leading to a less pronounced decrease in PCT. For example, a 22.4 wt% NaCl solution exhibits a latent heat of 222 to 228.14 kJ·kg⁻¹ with a PCT of -21.2 °C [93,94]. Meanwhile, glycerol, as investigated in this study, displays a latent heat of 147.5 kJ·kg⁻¹ with a PCT of -7 °C. These trends are clearly reflected in our study results, where latent heat capacities differ significantly across the mixtures: PCM-M3, with the highest NaCl content at 14 wt% and the lowest glycerol content at 18 wt%, achieves the highest latent heat capacity at 281.81 kJ·kg⁻¹, making it the most

promising candidate for efficient thermal energy storage. Meanwhile, PCM-M1 and PCM-M2, containing higher glycerol proportions (36 wt% and 28 wt%, respectively) and lower NaCl levels (2.2 wt% and 7.7 wt%, respectively), show much lower latent heat capacities of 97.58 kJ·kg⁻¹ and 99.75 kJ·kg⁻¹, respectively. Despite these variations in latent heat, the specific heat capacities remained relatively consistent across all mixtures, ranging from 3.22 to 3.56 kJ·kg⁻¹·K⁻¹ at liquid state (25 °C) and from 1.91 to 1.96 kJ·kg⁻¹·K⁻¹ in solid state (-74 °C). This indicates comparable sensible heat storage capabilities regardless of composition.

Based on these findings, PCM-M3 emerges as the most promising candidate for thermal energy storage applications in frozen food preservation, offering an optimal combination of suitable phase change temperature and high latent heat capacity.

### 3.7. Comparison with commercial PCM

Fig. 14 compares melting temperatures and latent heat values of various commercial PCMs and those investigated in the current study. The PCMs exhibit a PCT between -23 °C and -13 °C. A notable observation is that many of the commercial PCMs are hydrated salts. These materials are characterized by higher latent heat values ranging between 200 kJ·kg⁻¹ and 330 kJ·kg⁻¹. In contrast, mixtures investigated in this study—marked in diamond symbol—exhibit the appropriate PCT ranging between -22 °C and -18 °C, however, they also exhibit a very low latent heat ranging between 77 kJ·kg⁻¹ and 100 kJ·kg⁻¹. Interestingly, the addition of sodium chloride (NaCl) in significant quantities to the experimental formulations yields promising results. Particularly, the mixture PCM-M3 labeled 0.14NaCl:0.18G exhibits thermal properties comparable to some commercial products. This suggests that NaCl can effectively enhance PCM thermal characteristics, offering a potentially cost-effective alternative to conventional hydrated salt PCM.

### 3.8. Visualization of the melting process of the studied PCMs

This section presents the thermal performance of the studied PCMs during the melting process. The PCMs were initially placed in a freezer set at -40 °C to fully solidify (Charging Phase). Afterward, they were
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Thermal Properties of Phase Change Materials. (a) Temperature characteristics of three PCM formulations (PCM-M1, PCM-M2, PCM-M3) showing predicted PCT (red squares), measured PCT (orange squares), and supercooling temperature (blue squares). (b) Comparison of thermal storage properties across the same PCM formulations, displaying latent heat, specific heat at liquid phase (at 20 °C), and specific heat at solid phase (at -74 °C) with associated measurement uncertainties. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Comparative analysis of latent heat values: commercial PCMs versus novel mixtures developed in this study. The optimal mixture is circled in red. Commercial PCM data are sourced from technical data sheets without detailed information on DSC protocols [32]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

exposed to room temperature (22 °C) to observe their melting behavior over time (Discharging Phase). Fig. 15 presents images capturing the discharging process for the seven mixtures examined in this study, offering a comparative view of each mixture's behavior during melting. The water-based mixtures vary in composition, ranging from pure glycerol at concentrations of 25 to 45 wt% to NaCl:glycerol solutions with ratios of 2.2:36, 7.7:28, and 14:18 wt%. The melting process is documented at five instants: 0, 30, 50, 65, and 80 min. Initially, all samples appear as solid, translucent masses. During the process, a clear liquid phase begins to form at the bottom of each tube and gradually rises upward, with different compositions exhibiting varying rates of melting. Notably, the 45 wt% glycerol-based PCM was fully liquefied within 30 min, followed by the 40 wt% PCM at 50 min. The 35 wt% glycerol, PCM-M1, and PCM-M2 mixtures completed melting after 65 min. After 80 min, all samples have fully transitioned to the liquid state. This visual representation provides valuable insights into the melting kinetics and phase transition characteristics of these PCMs, emphasizing the significance of high latent heat in PCM performance.

### 3.9. Assessment of cyclic stability of the optimal PCM (PCM-M3)

Thermal cycling tests represent an essential method for evaluating the long-term effectiveness of PCMs. This test offers valuable insights into the durability of the material to maintain consistent thermal properties throughout repeated use. Following our previous analysis, we selected PCM-M3, which demonstrated high latent heat capacity, to assess its cyclic stability. The evaluation process involved measuring the material's latent heat through DSC over 100 melting-freezing cycles. The results are presented in Fig. 16 showing all measurement points. The initial latent heat value was recorded at 290.1 kJ·kg⁻¹, and throughout the cycling process, the values fluctuated within a narrow range between 288 and 295 kJ·kg⁻¹ during the first 20 cycles. The material exhibited slight variations in latent heat, with peak values reaching approximately 295.5 kJ·kg⁻¹, followed by a gradual and minimal decrease in subsequent cycles. Statistical analysis of the data reveals a standard deviation of approximately ±1.72 kJ·kg⁻¹ across all cycles, indicating minimal fluctuation in the latent heat capacity. This negligible change in latent heat capacity over repeated thermal cycles demonstrates that the material retains its energy storage capabilities without significant degradation in performance, confirming its suitability for long-term applications.

## 4. Numerical assessment of PCM on food product temperature

Temperature fluctuations during storage significantly impact the quality of frozen food [95,96]. This is primarily because temperature fluctuations directly affect ice crystal formation: larger temperature amplitudes lead to larger ice crystal formation, which causes substantial tissue damage and ultimately reduces food quality [97–99]. To address this issue, the present study aims to evaluate the effectiveness of a PCM/ Insulation layer in maintaining a stable food temperature during storage. The analysis focuses on two primary conditions: typical freezer operation, where air temperatures fluctuate, and defrost cycles, during which the freezer's internal temperature reaches its peak.

Given that most food products typically contain 75–95 % water [100,101], ice was selected as a simplified food model in this study. The thermal performance of this model was evaluated under four different scenarios.

- Case 1: Reference case with food model only;

- Case 2: System with a Polystyrene insulation layer;
<figure><img src="image_17.png" /><figcaption>Fig. 15. A series of photographs capturing the physical changes of the studied PCMs during melting at room temperature. Each image corresponds to a different PCM composition at a different time, from 0 min to 80 min. G stands for glycerol.</figcaption></figure>

- Case 3: System with a 40 % Pure Glycerol PCM layer;

- Case 4: System with a PCM-M3 layer (14 % NaCl, 18 % Glycerol);

$$ \rho_{eff}c_{eff}\frac{\partial T}{\partial t} = \nabla \cdot (\kappa_{eff}\nabla T) \quad (3) $$

## 4.1. Model description

The investigated system consists of a cylindrical food model encapsulated by an insulation layer (made of either PCMs or Polystyrene), forming a composite cylinder exposed to varying ambient air temperatures. Due to the axisymmetric aspect, the heat transfer problem is simplified to a one-dimensional transient model in cylindrical coordinates. This modeling approach builds upon previously validated work in the field of cryogenics published by Rouaud et al. [102]. The system comprises two distinct regions: the food product ($0 \le r \le r_1$) and the surrounding PCM layer ($r_1 < r \le r_2$), where $r_1$ and $r_2$ represent the food product radius and the outer radius, respectively (Fig. 17).

The effective properties method is used to consider the phase change phenomena. This approach defines the properties as functions of temperature (detailed in Section 4.3). The heat transfer within the system is modeled by the following equation:

where $\rho$ represents the density, $\kappa$ is the thermal conductivity, and $c$ denotes the specific heat capacity. The subscript *eff* indicates the effective properties.

## 4.2. Boundary conditions

The heat transfer boundary conditions for the one-dimensional model are as follows:

1. At the center of the food product ($r = 0$):

$$ \frac{\partial T}{\partial r}\bigg|_{r=0} = 0 \quad (4) $$
<figure><img src="image_18.png" /><figcaption>Fig. 16. Measured latent heat values for the PCM-M3 over multiple freezing-melting-freezing cycles. The graph shows how the latent heat remains stable across repeated cycles, indicating the thermal stability of the materials.</figcaption></figure>

<figure><img src="image_19.png" /></figure>

Studied Cases:

Case 1: No Insulation Layer; Case 2: Insulation Layer: Polystyrene

Case 3: Insulation Layer: PCM 40% Glycerol; Case 4: Insulation Layer: PCM-M3

<caption>Fig. 17. Schematic representation illustrating the one-dimensional heat transfer model in cylindrical coordinates. (a) Cross-sectional view of the food model, showing radial heat transfer. (b) Axial view, depicting heat transfer along the length of the food model.</caption>

2. At the outer surface of the PCM layer ($r = r_2$), a convective boundary condition is imposed:

$$ - \kappa_{\text{eff}} \frac{\partial T}{\partial r} \Big|_{r=r_2} = h_{\text{air}} (T_{r=r_2} - T_{\text{air}}) \quad (5) $$

where, $h_{\text{air}}$ is the convective heat transfer coefficient, and $T_{\text{air}}$ is the surrounding air temperature.

The model problem was solved using COMSOL Multiphysics® version 6.2 on a Dell® Precision 7670 computer equipped with a 12th Intel® Core™ i7-12850HX, at 2.1 GHz, with 32 GB RAM running on Windows® 10 Professional, 64 bits. A comprehensive grid independence study was conducted to ensure the numerical accuracy of the results. We evaluated the solution convergence using different mesh densities ranging from 25, 50, and 100 cells, finding that results became mesh-

independent with as few as 25 cells for this model. The final implementation used 50 cells to provide a conservative margin of accuracy while maintaining computational efficiency. More critical to solution accuracy was the temporal discretization. A time-step of 1 s was implemented to adequately capture the state changes in the system, particularly during periods of rapid temperature variation in response to external conditions. This combination of spatial and temporal resolution ensured that our numerical results were reliable and independent of the numerical conditions.

4.3. Thermal properties

The thermal properties of ice are modeled as a function of temperature (°C) as described in [103]. For the polystyrene insulation layer, the thermal properties are obtained from the COMSOL® materials library.
<table><caption>**Table 12**
Ice and polystyrene thermal properties.</caption><thead><tr><th>Material</th><th>Property</th><th></th></tr></thead><tbody><tr><td rowspan="3">Ice</td><td>Thermal Conductivity (W·m<sup>-1</sup>·K<sup>-1</sup>)</td><td>κ<sub>ice</sub> = 2.2196 – 6.2489 × 10<sup>-3</sup>T + 1.0154 × 10<sup>-4</sup>T<sup>2</sup></td></tr><tr><td>Density (kg·m<sup>-3</sup>)</td><td>ρ<sub>ice</sub> = 9.1689 × 10<sup>2</sup> – 1.3071 × 10<sup>-1</sup>T</td></tr><tr><td>Specific Heat (kJ·kg<sup>-1</sup>·K<sup>-1</sup>)</td><td>c<sub>ice</sub> = 2.0623 + 6.0769 × 10<sup>-3</sup>T</td></tr><tr><td rowspan="3">Polystyrene</td><td>Thermal Conductivity (W·m<sup>-1</sup>·K<sup>-1</sup>)</td><td>0.05</td></tr><tr><td>Density (kg·m<sup>-3</sup>)</td><td>12</td></tr><tr><td>Specific Heat (kJ·kg<sup>-1</sup>·K<sup>-1</sup>)</td><td>1.45</td></tr></tbody></table>

These values are summarized in Table 12.

The thermal properties of the PCMs incorporated into the simulation were defined as temperature-dependent functions, derived from experimental measurements. Fig. 18 illustrates the thermal properties of the PCMs during the phase change process. Sensitivity analysis revealed that variations in PCM thermal conductivity had minimal impact on the temperature profile of the product model. Consequently, rather than perform additional measurements for PCM-M3, we applied the Maxwell-Eucken model to predict its effective thermal conductivity [104,105]. To validate this choice, thermal conductivity was measured at 20 °C, yielding an average of 0.517 ± 0.076 W·m<sup>-1</sup>·K<sup>-1</sup>, while the Maxwell-Eucken model predicted a value of 0.527 W·m<sup>-1</sup>·K<sup>-1</sup>, demonstrating excellent agreement between experimental and theoretical values.

## 5. Numerical results

The experimental air temperature profile used in this study was obtained from a previous study by Sharqawy et al. [106]. The air temperature was experimentally measured within an empty walk-in freezer with a volume of 38 m³. The internal air temperature was maintained at –21 °C with a temperature differential of ±3 °C. Additionally, the freezer underwent periodic electric defrost cycles, each lasting 20 min. After each defrost cycle, it took approximately 74 min for the air temperature to return to the set-point range. A heat transfer coefficient (h<sub>air</sub>) of 15 W·m<sup>-2</sup>·K<sup>-1</sup> was used to simulate convective heat transfer within the freezer. This experimental temperature profile provides a practical assessment of the thermal performance of insulation/PCM layers in stabilizing food product temperatures.

In this study, the thermal resistance resulting from convection is significantly greater than the ice thermal resistance caused by conduction. This disparity leads to a relatively low Biot number (B<sub>ice</sub> = 0.12). As a result, the temperature at the center of the food product is found to be quite similar to the temperature at the surface. Therefore, our analysis primarily focuses on assessing the central region temperature only.

Fig. 19 illustrates the effect of incorporating protective layers on the thermal stability of the stored specimen, compared to both the baseline case without any insulation layer and the conventional case with a polystyrene insulation layer. Fig. 19(a) shows the temperature profiles during normal freezer operation, where the air temperature fluctuates with an amplitude of 3.51 K. In the baseline case without PCM, the product's core exhibits substantial temperature variations, with an observed fluctuation amplitude of 0.81 K. Adding a polystyrene insulation layer provides moderate temperature regulation, reducing the core temperature amplitude to 0.36 K. When PCM layers are introduced,

<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Graphical representation of the temperature-dependent thermophysical properties of PCMs –40 wt% Glycerol PCM and PCM-M3– used by the 1D model, illustrating how these properties vary across the phase transition temperature range.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Fig. 19.** Comparison of temperature profiles of the food model under different conditions. (a) Temperature variations during normal operation. (b) Temperature changes during the defrost cycle.</figcaption></figure>

further improvements in thermal stability are evident. Using a PCM with 40 % glycerol reduces the temperature amplitude to 0.21 K. The most effective thermal control is achieved with the PCM-M3 composition (14 % NaCl:18 % glycerol), maintaining the sample's temperature at -20 °C with a minimal variation of 0.065 K.

The impact of incorporating a PCM layer is particularly evident during the defrost period. As shown in Fig. 19(b), the air temperature increased significantly, reaching a maximum of -8 °C. During this phase, and for the reference case without PCM, the product's core temperature reached a maximum of -17 °C. By contrast, incorporating a polystyrene layer effectively mitigated this temperature rise, reducing the maximum temperature by 1.16 K lower than the reference (-18.13 °C). The PCM layer demonstrates remarkable heat absorption during defrosting, resulting in minimal temperature rise. For the 40 % PCM layer configuration, the core peak temperature was -18.7 °C, which is 1.72 K lower than the reference case. The most effective temperature stabilization occurred with the optimal PCM-M3, where the peak temperature at the product's core was 2.44 K lower than the no-PCM case, measuring -19.42 °C.

## 6. Conclusion

This study successfully developed a sustainable, bio-based phase change material suitable for sub-zero cold chain applications using a glycerol-water mixture with sodium chloride as an additive. The research demonstrated that glycerol concentration significantly influences the phase change temperature and latent heat capacity of the PCM. While increasing glycerol concentration lowered the PCT from -7 °C to -22 °C, it simultaneously reduced the latent heat capacity.

Through response surface methodology optimization, a promising PCM composition (PCM-M3) containing 14 wt% NaCl and 18 wt% glycerol was identified. This mixture achieved an ideal PCT appropriate for frozen food storage (-20 °C to -18 °C) and a large latent heat of 281.81 kJ·kg⁻¹, positioning it competitively with existing commercial alternatives. The PCM also showed excellent thermal stability, with only

a minimal decrease in latent heat capacity after 100 freezing/melting cycles.

Maintaining stable temperatures is essential for preserving the quality of perishable food products. Our numerical analysis demonstrates that PCMs provide an effective method for temperature stabilization. The integration of PCM-M3 resulted in a substantial reduction of the product's temperature amplitude, limiting fluctuations to ±0.065 K during freezer normal operation periods. Moreover, during defrost cycles, the product's core temperature was 2.44 K lower compared to the reference case without PCM. These findings indicate that the developed PCM represents a promising solution for maintaining consistent temperatures in cold chain applications, thus preserving the quality of perishable goods.

Future research should investigate the use of crude glycerol directly obtained from biodiesel production. This approach could significantly reduce the environmental footprint associated with the conventional purification process, which requires substantial amounts of acids like HCl, H₂SO₄, or H₃PO₄ for neutralization. The crude glycerol, which contains fatty acids and salt residues from the transesterification process, presents a dual opportunity: addressing an environmental challenge by minimizing chemical-intensive purification steps while also improving economic feasibility. Additionally, the existing salt content in crude glycerol may enhance PCM properties, as our research has demonstrated that salts can positively influence phase change characteristics.

Further research should also examine the corrosiveness of the crude glycerol to ensure its compatibility with different encapsulation materials and guarantee safe application. Overall, this work provides very useful knowledge for the development of efficient, cost-effective, and sustainable PCMs for cold chain applications.

Additionally, to gain a deeper understanding of the material's microstructure, advanced characterization techniques such as Transmission/Scanning Electron Microscopy (T/SEM), X-ray Diffraction (XRD), and spectroscopic analysis should be employed. These analyses will provide valuable insights into the micro and molecular morphology
features of the developed PCM.

### CRediT authorship contribution statement

**Zakaria Ouauja:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Conceptualization. **Michel Havet:** Writing – review & editing, Validation, Supervision, Investigation, Formal analysis, Conceptualization, Project administration, Methodology. **Olivier Rouaud:** Writing – review & editing, Validation, Supervision, Software, Investigation, Formal analysis, Conceptualization, Project administration, Methodology. **Cyril Toublanc:** Writing – review & editing, Validation, Supervision, Investigation, Formal analysis, Conceptualization, Project administration, Methodology. **Abdellah Ousegui:** Writing – review & editing, Validation, Supervision, Investigation, Formal analysis, Conceptualization, Methodology, Project administration.

### Declaration of competing interest

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

### Acknowledgements

This work represents a collaboration between the GEPEA Laboratory at Oniris, Nantes, France, and RIPA team at Université Moulay Ismaïl, Meknès, Morocco. The authors extend their sincere gratitude to the “Partenariat Hubert Curien (PHC) TOUBKAL 2022” for their financial support.

### Data availability

Data will be made available on request.

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