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<front>
<journal-meta>
<journal-id journal-id-type="pmc">FDMP</journal-id>
<journal-id journal-id-type="nlm-ta">FDMP</journal-id>
<journal-id journal-id-type="publisher-id">FDMP</journal-id>
<journal-title-group>
<journal-title>Fluid Dynamics &#x0026; Materials Processing</journal-title>
</journal-title-group>
<issn pub-type="epub">1555-2578</issn>
<issn pub-type="ppub">1555-256X</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">55890</article-id>
<article-id pub-id-type="doi">10.32604/fdmp.2024.055890</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Enhancing Thermal Performance of Building Envelopes Using Hemp Wool and Wood Wool with Phase Change Materials</article-title><alt-title alt-title-type="left-running-head">Enhancing Thermal Performance of Building Envelopes Using Hemp Wool and Wood Wool with Phase Change Materials</alt-title><alt-title alt-title-type="right-running-head">Enhancing Thermal Performance of Building Envelopes Using Hemp Wool and Wood Wool with Phase Change Materials</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Kouzzi</surname><given-names>Salma</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref><email>salma.kouzzi@etu.uae.ac.ma</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Redah</surname><given-names>Mouniba</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Morsli</surname><given-names>Souad</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Ganaoui</surname><given-names>Mohammed El</given-names></name>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Lahlaouti</surname><given-names>Mohammed Lhassane</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>Laboratory of Energy, Faculty of Sciences of Tetuan, University of Abdelmalek Essaadi</institution>, <addr-line>Tetuan, 93002</addr-line>, <country>Morocco</country></aff>
<aff id="aff-2"><label>2</label><institution>LEM3, ENIM, University of Lorraine</institution>, <addr-line>Metz, 57078</addr-line>, <country>France</country></aff>
<aff id="aff-3"><label>3</label><institution>LERMAB, IUT Henri Poincar&#x00E9; de Longwy, University of Lorraine</institution>, <addr-line>Longwy, 54400</addr-line>, <country>France</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Salma Kouzzi. Email: <email>salma.kouzzi@etu.uae.ac.ma</email></corresp></author-notes>
<pub-date date-type="collection" publication-format="electronic">
<year>2024</year>
</pub-date>
<pub-date date-type="pub" publication-format="electronic">
<day>23</day><month>12</month><year>2024</year>
</pub-date>
<volume>20</volume>
<issue>12</issue>
<fpage>2741</fpage>
<lpage>2755</lpage>
<history>
<date date-type="received"><day>09</day><month>7</month><year>2024</year></date>
<date date-type="accepted"><day>21</day><month>8</month><year>2024</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2024 The Authors.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Published by Tech Science Press.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_FDMP_55890.pdf"></self-uri>
<abstract>
<p>This study investigates the potential for enhancing the thermal performance of external walls insulation in warmer climates through the combination of phase change materials (PCMs) and bio-based materials, specifically hemp wool and wood wool. Experimental tests using the heat flow method (HFM), and numerical simulations with ANSYS Fluent software were conducted to assess the dynamic thermal distribution and fluid-mechanical aspects of phase change materials (PCMs) within composite walls. The results demonstrate a notable reduction in peak indoor temperatures, achieving a 58% reduction with hemp wool with a close 40% reduction with wood wool when combined with PCMs. Fluid-mechanical analysis indicates that PCMs act as efficient indoor temperature regulators by storing excess heat during hot periods and releasing it later during phase transitions. Furthermore, the homogeneous distribution of the liquid fraction and natural convection during phase change contribute significantly to the improvement in heat transfer rates, resulting in a 96% reduction compared to hemp wool and wood wool without PCMs.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Bio-based materials</kwd>
<kwd>phase change material (PCM)</kwd>
<kwd>heat flow method</kwd>
<kwd>thermal performance</kwd>
<kwd>external wall insulation</kwd>
<kwd>hemp wool</kwd>
<kwd>wood wool</kwd>
<kwd>ANSYS Fluent software</kwd>
<kwd>dynamic thermal distribution</kwd>
<kwd>fluid-mechanical analysis</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>The future of energy and sustainable construction is a growing area of interest and concern. According to the IEA&#x2019;s &#x201C;World Energy Outlook 2022&#x201D; report [<xref ref-type="bibr" rid="ref-1">1</xref>], enhancing the energy efficiency of buildings is crucial for achieving greenhouse gas emission reduction targets and combating climate change. The Global State of Buildings and Construction Report 2022 [<xref ref-type="bibr" rid="ref-2">2</xref>] indicates that the building sector contributes almost 40% of global energy consumption and about one-third of greenhouse gas emissions.</p>
<p>Various studies have focused on evaluating and improving the energy consumption of buildings by reducing heating and cooling needs. Hoseinzadeh et al. [<xref ref-type="bibr" rid="ref-3">3</xref>] underlined the importance of implementing specific strategies based on geographical and climatic conditions to achieve energy-saving improvements in buildings located in a mountainous, humid zone.</p>
<p>Researchers have evaluated insulation materials used in buildings to address energy losses through building envelopes. They highlight the importance of selecting appropriate insulation materials to enhance energy performance, taking into account their environmental aspects [<xref ref-type="bibr" rid="ref-4">4</xref>], and examining thermal inertia and insulation effectiveness in building structures [<xref ref-type="bibr" rid="ref-5">5</xref>].</p>
<p>The use of phase-change material (PCM) in exterior walls has been explored for their energy efficiency and CO<sub>2</sub> emissions reduction benefits [<xref ref-type="bibr" rid="ref-6">6</xref>], as well as their potential in enhancing thermal regulation in specific climatic conditions [<xref ref-type="bibr" rid="ref-7">7</xref>]. Research on PCMs demonstrates their ability to store and release substantial thermal energy, thereby attenuating temperature variations in buildings and reducing energy consumption [<xref ref-type="bibr" rid="ref-8">8</xref>]. El-Ganaoui et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] have provided innovative analytical solutions to heat transfer problems involving phase changes and interfaces, forming the basis for numerous advances. Recent advancements in PCM technology highlight their potential for storing thermal energy in buildings [<xref ref-type="bibr" rid="ref-10">10</xref>,<xref ref-type="bibr" rid="ref-11">11</xref>]. Hekimo&#x011F;lu et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] noted the integration of PCMs into building cooling systems, which reduces the thermal load on air-conditioning systems and minimizes energy consumption, while Zhan et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] focused on the integration of PCMs in buildings in hot climates.</p>
<p>Anter et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] demonstrated the efficiency of integrating PCMs into building walls for thermal energy savings, highlighting the importance of optimizing the design, choice, and quantity of PCMs to maximize thermal benefits. M&#x2019;hamdi et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] analyzed the energy, environmental, and economic impacts of different building envelopes incorporating PCMs in different climates, showing that PCMs can reduce energy consumption and carbon emissions while offering economic benefits [<xref ref-type="bibr" rid="ref-16">16</xref>,<xref ref-type="bibr" rid="ref-17">17</xref>].</p>
<p>The potential of bio-based materials to enhance the sustainability and energy efficiency of buildings has also been studied [<xref ref-type="bibr" rid="ref-18">18</xref>&#x2013;<xref ref-type="bibr" rid="ref-20">20</xref>]. These materials have demonstrated promising thermal and hygrothermal performances [<xref ref-type="bibr" rid="ref-21">21</xref>,<xref ref-type="bibr" rid="ref-22">22</xref>] and a low carbon footprint [<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]. Using bio-based materials with PCMs improves energy performance in buildings [<xref ref-type="bibr" rid="ref-25">25</xref>], but careful assessment of their hygrothermal behavior is essential to prevent building deterioration [<xref ref-type="bibr" rid="ref-26">26</xref>,<xref ref-type="bibr" rid="ref-27">27</xref>].</p>
<p>Researchers have explored the combined use of PCMs with other insulating materials to enhance energy efficiency, such as dynamic insulation boards [<xref ref-type="bibr" rid="ref-28">28</xref>] and recycled waste paper in building enclosures, demonstrating potential for improved thermal performance and sustainability [<xref ref-type="bibr" rid="ref-29">29</xref>].</p>
<p>Recent studies have tackled the importance of fluid dynamics in these systems. Numerical simulations by Wang et al. [<xref ref-type="bibr" rid="ref-30">30</xref>] explored the coupling between solid-liquid phase change and thermal flow, providing valuable insights into fluid behavior in these materials. These studies also underline the crucial role of convection in the behavior of PCMs, as demonstrated by Lappa [<xref ref-type="bibr" rid="ref-31">31</xref>], with significant impacts on boundary conditions, material properties, and the integration of nanoparticles. A multi-physics modeling approach that considers the interactions between heat, mass, and fluid movement is necessary to study natural convection phenomena and heat transfer in phase change materials.</p>
<p>Optimizing material configurations is vital for maximizing building energy efficiency [<xref ref-type="bibr" rid="ref-32">32</xref>]. The application of new technologies, numerical modeling, and advanced simulation methods like Computational Fluid Dynamics (CFD) have been used to analyze and optimize thermal performance and design in buildings [<xref ref-type="bibr" rid="ref-33">33</xref>].</p>
<p>Zhou et al. [<xref ref-type="bibr" rid="ref-34">34</xref>] used CFD modeling to validate the thermal performance of dynamic Trombe walls incorporating PCMs, providing a better understanding of heat flows and more efficient solutions.</p>
<p>Integration PCMs and bio-based materials with advanced modeling techniques has shown promise in improving building efficiency [<xref ref-type="bibr" rid="ref-35">35</xref>]. Khoukhi et al. [<xref ref-type="bibr" rid="ref-36">36</xref>] focused on the effect of varying the dynamic thermal conductivity of insulation materials on temperature variation across wall assemblies.</p>
<p>While PCMs may have varying thermal performance depending on environmental conditions, they may be less effective in extreme climates or environments with minimal temperature variations [<xref ref-type="bibr" rid="ref-37">37</xref>]. To achieve thermal performance equivalent to conventional insulating materials, bio-based materials may require a greater thickness of insulating panels [<xref ref-type="bibr" rid="ref-38">38</xref>].</p>
<p>The importance of thermal performance in building envelopes is well-recognized for its impact on energy efficiency and occupant comfort. Traditional insulation materials often fail to provide adequate thermal regulation, especially in warmer climates.</p>
<p>While numerous studies have explored the use of PCMs and bio-based materials individually for thermal regulation, there is a significant research gap exploring the synergistic effects of combining these materials to maximize their benefits.</p>
<p>This article addresses this gap by investigating the potential benefits of combining PCMs with biobased insulation materials, specifically Wood Wool (WW) and Hemp Wool (HW), in building envelopes to enhance thermal performance. By exploring the latent heat storage capabilities of PCMs and the natural insulating properties of bio-based materials, this research aims to develop sustainable and efficient insulation solutions.</p>
<p>This study&#x2019;s novelty lies in the experimental and numerical analysis of these composite materials, providing valuable insights into their thermal behavior and practical applications. The research subjects the wall to a sinusoidal outside temperature, simulating typical summer day weather in Morocco, through experimental analysis using the heat flow method and numerical simulations using ANSYS Fluent software. The study provides insights into the dynamic thermal distribution within the insulation wall, with thorough assessment of the thermal performance and fluid mechanical aspects associated with the transition phase change of the different scenarios to determine indoor temperature reduction and heat transfer decrease.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Materials and Methods</title>
<p>The Heat Flow Method (HFM) [<xref ref-type="bibr" rid="ref-39">39</xref>] experimental study investigates two different external wall insulation configurations using HW as the main material for its numerous advantages and thermal properties. The study also explores the impact of adding PCM on temperature variation to take advantage of its thermal storage capacity for regulating internal temperature.</p>
<p>HW, with its low thermal conductivity, helps limit heat transmission through walls, ultimately reducing the need for heating and cooling and lowering energy costs. PCM materials have the ability to store and release large amounts of heat energy by transitioning between solid and liquid phases. The study will analyze the thermal properties of HW and the effects of PCM integration, aiming to enhance insulation designs and optimize the thermal performance of buildings.</p>
<sec id="s2_1">
<label>2.1</label>
<title>Experiment Model</title>
<p>The experiments focused on the thermal distribution within the external insulation wall. The heat flow method was utilized by placing the sample between two isothermal aluminum heat exchange plates connected to thermostatically controlled water baths [<xref ref-type="bibr" rid="ref-40">40</xref>], as illustrated in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Experimental setup of HFM. 1: Insulation sample, 2: Isothermal heat exchange plate <inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, 3: Isothermal heat exchange plate <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>
</inline-formula>, 4: Thermostatically-controlled water baths, 5: PCM layer, 6: Data acquisition system DAS220/240, Seframviewer 3.6</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-1.tif"/>
</fig>
<p>The thermal response of the wall with and without the PCM layer was examined by collecting temperature measurements <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mtext>,</mml:mtext></mml:mstyle></mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>o</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> using type K thermocouples on the underside, placed between the layers of PCM and biobased insulation, as well as on the top face and underside of the sample.</p>
<p>The heat flux is monitored by HFS sensors with dimensions of 50 &#x00D7; 50 &#x00D7; 0.5 mm<sup>3</sup>; on the upside and underside of the sample.</p>
<p>In Case 1 of the experiment, the sample consisted of HW (30 &#x00D7; 30 &#x00D7; 7 <inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>
</inline-formula>). In Case 2, a layer of PCM (30 &#x00D7; 30 &#x00D7; 1 <inline-formula id="ieqn-5">
<mml:math id="mml-ieqn-5"><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>
</inline-formula>) was added on top of the HW sample, resulting in a total dimension of (30 &#x00D7; 30 &#x00D7; 8 <inline-formula id="ieqn-6">
<mml:math id="mml-ieqn-6"><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>
</inline-formula>).</p>
<p>The upper part of the specimen underwent temperature variations ranging from 20&#x00B0;C to 40&#x00B0;C over time, following a sinusoidal pattern described in <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>, while the temperature of the lower part remained constant at 22&#x00B0;C throughout the experiment. Data was collected at 60 s intervals over a 24 h period.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Computational Model</title>
<p>The distribution of temperature in a wall due to heat transfer by conduction in a transient regime is determined by the heat equation, also known as the thermal diffusion equation. This equation illustrates how temperature changes over time and space based on the thermal properties of the material. The simplified form of the basic linear heat <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, according to Fourier&#x2019;s law, is typically written as:</p>
<p><disp-formula id="eqn-1"><label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mi>T</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mtext>&#xA0;</mml:mtext><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>a</mml:mi></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-2"><label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:mrow><mml:mi mathvariant="normal">W</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mi mathvariant="normal">h</mml:mi></mml:mrow><mml:mspace width="1em" /><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x03C1;</mml:mi><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</disp-formula>where the <inline-formula id="ieqn-7">
<mml:math id="mml-ieqn-7"><mml:mi>a</mml:mi></mml:math>
</inline-formula> is the thermal diffusivity of the material (m<sup>2</sup>/s). T (<italic>x, t</italic>) is the measured temperature (K); &#x03BB; is the thermal conductivity (W/m.K), &#x03C1; is the density of the considered material (kg/m<sup>3</sup>), and <inline-formula id="ieqn-8">
<mml:math id="mml-ieqn-8"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula> is the specific heat capacity (J/kg.K).</p>
<p>In the case of phase change material (PCM), such as melting/solidification phenomena, additional considerations and equations may be required:</p>
<p>The heat equation with convection become:<disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mi>T</mml:mi></mml:mstyle></mml:math>
</disp-formula>where <italic>u</italic> is the velocity vector of the fluid. If the dynamic field is concerned, additional melting/solidification model can be added, using well known models as Darcy law and other approximations to take into account the fluid flowing only in the liquid zone.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Numerical Methodology</title>
<p>The simulation was conducted using ANSYS Fluent student version 2023 R2 software [<xref ref-type="bibr" rid="ref-44">44</xref>], allowing to analyze the temperature, velocity, liquid fraction and heat flux within PCM &#x002B; (HW and WW) during phase change processes.</p>
<p>To model the temperature distribution using the heat <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, numerical methods, and assumptions about the wall material subjected to transient unidirectional heat transfer were taken into account [<xref ref-type="bibr" rid="ref-45">45</xref>,<xref ref-type="bibr" rid="ref-46">46</xref>].</p>
<p>The simulation of fluid flow and heat transfer in PCMs involves solving the Navier-Stokes equations <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref> for fluid motion, coupled with the energy equation for heat transfer. Here, we consider the Boussinesq approximation for natural convection, which assumes that density variations are significant only in the buoyancy term.</p>
<p>The continuity, momentum, and energy equations for an incompressible fluid with phase change are as follows:</p>
<p>Continuity Equation:<disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mo>.</mml:mo><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>
</disp-formula></p>
<p>Momentum Equation (Navier-stokes):<disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>u</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>&#x03C1;</mml:mi></mml:mfrac></mml:mrow><mml:mo>.</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>P</mml:mi><mml:mo>+</mml:mo><mml:mi>v</mml:mi><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:mi>g</mml:mi></mml:mstyle></mml:mstyle></mml:math>
</disp-formula>where <italic>P</italic> is the pressure, <inline-formula id="ieqn-9">
<mml:math id="mml-ieqn-9"><mml:mi>v</mml:mi></mml:math>
</inline-formula> is the kinematic viscosity and <italic>g</italic> is the gravity.</p>
<p>To model the phase change, the enthalpy-porosity technique is often used. In this method, the liquid fraction <italic>f<sub>s</sub></italic> is determined based on the temperature field:</p>
<p>Energy Equation with phase change:<disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mi>u</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:msup><mml:mi mathvariant="normal">&#x2207;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mi>L</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula><disp-formula id="eqn-7"><label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em" columnalign="left"><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>;</mml:mo><mml:mspace width="1em" /><mml:mi>T</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:mo>;</mml:mo></mml:mrow></mml:mrow><mml:mspace width="1em" /><mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mi>T</mml:mi><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>1</mml:mn><mml:mo>;</mml:mo><mml:mtable rowspacing="4pt" columnspacing="1em"><mml:mtr><mml:mtd><mml:mrow><mml:mrow></mml:mrow></mml:mrow><mml:mspace width="1em" /><mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mi>T</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable><mml:mo fence="true" stretchy="true" symmetric="true"></mml:mo></mml:mrow></mml:math>
</disp-formula>where <italic>T</italic><sub><italic>s</italic></sub> and <italic>T</italic><sub><italic>l</italic></sub> are the solidus and liquidus temperatures, respectively.</p>
<p>Heat transfer analysis of the wall envelope was simulated by the user-defined function (UDF) representing outdoor temperature variation on a typical summer day, modeled as a sinusoidal temperature oscillation. <inline-formula id="ieqn-10">
<mml:math id="mml-ieqn-10"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula> <xref ref-type="disp-formula" rid="eqn-8">Eq. (8)</xref>, ranging from 20&#x00B0;C to 40&#x00B0;C. Using the same thermal properties as the thermal insulation materials detailed in <xref ref-type="table" rid="table-1">Table 1</xref>.</p>
<p><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mn>303</mml:mn><mml:mo>+</mml:mo><mml:mn>10</mml:mn><mml:mo>&#x2217;</mml:mo><mml:mi>sin</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C9;</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
</disp-formula></p>
<table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Thermophysical material characteristics</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th>PCM [<xref ref-type="bibr" rid="ref-41">41</xref>]</th>
<th>Wood-Wool [<xref ref-type="bibr" rid="ref-42">42</xref>]</th>
<th>Hemp-Wool [<xref ref-type="bibr" rid="ref-43">43</xref>]</th>
</tr>
</thead>
<tbody>
<tr>
<td>Density (kg/m<sup>3</sup>)</td>
<td>810</td>
<td>50</td>
<td>40</td>
</tr>
<tr>
<td>Thermal conductivity for solid phase <inline-formula id="ieqn-11">
<mml:math id="mml-ieqn-11"><mml:mrow><mml:mi mathvariant="normal">W</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>.</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</inline-formula></td>
<td>0.18</td>
<td>0.046</td>
<td>0.04</td>
</tr>
<tr>
<td>Thermal conductivity for liquid phase (<inline-formula id="ieqn-12">
<mml:math id="mml-ieqn-12"><mml:mrow><mml:mi mathvariant="normal">W</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>.</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</inline-formula></td>
<td>0.14</td>
<td>&#x2013;</td>
<td>&#x2013;</td>
</tr>
<tr>
<td>Specific heat capacity for solid phase (kJ/kg.K)</td>
<td>4</td>
<td>2.1</td>
<td>1.8</td>
</tr>
<tr>
<td>Specific heat capacity for liquid phase (kJ/kg.K)</td>
<td>3.8</td>
<td>&#x2013;</td>
<td>&#x2013;</td>
</tr>
<tr>
<td>Latent heat (kJ/kg)</td>
<td>136.2</td>
<td rowspan="2">&#x2013;</td>
<td rowspan="2">&#x2013;</td>
</tr>
<tr>
<td>Melting point (&#x00B0;C)</td>
<td>28</td>
</tr>
<tr>
<td>Freezing point (&#x00B0;C)</td>
<td>10</td>
<td>&#x2013;</td>
<td>&#x2013;</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Here <italic>t</italic> is the time, and <inline-formula id="ieqn-13">
<mml:math id="mml-ieqn-13"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C9;</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>&#x03C4;</mml:mi></mml:mrow></mml:math>
</inline-formula>, where <inline-formula id="ieqn-14">
<mml:math id="mml-ieqn-14"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C4;</mml:mi></mml:mrow></mml:mrow></mml:math>
</inline-formula> is the 24 h period.</p>
<p>The temperature evolution <italic>T</italic> (<italic>x, t</italic>) in the model was studied under certain assumptions [<xref ref-type="bibr" rid="ref-47">47</xref>]. These assumptions include considering laminar flow, neglecting radiation effects due to slow temperature changes, assuming adiabatic horizontal walls, and considering walls to be homogeneous and isotropic. In addition, the model assumes that the thermal properties of the material are constant in space and time and that there are no internal heat sources. These assumptions provide a simplified framework for understanding the temperature distribution within the system.</p>
<p>Boundary conditions for this case require a specific value to be specified, with both the external wall and inner wall having a Dirichlet condition as the type of boundary condition imposed.</p>
<p><bold><italic>Boundary conditions</italic></bold></p>
<p>The bottom and top of the insulation wall are adiabatic:<disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mstyle></mml:math>
</disp-formula></p>
<p>The temperature at x &#x003D; 0 is <inline-formula id="ieqn-15">
<mml:math id="mml-ieqn-15"><mml:mtext>&#x00A0;</mml:mtext><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mrow><mml:mstyle displaystyle="false" scriptlevel="0"><mml:mtext>,</mml:mtext></mml:mstyle></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula>, and the temperature at x &#x003D; e is set to 295.96 K.</p>
<p>The finite element method (FME) is used to solve these equations with ANSYS Fluent by discretizing the heat equations and solving them numerically on a mesh of the wall to determine the temperature distribution.</p>
<p>Geometric modeling was performed using the Design Modeler tool in ANSYS software. The study considered four different wall scenarios, as shown in <xref ref-type="fig" rid="fig-2">Fig. 2</xref>. A quadratic mesh was then generated, comprising 40,000 elements for PCM/HW and PCM/WW, and 35,000 elements for HW or WW.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>The schematic heat transfer of the insulation wall: (a) PCM &#x002B; HW, (b) PCM &#x002B; WW</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-2.tif"/>
</fig>
<p>Simulations were solved using a pressure-based and transient solver configured with implicit pressure and coupled operator splitting, along with a second-order upwind scheme.</p>
<p>Running the simulation allowed for calculating the temperature distribution across the walls and plotting the temperature evolution inside the wall over a 24 h period to analyze heat transfer through the wall.</p>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and Discussion</title>
<sec id="s4_1">
<label>4.1</label>
<title>Model Validation</title>
<p>In the present study, simulation results were compared with experimental data for validation purposes, using two plates with imposed temperatures, one simulating outdoor conditions and the other indoor conditions. The test involved an envelope containing a 7-cm-thick layer of HW (Case 1). Subsequently, a multi-layer envelope was examined, consisting of a 1 cm layer of PCM added to the HW (Case 2). The dimensions of these configurations were 30 &#x00D7; 30 &#x00D7; 7 cm<sup>3</sup> and 30 &#x00D7; 30 &#x00D7; 8 cm<sup>3</sup>, respectively.</p>
<p><xref ref-type="fig" rid="fig-3">Fig. 3</xref> depicts the measured temperature <italic>vs</italic>. time for HW and PCM_HW on the top (x &#x003D; 0) and bottom (x &#x003D; e) surfaces of the sample in comparison with simulation results, where x &#x003D; 0 represents outdoor conditions and x &#x003D; e represents indoor temperature. To validate the simulated results, the average error (AE) was calculated using <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>:</p>
<p><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">v</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mtext>&#xA0;</mml:mtext><mml:mrow><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x0025;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#xA0;</mml:mtext><mml:mn>2...</mml:mn><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>exp</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>exp</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mn>100</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula></p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Comparison between the simulated and experimental temperature results for (a) HW and (b) HW with PCM</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-3.tif"/>
</fig>
<p>The average error of the numerical model is 0.14% in the first case and 0.06% in the second case. The small discrepancies between the experimental and numerical results may be attributed to the infiltration of free air into the HW layers. These low relative errors demonstrate the accuracy of the numerical model compared to the experiment, affirming its validity and reliability for further studies.</p>
<p>A 24 h test was conducted on a typical summer day using a reference insulating wall made of WW (Case 3). Subsequently, a similar test was performed by adding a layer of PCM (Case 4). Both tests were carried out utilizing ANSYS Fluent and adhering to the same numerical methodology outlined previously.</p>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> compares the experimental and simulated heat fluxes for PCM &#x002B; HW over 24 h period. Both data sets show similar profiles, with an initial peak (initial phase change), followed by a significant decrease with negative flux (liquid to solid), and then a rise towards the end (heat absorption). Some differences amplitude and timing are observed between the experimental and simulated results. These discrepancies could be attributed to various factors, such as simplifications in the simulation model, experimental measurement errors, or inherent material property variations.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Comparison of experimental and simulated heat flux in PCM &#x002B; HW composite over time</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-4.tif"/>
</fig>
</sec>
<sec id="s4_2">
<label>4.2</label>
<title>Thermal Performance</title>
<p>Thermal performance was evaluated in this study by comparing the interior thermal characteristics, such as thermal amplitude, time lag, and decrement factor [<xref ref-type="bibr" rid="ref-48">48</xref>], for walls made of eco-materials (HW and WW) with and without a PCM layer. The graphs presented in <xref ref-type="fig" rid="fig-5">Fig. 5</xref>. illustrate the impact of incorporating PCM into HW (a) and WW (b) walls insulation on the surface temperature. The results show that the addition of PCM layers help in reducing internal temperature variations and providing a more stable indoor surface temperature profile compared to HW and WW alone.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>The impact of incorporating PCM into the HW (a) and WW (b) insulating wall on surface temperature</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-5.tif"/>
</fig>
<p>The thermal amplitude of PCM_HW is 2.79 in comparison to HW 6.7, with a 58.36% reduction, and 2.56 for PCM_WW in comparison to WW 4.25, with a 39.62% reduction.</p>
<p>The lag time for PCM_HW and PCM_WW is 1 h relative to the external environment, indicating that the addition of PCM helps to minimize overheating hours. The decrement factor for PCM_HW and PCM_WW was calculated to be 0.14 and 0.13, respectively, using the formula provided by Jin et al. [<xref ref-type="bibr" rid="ref-49">49</xref>]. The determination of the decrement factor is largely dependent on thermophysical properties and wall thickness [<xref ref-type="bibr" rid="ref-50">50</xref>]. A lower decrement factor indicates a higher level of indoor thermal comfort.</p>
<p><xref ref-type="fig" rid="fig-6">Fig. 6</xref> illustrates the distribution of surface temperatures for different types of walls insulation: HW, WW, PCM &#x002B; WW, and PCM &#x002B; HW.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Temperature distribution within the wall insulation; Case 1: HW, Case 2: PCM_HW, Case 3: WW and Case 4: PCM_WW</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-6.tif"/>
</fig>
<p>Walls with PCM layers (Cases 2 and 4) have a more uniform temperature distribution and lower temperatures, especially on the indoor side, as indicated by the blue areas in the contours. This highlights the effectiveness of adding PCM layers in enhancing the thermal regulation of wall insulations.</p>
</sec>
<sec id="s4_3">
<label>4.3</label>
<title>Fluid-Mechanical Aspect in Phase Change Materials</title>
<p>In this section, the fluid-mechanical properties of phase change material (PCM) used in conjunction with HW and WW are analyzed. Specifically, the velocity, liquid fraction, and heat flux within the PCM composites. These aspects are considered crucial for evaluating the thermal insulation performance and efficiency of PCM-based materials in various applications.</p>
<sec id="s4_3_1">
<label>4.3.1</label>
<title>Liquid Fraction Evolution</title>
<p>The liquid fraction allows visualizing the evolution of the liquid fraction in the phase change material (PCM), as shown in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>. The curves indicate similar melting and solidification cycles for PCM, with a slight phase advance for PCM &#x002B; HW compared to PCM &#x002B; WW. The right visualization illustrates the contour of the liquid fraction distribution at t &#x003D; 22 h for both composite walls, where it&#x2019;s clearly shown the presence of wavy colors in the distribution suggesting natural convection effects within the PCM.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>(a) Liquid fraction distribution in PCM for PCM &#x002B; HW and PCM &#x002B; WW Composites (b) Liquid fraction distribution in the PCM part of the composite at t &#x003D; 22 h</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-7.tif"/>
</fig>
<p>The faster progression towards a complete liquid state for PCM &#x002B; HW can be attributed to the distinct thermal properties of HW and WW. Hemp wool&#x2019;s lower thermal conductivity (0.04 W/m.K) compared to Wood wool (0.046 W/m.K) results in less heat being conducted away from the PCM layer, allowing for more rapid melting. During the liquid phase, natural convection within the PCM helps in distributing the absorbed heat more uniformly across the wall. This phenomenon prevents localized overheating and contributes to a more uniform temperature across the external wall insulation.</p>
<p>Thus the incorporation of PCM in building materials, as observed in the studies by Mahdaoui et al. [<xref ref-type="bibr" rid="ref-51">51</xref>] and Hamdaoui et al. [<xref ref-type="bibr" rid="ref-52">52</xref>], significantly improves thermal performance by promoting balanced heat distribution and a more controlled phase transition.</p>
</sec>
<sec id="s4_3_2">
<label>4.3.2</label>
<title>Velocity</title>
<p>Analyzing the velocity field helps study the natural convection effects within the molten PCM.</p>
<p>The graph in <xref ref-type="fig" rid="fig-8">Fig. 8</xref> shows the velocity distribution in PCM for both PCM &#x002B; HW and PCM &#x002B; WW composites over a 24 h period. The velocity curves for both composites are similar, with PCM &#x002B; HW showing slightly higher velocities between 2 and 12 h.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>Velocity distribution in PCM for PCM &#x002B; HW and PCM &#x002B; WW composites</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-8.tif"/>
</fig>
<p>Since the profile contour of velocity for both composites are similar, the velocity magnitude visualization at 14 h (right side of the figure) shows higher velocities near the edges of the PCM layer, suggesting the presence of convection currents within the melted PCM. This natural convection plays a crucial role in heat distribution within the composites.</p>
<p>Due to the temperature gradients causing density differences in the molten PCM, higher velocities were noticed near the edges indicating the formation of boundary layers, where buoyancy-driven flow is strongest. This behavior aligns with studies on PCM in similar configurations. Soliman et al. [<xref ref-type="bibr" rid="ref-53">53</xref>] Observed comparable convection effects in their simulations of PCM confined in cylindrical enclosures under constant heat flux. However, adding bio-based materials (HW and WW) could improve heat storage and release by slightly enhancing convective movements without creating major imbalances. As described by Cheng et al. [<xref ref-type="bibr" rid="ref-54">54</xref>], enhancing the thermal conductivity of stabilized PCM can optimize underfloor heating systems, which could be similar to the effect observed with HW and WW.</p>
</sec>
<sec id="s4_3_3">
<label>4.3.3</label>
<title>Heat Flux</title>
<p>Heat flux is a key parameter for evaluating the thermal performance of insulation materials.</p>
<p><xref ref-type="fig" rid="fig-9">Fig. 9</xref> demonstrates the impact of integrating PCM on heat flux. The curves for the two composites with PCM &#x002B; HW and PCM &#x002B; WW are quite similar, suggesting that the PCM dominates the thermal behavior of the composite. The PCM composites show a period of significant heat absorption (negative flux), followed by a period of heat release (positive flux). This can be attributed to the high latent heat of the PCM allowing to absorb a significant amount of thermal energy during phase change and release it later. Achieving an average reduction of the heat transfer rate of 95.82% compared to WW without PCM and a decrease of 95,65% compared to HW without PCM. The results demonstrate the enhanced thermal management capabilities of PCM incorporated to biobased insulation materials. The studies by Bouzennada et al. [<xref ref-type="bibr" rid="ref-55">55</xref>] and Babaharra et al. [<xref ref-type="bibr" rid="ref-56">56</xref>] highlighted the importance of managing heat flux in PCM applications, claiming that well-controlled heat flux improves the thermal storage capacity; the results of this study support these conclusions.</p>
<fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>Comparison of heat flux in HW and WW insulation materials with and without PCM</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="FDMP_55890-fig-9.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>This study asserts the significant potential of the combination PCM and biobased insulation materials to enhance the thermal performance of building envelopes.</p>
<p>The combination of phase change material (PCM) with biobased insulation materials resulted in significant reductions in temperature oscillations within walls. PCM_HW exhibited a temperature decreases of 3.8 K, while PCM_WW showed a reduction of 1.45 K compared to their respective reference wall insulation without PCM.</p>
<p>PCM composites demonstrated superior thermal management capabilities. The addition of PCM to both Hemp Wool and Wood Wool significantly improved their effectiveness as thermal insulation materials, providing more stable indoor temperatures. This enhancement in thermal stability contributes to improved occupant comfort and reduced energy needs for heating and cooling.</p>
<p>Regarding heat flux, the addition of PCMs resulted in a significant reduction in heat transfer rates. An average decrease of 96% for PCM &#x002B; (HW, WW) compared to HW and WW without PCM.</p>
<p>The homogeneous distribution of the liquid fraction within the PCM layer and moderate velocities indicate efficient thermal energy storage and release process, which is crucial for maintaining consistent thermal performance in sustainable building applications and contribute to the effectiveness of the composite insulation system.</p>
<p>Future research will explore the hygrothermal performances of these materials, examining how PCM integration affects moisture management and thermal behavior over extended periods. Moreover, exploring the wider impact of PCM usage on sustainable construction and environmental management will provide valuable insights into their role in ecofriendly building solutions.</p>
</sec>
</body>
<back>

<glossary content-type="abbreviations" id="glossary-1">
<title>Nomenclature</title>
<def-list>
<def-item>
<term><inline-formula id="ieqn-16">
<mml:math id="mml-ieqn-16"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03C1;</mml:mi></mml:mrow></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Density <inline-formula id="ieqn-17">
<mml:math id="mml-ieqn-17"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">k</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-18">
<mml:math id="mml-ieqn-18"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Thermal conductivity (<inline-formula id="ieqn-19">
<mml:math id="mml-ieqn-19"><mml:mrow><mml:mi mathvariant="normal">W</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mo>.</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</inline-formula>)</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-20">
<mml:math id="mml-ieqn-20"><mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Temperature (K)</p>
</def>
</def-item>
<def-item>
<term>T<sub>s</sub></term>
<def>
<p>Solidus temperature (K)</p>
</def>
</def-item>
<def-item>
<term>T<sub>l</sub></term>
<def>
<p>Liquidus temperature (K)</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-21">
<mml:math id="mml-ieqn-21"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">o</mml:mi><mml:mi mathvariant="normal">u</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Outside temperature <inline-formula id="ieqn-22">
<mml:math id="mml-ieqn-22"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">K</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-23">
<mml:math id="mml-ieqn-23"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Inside temperature <inline-formula id="ieqn-24">
<mml:math id="mml-ieqn-24"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">K</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></p>
</def>
</def-item>
<def-item>
<term>t</term>
<def>
<p>Time (s)</p>
</def>
</def-item>
<def-item>
<term>Cp</term>
<def>
<p>Specific heat capacity (J/(kg.K))</p>
</def>
</def-item>
<def-item>
<term>L</term>
<def>
<p>Latent heat (kJ/kg)</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-25">
<mml:math id="mml-ieqn-25"><mml:mi>e</mml:mi></mml:math>
</inline-formula></term>
<def>
<p>Thickness <inline-formula id="ieqn-26">
<mml:math id="mml-ieqn-26"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</inline-formula></p>
</def>
</def-item>
<def-item>
<term>HW</term>
<def>
<p>Hemp Wool</p>
</def>
</def-item>
<def-item>
<term>WW</term>
<def>
<p>Wood Wool</p>
</def>
</def-item>
<def-item>
<term>PCM</term>
<def>
<p>Phase Change Materials</p>
</def>
</def-item>
<def-item>
<term>HFM</term>
<def>
<p>Heat Flow Method</p>
</def>
</def-item>
</def-list>
</glossary>
<ack>
<p>We would like to thank PHC Maghreb for its financial support to the first author and LERMAB Laboratory for agreeing to host.</p>
</ack>
<sec>
<title>Funding Statement</title>
<p>The authors received no specific funding for this study.</p>
</sec>
<sec>
<title>Author Contributions</title>
<p>The authors confirm contribution to the paper as follows: conception and design: Salma Kouzzi; data collection: Salma Kouzzi; simulation: Salma Kouzzi, Mouniba Redah; analysis and interpretation of results: Salma Kouzzi, Souad Morsli; draft manuscript preparation: Salma Kouzzi, Mouniba Redah; writing: Salma Kouzzi, Souad Morsli, Mouniba Redah; review and editing: Salma Kouzzi, Mohammed El Ganaoui, Souad Morsli; supervision and administration: Mohammed El Ganaoui, Mohammed Lhassane Lahlaouti. All authors reviewed the results and approved the final version of the manuscript.</p>
</sec>
<sec sec-type="data-availability">
<title>Availability of Data and Materials</title>
<p>The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.</p>
</sec>
<sec>
<title>Ethics Approval</title>
<p>Not applicable.</p>
</sec>
<sec sec-type="COI-statement">
<title>Conflicts of Interest</title>
<p>The authors declare no conflicts of interest to report regarding the present study.</p>
</sec>
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