<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.1 20151215//EN" "http://jats.nlm.nih.gov/publishing/1.1/JATS-journalpublishing1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en" article-type="research-article" dtd-version="1.1">
<front>
<journal-meta>
<journal-id journal-id-type="pmc">JRM</journal-id>
<journal-id journal-id-type="nlm-ta">JRM</journal-id>
<journal-id journal-id-type="publisher-id">JRM</journal-id>
<journal-title-group>
<journal-title>Journal of Renewable Materials</journal-title>
</journal-title-group>
<issn pub-type="epub">2164-6341</issn>
<issn pub-type="ppub">2164-6325</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">49392</article-id>
<article-id pub-id-type="doi">10.32604/jrm.2024.049392</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Study of Hygrothermal Behavior of Bio-Sourced Material Treated Ecologically for Improving Thermal Performance of Buildings</article-title><alt-title alt-title-type="left-running-head">Study of Hygrothermal Behavior of Bio-Sourced Material Treated Ecologically for Improving Thermal Performance of Buildings</alt-title><alt-title alt-title-type="right-running-head">Study of Hygrothermal Behavior of Bio-Sourced Material Treated Ecologically for Improving Thermal Performance of Buildings</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Mounir</surname><given-names>Soumia</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref><email>s.mounir@enaagadir.ac.ma</email>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Slaoui</surname><given-names>Miloudia</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western"><surname>Maaloufa</surname><given-names>Youssef</given-names></name>
<xref ref-type="aff" rid="aff-1">1</xref>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Wardi</surname><given-names>Fatima Zohra El</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Dodo</surname><given-names>Yakubu Aminu</given-names></name>
<xref ref-type="aff" rid="aff-4">4</xref>
<xref ref-type="aff" rid="aff-5">5</xref>
</contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Ibn-Elhaj</surname><given-names>Sara</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-7" contrib-type="author">
<name name-style="western"><surname>Khabbazi</surname><given-names>Abdelhamid</given-names></name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<aff id="aff-1"><label>1</label><institution>National School of Architecture Agadir, New Complex Ibn Zohr Agadir, Hay dakhla, 80000</institution>, <country>Morocco</country></aff>
<aff id="aff-2"><label>2</label><institution>EMDD, CERNE2D, University Mohammed V in Rabat, Est Sal&#x00E9;, Sal&#x00E9; Medina</institution>, <country>Morocco</country></aff>
<aff id="aff-3"><label>3</label><institution>Physics Department, LPMAT Laboratory, Faculty of Sciences Ain Chock, Hassan II University</institution>, <addr-line>Casablanca</addr-line>, <country>Morocco</country></aff>
<aff id="aff-4"><label>4</label><institution>Architectural Engineering Department College of Engineering, Najran University</institution>, <addr-line>Najran, 66426</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5"><label>5</label><institution>The Centre of Scientific and Engineering Research, Najran University</institution>, <addr-line>Najran</addr-line>, <country>Saudi Arabia</country></aff>
</contrib-group><author-notes><corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Soumia Mounir. Email: <email>s.mounir@enaagadir.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>17</day><month>7</month><year>2024</year></pub-date>
<volume>12</volume>
<issue>5</issue>
<fpage>1007</fpage>
<lpage>1027</lpage>
<history>
<date date-type="received"><day>05</day><month>1</month><year>2024</year></date>
<date date-type="accepted"><day>11</day><month>3</month><year>2024</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2024 Mounir et al.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Mounir et al.</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_JRM_49392.pdf"></self-uri>
<abstract>
<p>Creating sustainable cities is the only way to live in a clean environment, and this problem can be solved by using bio-sourced and recycled materials. For this purpose, the authors contribute to the valuation of sheep wool waste as an eco-friendly material to be used in insulation. The paper investigates the thermal, hygrothermal, and biological aspects of sheep wool by testing a traditional treatment. The biological method of aerobic mesophilic flora has been applied. Fluorescence X was used to determine the chemical composition of the materials used. Also, thermal characterization has been conducted. The thermal conductivity is above 0.046 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>) and the thermal diffusivity is 1.56.10<sup>&#x2212;6</sup> m<sup>2</sup>&#x00B7;s<sup>&#x2212;1</sup>. Besides, the energy efficiency of using sheep wool in buildings was studied. Furthermore, its humidity behavior was evaluated in different aspects in both winter and summer. Results of biological analyses show the efficiency of the treatment by removing the majority of the microorganisms: the value of yeast and mildew was reduced from 38.10<sup>2</sup> to 2.10<sup>2</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>). In addition to that, sheep wool permits obtaining a low thermal transmittance on the scale of the walls and low cooling needs on the scale of the building with a gain of 45% and 52%, respectively.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Sustainability</kwd>
<kwd>sheep wool</kwd>
<kwd>biological treatment</kwd>
<kwd>hygrothermal wool behavior</kwd>
<kwd>hot wire method</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Creating sustainable cities and sustainable rural areas has become a necessity in the global context of the increase in greenhouse gas emissions and the temperature of the earth; however, buildings are a huge sector of energy consuming, which is why the use of insulation is the most effective way to reduce pollution, carbon emissions, and energy consumption by acting on the building envelope. Sheep wool is a bio-sourced material with a low carbon footprint, which allows the construction of sustainable buildings and then assures sustainable cities. The use of this material for insulation, using the traditional treatment proposed in this study, will make sheep wool affordable for both rural and urban inhabitants, and industrial insulating material will also benefit from this study by using this treatment that does not pollute the environment. The authors valued the use of sheep wool as an insulating building material using a traditional treatment, which will be useful for citizens and industry, and it will also be a manner of waste management, especially in Arabian countries where this material is thrown everywhere in the feast of <italic>Aid Al Adha</italic>. The paper gives a clear idea about the thermal properties of sheep wool in terms of thermal conductivity and thermal diffusivity; however, the hygrothermal behavior is clearly shown in this study. The novelty of this paper is the use of traditional treatments for sheep wool to remove microorganisms in a simple way that can be used by industrialists and inhabitants of rural areas. Also, the paper gives a clear idea about the thermal and hygrothermal behavior of sheep wool and its energy efficiency when it is used in buildings. In this paper, the authors tried to investigate the effect of a traditional treatment to remove microorganisms from sheep wool by analyzing the physico-chemical elements of sheep wool and the materials used for this natural treatment. For this purpose, the fluorescence X method has been conducted, and a biological study has been done using the total aerobic mesophilic flora to see the effect of this treatment on removing microorganisms. Moreover, a thermal characterization using the hot wire and flash methods was done to determine the thermal properties of sheep wool. Furthermore, an investigation of the hygrothermal behavior of this material was studied in the winter and summer seasons, and finally, a study of the thermal transmittance using this insulating material and an analysis of its energy efficiency by determining the cooling need with and without insulation by sheep wool were conducted over a year using the tools TRNSYS.</p>
<p>In this context, several studies have been done concerning insulating materials. As the work of Jelle [<xref ref-type="bibr" rid="ref-1">1</xref>] studied the state of the art of both traditional and possible development of other materials, it treats wool as an insulating material that presents good thermal properties; however, the work did not determine the thermal properties of sheep wool. That is why the contribution of our work consists of conducting thermal characterization of sheep wool by determining thermal conductivity and thermal diffusivity. Pennachio et al. [<xref ref-type="bibr" rid="ref-2">2</xref>] studied the characteristics of new ecological panels of sheep wool and hemp. Thermal conductivity was measured, and results show that this thermal property is influenced by temperature and humidity, which vary from 0.039 to 0.044 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>). Thermal transmittance was evaluated using the heat flowmeter, and the value obtained shows good results compared to fiberglass and mineral wool. The acoustic study also evaluated the weighted sound absorption, and panels with sheep wool present a low coefficient of 0.55. This study proves the efficiency of sheep wool in the building sector. Based on this study, the authors contribute to this work by studying the thermal and hygrothermal behavior of sheep&#x2019;s wool in both the winter and summer seasons. Corscadden et al. [<xref ref-type="bibr" rid="ref-3">3</xref>] infer that sheep wool must be promoted to be integrated into the building because it is a bioproduct, a natural and renewable resource in the construction industry, and it was used in a pilot project. This study proves that our research solves this problem by promoting industrial use of this material based on the proposed traditional treatment. Patnaik et al. [<xref ref-type="bibr" rid="ref-4">4</xref>] considered a specimen of 100% wool, and they say that wool is a natural fiber obtained from shearing the short one of sheep considered a waste. Sheep wool has many outstanding properties, including excellent insulation and low flammability.</p>
<sec id="s1_1">
<label>1.1</label>
<title>Background and Literature</title>
<p>The work of Zach et al. [<xref ref-type="bibr" rid="ref-5">5</xref>] explains the necessity for the authors to study sheep wool as a bio-sourced material with good thermal properties in order to improve comfort in buildings and reduce carbon emissions. The work of Zach et al. [<xref ref-type="bibr" rid="ref-5">5</xref>] responded to the demand for increasing ecological materials by supporting research and publications on alternative materials in which they specify the thermal and acoustic properties of sheep wool and conclude that sheep wool has comparable characteristics with conventional materials. This work contributes to the same logic for authors to contribute to the valuation of alternative materials in construction, such as sheep wool, for the purpose of reducing pollution and improving the ambiance of buildings.</p>
<p>In addition, Tiza et al. [<xref ref-type="bibr" rid="ref-6">6</xref>] assessed the role of bamboo and sheep wool fiber on sustainability in construction in order to save energy and use those materials in the industry. The authors described the characteristics of bamboo in terms of species, mechanical, biological, and moisture aspects: it has a tensile strength of up to 370 N&#x00B7;mm<sup>&#x2212;2</sup>, production energy lower than steel, and energy 50 times lower than steel in its industrialization. By analyzing this work, we tried to study the traditional biological treatment of sheep wool and the moisture aspect of the bio-sourced material, sheep wool, to analyze its characteristics compared to other alternative materials. Ghermezgoli et al. [<xref ref-type="bibr" rid="ref-7">7</xref>] studied the thermal and acoustical properties of samples of wool fabrics. Results indicate that fabrics made from wool fiber show interesting properties compared to mineral wool with less impact on the environment, which pushes the authors of our work to study the thermal characterization and energy efficiency of sheep wool to compare its physical characteristics with other industrial materials. Meanwhile, D&#x00E9;nes et al. [<xref ref-type="bibr" rid="ref-8">8</xref>] assessed the properties of sheep wool in the reinforcement of concrete compared to materials such as polypropylene and polyacrylonitrile. Results indicate that the performance of wool fibers is less than that of polypropylene; however, it can replace hydrocarbon-based products, with wool yielding carbon between 16% and 25% after being treated, stabilized at 160&#x00B0;C for 10 min in the presence of air, and carbonized at 800&#x00B0;C in an atmosphere containing nitrogen. By analyzing this work, the authors of this paper confirm the necessity of studying the material sheep wool as an insulating building material that has similar properties as other industrial ones.</p>
<p>The work of Mounir et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] studied the thermal characterization and thermal inertia of the composite clay-wool and revealed the important effect of wool combined with clay in terms of thermal inertia parameters: damping factor, delay of temperature, and heat flow. They also estimated the low carbon impact of the clay-wool on the environment. This work proves the utility of studying wool as an insulating building material that possesses good thermal inertia. Maaloufa et al. [<xref ref-type="bibr" rid="ref-10">10</xref>] also investigated the mechanical characteristics and the effect of insulating materials such as fiber on improving the flexure strength of composites. The work of Alyousef et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] studied the management of wool waste as an element integrated with concrete as a cheap material. For this goal, the authors investigated the mechanical and microstructural properties of eight samples mixed with four kinds of concrete. Results indicated that the incorporation of wool fiber in concrete decreased the compressive strength; however, the tensile and flexural strength values of the concrete improved. Also, the microstructural characteristics of sheep wool fiber reinforced concrete were found to have good bonding and low voids. The work of Mounir et al. [<xref ref-type="bibr" rid="ref-9">9</xref>] and Alyoussef et al. [<xref ref-type="bibr" rid="ref-11">11</xref>] proves the excellent mechanical properties of sheep wool in improving flexural strength, not only in terms of thermal properties but also in terms of mechanical characteristics. The work of Parlato et al. [<xref ref-type="bibr" rid="ref-12">12</xref>] studied the possibility of valuing sheep wool as an insulation material by developing a chain product industry in Italy; they studied the correct scale required for sustainable production of sheep wool insulation products. Our work contributes to the same context of promoting the use of sheep wool in industry as an eco-friendly material with excellent thermal properties.</p>
<p>The use of fibers as additives with the main matrix improves the insulating properties of materials, as the research of Zormati et al. [<xref ref-type="bibr" rid="ref-13">13</xref>] analyzed the effect of using cellulose nanofibers as an admixture in cement mortars. The authors investigated the physical properties of the new composite as the thermal conductivity, and they found a value between 0.95 and 2.25 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>). This finding encourages the authors of this research to investigate the insulating properties of sheep wool as a fiber.</p>
<p>Management of waste is the only way to reduce pollution and obtain a clean environment, as the work of Alsamaraie et al. [<xref ref-type="bibr" rid="ref-14">14</xref>] assessed the benefit of using feather as an insulating material due to its low thermal conductivity ranges from 0.024 to 0.034 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>), its low density of 0.68 g.cm<sup>&#x2212;3</sup>, and its chemical composition and microstructure of trap air, which produce a good barrier. According to those properties, the feather can be used as an effective thermal and acoustic insulation material even if its use presents some limitations, such as the restriction by the U.K. to use this material, its biodegradation decomposes, and the fire resistance of the thermal insulation, which is a crucial concern. The work of Aloulou et al. [<xref ref-type="bibr" rid="ref-15">15</xref>] investigated the influence of nanofiber wood as an industrial waste on the properties of fresh cement mortar. Results showed that the compressive strength increased by more than 50% and the thermal conductivity decreased by adding 1% of nanofiber wood. Those findings can be explained by the modification of the chemical composition of the cement mortar by reducing the quantity of water and minimizing the pores. Also, it is observed that the hydration of cement increased due to the introduction of nanofiber wood, which contains calcium silicate gel and portlandite. Abdulmunem et al. [<xref ref-type="bibr" rid="ref-16">16</xref>] assessed the role of adding palm oil as a sustainable and passive cooling material for lithium batteries because when the ion lithium battery temperature increases, the power produced decreases. Palm fatty acid distillate (PFEA) was chosen as a Phase Change Material (PCM) to contribute to the reduction of LIB cells temperature and the increase of cells&#x2019; electrical power. Abdulmunem et al. [<xref ref-type="bibr" rid="ref-17">17</xref>] revealed that feather waste can be used with phase change material as insulation because it delivers excellent thermal and acoustic insulation, and by doing so, the cooling load and the electricity cost decreased. The authors developed a new bio-composite material based on PCM and feather waste (WCF) within polyvinyl chloride panels. Results indicate that the integration of WCF by a ratio of 75% improved the acoustic insulation by 9%, reduced the cooling load by 20.3%, and increased by 22.5% the electricity cost savings for the testing room located in Baghdad city. According to those studies, the authors of this research tried to manage the waste of sheep wool as an insulating material in buildings due to the interesting properties of additives and the improvement of thermal and mechanical properties of materials.</p>
<p>The research gap and objectives of this study are to promote the use of sheep wool in rural and urban areas by proposing an ecological treatment using Silini Folgariss and Camphor. The results of this treatment were determined by the method of aerobic mesophilic flora. Also, this research gives a clear idea about the thermal properties of this material by determining the thermal conductivity, which shows the power of insulating buildings, and investigating the thermal diffusivity to give a clear idea about the thermal inertia behavior of this bio-sourced material. Moreover, this work assesses the hygrothermal behavior of sheep wool in different forms compacted and expanded in both winter and summer, which permits understanding the behavior of this material toward humidity. Furthermore, the research studied the energy efficiency of this material used in buildings by evaluating the thermal transmittance and cooling needs during a year in dry climates. Finally, the research contributes to the management of sheep wool waste by proposing to use it as an insulating material in buildings treated ecologically.</p>
</sec>
</sec>
<sec id="s2">
<label>2</label>
<title>Materials and Methods</title>
<sec id="s2_1">
<label>2.1</label>
<title>Description of the Materials Used</title>
<p>The method of treating sheep wool was described below:<list list-type="bullet"><list-item>
<p>Washing sheep wool with Silini Folgariss traditional material;</p></list-item><list-item>
<p>Sun-backed specimen of sheep wool;</p></list-item><list-item>
<p>Use of camphor to kill microorganisms;</p></list-item><list-item>
<p>Use of traditional combs, which women utilize to prepare carpet.</p></list-item></list></p>
<p>The wool used was taken from the sheep, as shown in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>, and treated with Silini Folgariss, as illustrated in <xref ref-type="fig" rid="fig-2">Fig. 2</xref> and camphor. The diameter of sheep wool studied is described in paragraph 3.6 before and after treatment; however, the length is between 3.5 and 6.5 cm. Sheep wool has important thermal and environmental characteristics. It has a low density of 20 kg.m<sup>&#x2212;3</sup>. Its thermal performance was characterized, and <xref ref-type="fig" rid="fig-1">Fig. 1</xref> shows the sample studied.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Specimen of sheep wool studied</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-1.tif"/>
</fig><fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>Specimen of Tighecht (Silini Folgariss) used in washing sheep wool</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-2.tif"/>
</fig>
<p>The camphor studied as shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref> is a traditional composite, which is a solid bicyclic organic composite taken from the camphor tree; its natural aspect is shown in <xref ref-type="fig" rid="fig-3">Fig. 3</xref>. Its chemical formula is C<sub>6</sub>H<sub>16</sub>O. It is found in many plants [<xref ref-type="bibr" rid="ref-18">18</xref>], such as in the wood of the camphor laurel (<italic>Cinnamomum camphora</italic>), a large evergreen tree found in Asia, and also in the unrelated Kapur tree, which is a tall timber tree from the same region. It also occurs in some other related trees in the laurel family, notably <italic>Ocotea usambarensis</italic>, and in the oil rosemary leaves. The mint family contains 10% to 20% camphor, while camphorweed (Heterotheca) only contains 5%. Camphor can also be synthetically produced from the oil of turpentine. <xref ref-type="table" rid="table-1">Tables 1</xref>&#x2013;<xref ref-type="table" rid="table-3">3</xref> show the chemical components of the materials, respectively, sheep wool, camphor, and silini folgariss.</p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Camphor in its natural aspect</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-3.tif"/>
</fig><table-wrap id="table-1"><label>Table 1</label>
<caption>
<title>Sheep wool fluorescence X</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Chemical element</th>
<th>PaF</th>
<th colspan="2">SO<sub>3</sub></th>
<th>Cl</th>
<th>Na<sub>2</sub>O</th>
<th>CaO</th>
<th>Al<sub>2</sub>O<sub>3</sub></th>
<th>SiO<sub>2</sub></th>
<th>K<sub>2</sub>O</th>
<th>MgO</th>
<th>P<sub>2</sub>O<sub>5</sub></th>
<th>Fe<sub>2</sub>O<sub>3</sub></th>
<th>ZnO</th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>97.52</td>
<td colspan="2">1.512</td>
<td>0.4486</td>
<td>0.1970</td>
<td>0.1312</td>
<td>0.07462</td>
<td>0.03770</td>
<td>0.03253</td>
<td>0.02028</td>
<td>0.01176</td>
<td>0.005477</td>
<td>0.002657</td>
</tr>
<tr>
<td>Chemical element</td>
<td>SrO</td>
<td colspan="2">Ac</td>
<td>NiO</td>
<td>Sum</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.0007131</td>
<td colspan="2">0.0005588</td>
<td>0.0005367</td>
<td>100</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Element</th>
<th>O</th>
<th>C</th>
<th colspan="2">S</th>
<th>Cl</th>
<th>Na</th>
<th>Ca</th>
<th>Al</th>
<th>K</th>
<th>Si</th>
<th>Mg</th>
<th>P</th>
<th>Fe</th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>71.98</td>
<td>26.62</td>
<td colspan="2">0.6057</td>
<td>0.4486</td>
<td>0.1462</td>
<td>0.09374</td>
<td>0.03949</td>
<td>0.02700</td>
<td>0.01762</td>
<td>0.01223</td>
<td>0.005132</td>
<td>0.003831</td>
</tr>
<tr>
<td>Element</td>
<td>Zn</td>
<td>Sr</td>
<td colspan="2">Ac</td>
<td>Ni</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.002135</td>
<td>0.0006030</td>
<td colspan="2">0.0005588</td>
<td>0.0004218</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-2"><label>Table 2</label>
<caption>
<title>Camphor fluorescence</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Chemical element</th>
<th>CaO</th>
<th>SO<sub>3</sub></th>
<th>PaF</th>
<th>SiO<sub>2</sub></th>
<th>MgO</th>
<th>SrO</th>
<th>In<sub>2</sub>O<sub>3</sub></th>
<th>Al<sub>2</sub>O<sub>3</sub></th>
<th>Fe<sub>2</sub>O<sub>3</sub></th>
<th>K<sub>2</sub>O</th>
<th>Au</th>
<th>Bi<sub>2</sub>O<sub>3</sub></th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>46.83</td>
<td>43.01</td>
<td>8.972</td>
<td>0.3692</td>
<td>0.2394</td>
<td>0.2038</td>
<td>0.1261</td>
<td>0.1206</td>
<td>0.08776</td>
<td>0.02754</td>
<td>0.005172</td>
<td>0.004298</td>
</tr>
<tr>
<td>Chemical element</td>
<td>Ac</td>
<td>Sum</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.003769</td>
<td>100</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Element</th>
<th>O</th>
<th>Ca</th>
<th>S</th>
<th>C</th>
<th>Si</th>
<th>Sr</th>
<th>Mg</th>
<th>In</th>
<th>Al</th>
<th>Fe</th>
<th>K</th>
<th>Au</th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>46.10</td>
<td>33.47</td>
<td>17.22</td>
<td>2.449</td>
<td>0.1726</td>
<td>0.1723</td>
<td>0.1444</td>
<td>0.1043</td>
<td>0.06381</td>
<td>0.06138</td>
<td>0.02286</td>
<td>0.005172</td>
</tr>
<tr>
<td>Element</td>
<td>Bi</td>
<td>Ac</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.003855</td>
<td>0.003769</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-3"><label>Table 3</label>
<caption>
<title>Silini folgariss fluorescence</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Chemical element</th>
<th>PaF</th>
<th>SiO<sub>2</sub></th>
<th>CaO</th>
<th>Al<sub>2</sub>O<sub>3</sub></th>
<th>Fe<sub>2</sub>O<sub>3</sub></th>
<th>K<sub>2</sub>O</th>
<th>SO<sub>3</sub></th>
<th>MgO</th>
<th>Cl</th>
<th>P<sub>2</sub>O<sub>5</sub></th>
<th>TiO<sub>2</sub></th>
<th>Na<sub>2</sub>O</th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>92.04</td>
<td>2.505</td>
<td>2.263</td>
<td>1.017</td>
<td>0.8139</td>
<td>0.5721</td>
<td>0.2100</td>
<td>0.1608</td>
<td>0.1570</td>
<td>0.07510</td>
<td>0.07174</td>
<td>0.04583</td>
</tr>
<tr>
<td>Chemical element</td>
<td>MnO</td>
<td>SrO</td>
<td>CuO</td>
<td>Rb2O</td>
<td>NiO</td>
<td>ZnO</td>
<td>PbO</td>
<td>Sum</td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.03470</td>
<td>0.01310</td>
<td>0.006713</td>
<td>0.004515</td>
<td>0.004346</td>
<td>0.003177</td>
<td>0.001765</td>
<td>100</td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Element</th>
<th>O</th>
<th>C</th>
<th>Ca</th>
<th>Si</th>
<th>Fe</th>
<th>Al</th>
<th>K</th>
<th>Cl</th>
<th>Mg</th>
<th>S</th>
<th>Ti</th>
<th>Na</th>
</tr>
</thead>
<tbody>
<tr>
<td>Conc%</td>
<td>70.01</td>
<td>25.12</td>
<td>1.617</td>
<td>1.171</td>
<td>0.5693</td>
<td>0.5385</td>
<td>0.4749</td>
<td>0.1570</td>
<td>0.0970</td>
<td>0.08412</td>
<td>0.04301</td>
<td>0.03400</td>
</tr>
<tr>
<td>Element</td>
<td>P</td>
<td>Mn</td>
<td>Sr</td>
<td>Cu</td>
<td>Rb</td>
<td>Ni</td>
<td>Zn</td>
<td>Pb</td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Conc%</td>
<td>0.03278</td>
<td>0.02688</td>
<td>0.01108</td>
<td>0.005363</td>
<td>0.004128</td>
<td>0.003415</td>
<td>0.002552</td>
<td>0.001639</td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Physic-Chemical Analysis</title>
<sec id="s2_2_1">
<label>2.2.1</label>
<title>Fluorescence Method</title>
</sec>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>The Microbiological Study</title>
<p>Wool is continuously exposed to contamination by microorganisms of all kinds (pathogenic or not, as well as bacteria and fungi), which are able to multiply rapidly under favorable conditions (moisture). This leads to a loss of resistance or other forms of degradation in wool fibers. In order to use this natural material in construction, we tested a traditional treatment (Silini Folgariss and camphor) to eliminate these microorganisms.</p>
<sec id="s2_3_1">
<label>2.3.1</label>
<title>Description of the Mesophilic Aerobic Flora</title>
<p>The mesophilic aerobic flora method was used to determine the effect of the microbiological treatment on removing organisms from sheep wool. Samples are shown in <xref ref-type="fig" rid="fig-4">Figs. 4</xref> and <xref ref-type="fig" rid="fig-5">5</xref>. The wool used came from sheep. The authors prepared three samples: a sample of raw wool, a sample of wool washed with tighecht, and a third sample corresponding to wool treated with tighecht and camphor.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Samples of the first test using silini folgariss</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-4.tif"/>
</fig><fig id="fig-5">
<label>Figure 5</label>
<caption>
<title>Samples of the second test using tighecht and camphor</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-5.tif"/>
</fig>
<p>Mesophilic aerobic flora is a technical indicator that represents the total microbial load. These are all bacteria, yeasts, and mildew capable of developing in aerobiosis on well-defined culture media. After preparation of the samples and appropriate dilutions, the microbiological analysis of the three wool samples was carried out on the count of total aerobic mesophilic flora (FMAT): yeast and mildew.</p>
<p>The abundance of the Total Aerobic Mesophilic Flora (FMAT), which provides information on the overall bacterial load, was estimated on PCA (Plate Count Agar) medium incubated for 48 h at 30&#x00B0;C according to the Moroccan standard [<xref ref-type="bibr" rid="ref-19">19</xref>]. And is expressed as CFU (colony forming units).</p>
<p>The enumeration of yeast and mildew counts is done on PDA (Potato Dextro Agar) medium after incubation for 48 h at 30&#x00B0;C for yeast and 5&#x2013;7 days at 25&#x00B0;C for mildew according to the Moroccan standard [<xref ref-type="bibr" rid="ref-19">19</xref>]. The tests are repeated three times.</p>
</sec>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Thermal Characterizations</title>
<p>The hot wire method was used to characterize the thermal conductivity of sheep wool [<xref ref-type="bibr" rid="ref-20">20</xref>&#x2013;<xref ref-type="bibr" rid="ref-22">22</xref>], as illustrated in <xref ref-type="fig" rid="fig-6">Fig. 6</xref>. <xref ref-type="disp-formula" rid="eqn-1">Eqs. (1)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-10">(10)</xref> describe the principle of this method.</p>
<fig id="fig-6">
<label>Figure 6</label>
<caption>
<title>Principle of the hot wire method</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-6.tif"/>
</fig>
<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:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mrow><mml:msup><mml:mi>r</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>r</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>x</mml:mi><mml:mi>R</mml:mi></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:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mstyle></mml:mstyle></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:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mtext>&#x00A0;&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-3"><label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">&#x221E;</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-4"><label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mi>h</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><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:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x2202;</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mstyle></mml:math>
</disp-formula></p>
<p><disp-formula id="eqn-5"><label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mi>S</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mstyle></mml:math>
</disp-formula></p>
<p>To determine the resolution of the heat in <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref> based on the initial and limit conditions in <xref ref-type="disp-formula" rid="eqn-2">Eqs. (2)</xref> and <xref ref-type="disp-formula" rid="eqn-3">(3)</xref> of this system using the quadrupole method, we write the formula of the Laplace transform T<sub>s</sub>(t) in this way, as represented in <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref>.<disp-formula id="eqn-6"><label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></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:mi mathvariant="normal">W</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext><mml:mi mathvariant="normal">A</mml:mi></mml:mrow><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>;</mml:mo><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mi>B</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>&#x03C1;</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mi>&#x03C0;</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>0</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03C1;</mml:mi><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mi>&#x03C0;</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>0</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mi>L</mml:mi><mml:mi>p</mml:mi><mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula><disp-formula id="eqn-8"><label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>Z</mml:mi></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi><mml:mi>q</mml:mi><mml:mi>r</mml:mi><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p>where</p>
<p>&#x0398;s is the Laplace transform of the difference T<sub>s</sub>(t) &#x2212; T<sub>s</sub>(t &#x003D; 0)</p>
<p>&#x0398; is the Laplace transform of the difference T(t) &#x2212; T(t &#x003D; 0)</p>
<p>R<sub>c</sub> the resistance of contact in the interface heating element/sample</p>
<p>C<sub>S</sub>: heat capacity of thermocouple-resistance</p>
<p>&#x03BB;: thermal conductivity of the sample</p>
<p>a: thermal diffusivity of the sample</p>
<p>P: Laplace variable</p>
<p>r<sub>0</sub>: radius of hot wire element</p>
<p>L: Length of the hot wire</p>
<p>&#x03D5;<sub>0</sub>: dissipated power in the heating element</p>
<p>I<sub>0</sub>, I<sub>1</sub>, K<sub>0</sub>, K<sub>1</sub>: Bessel Functions</p>
<p>If we consider a thin wire (r<sub>0</sub> small) and if we are in the long time (<inline-formula id="ieqn-1">
<mml:math id="mml-ieqn-1"><mml:mi>p</mml:mi><mml:mo stretchy="false">&#x2192;</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
</inline-formula> (we can use the limit development of Bessel functions near zero), we have:<disp-formula id="eqn-9"><label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mrow><mml:mi mathvariant="normal">K</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>;</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mo>;</mml:mo><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:math>
</disp-formula><disp-formula id="eqn-10"><label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mi mathvariant="normal">W</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">c</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mspace width="1em" /><mml:mrow><mml:mtext>&#x00A0;</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03C1;</mml:mi><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mi>&#x03C0;</mml:mi><mml:msubsup><mml:mi>r</mml:mi><mml:mn>0</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mi>L</mml:mi><mml:mi>p</mml:mi><mml:mspace width="1em" /><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mspace width="1em" /><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>Z</mml:mi></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>q</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:math>
</disp-formula><disp-formula id="eqn-11"><label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:msub><mml:mi>&#x03B8;</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:mfrac></mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>Z</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi>Z</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:mfrac></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>Z</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mi>p</mml:mi></mml:mfrac></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:msqrt><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mi>p</mml:mi><mml:mi>a</mml:mi></mml:mfrac></mml:mrow></mml:mstyle></mml:msqrt></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mi>P</mml:mi></mml:mfrac></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:msqrt><mml:mi>a</mml:mi></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p>Using Laplace transform inverse, we calculate the temperature T<sub>s</sub>(t) in the length time as shown in <xref ref-type="disp-formula" rid="eqn-12">Eq. (12)</xref>.<disp-formula id="eqn-12"><label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></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:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:msqrt><mml:mi>a</mml:mi></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p>where &#x03B3; &#x003D; 0.57721 is the constant of Euler.<disp-formula id="eqn-13"><label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mi>ln</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">l</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:msqrt><mml:mi>a</mml:mi></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mstyle></mml:math>
</disp-formula></p>
<p>The drawing function Ts (t) &#x2212; Ts (0) in function of ln(t) is a linear curve of slope <inline-formula id="ieqn-2">
<mml:math id="mml-ieqn-2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</inline-formula>. When we determine this slope, we can calculate the thermal conductivity.</p>
<sec id="s2_4_1">
<label>2.4.1</label>
<title>Thermal Diffusivity</title>
<p>The thermal diffusivity of the wool samples studied was characterized using the flash method [<xref ref-type="bibr" rid="ref-23">23</xref>&#x2013;<xref ref-type="bibr" rid="ref-25">25</xref>].</p>
</sec>
<sec id="s2_4_2">
<label>2.4.2</label>
<title>Humidity Study</title>
<p>The behavior towards humidity was studied by saturating samples of sheep wool as presented in <xref ref-type="fig" rid="fig-7">Fig. 7</xref>, with water compacted volume and none compacted volume, and the results were reported according to the weight measured during a lot of days at 24&#x00B0;C.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title>Sheep wool samples to study their humidity behavior-a) Compacted wool-b) Combed wool</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-7.tif"/>
</fig>
<p>The weight of dried samples is 2 g before being saturated with water. The saturated mass of sheep wool measured 28 g at time zero before the experience.</p>
</sec>
</sec>
<sec id="s2_5">
<label>2.5</label>
<title>Simulation Study</title>
<p>A simulation study concerning the cooling needs during a year has been done using the tool TRNSYS, which evaluates the cooling needs in each hour during the year. The building studied is a simple ground floor with 60 m<sup>2</sup> located in Marrakech, a city with arid weather. The building contains one floor composed of four double glazing windows built with full brick, whose characteristics are &#x03BB; &#x003D; 0.19 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>); C &#x003D; 0.794 (KJ&#x00B7;K<sup>&#x2212;1</sup>); and &#x03C1; &#x003D; 1700 (kg&#x00B7;m<sup>&#x2212;3</sup>). The software TRNSYS permits the evaluation of cooling needs for each hour during a year.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Results and Discussion</title>
<sec id="s3_1">
<label>3.1</label>
<title>Microbiological Results</title>
<p>By counting the microbial load of the wool, it is possible to establish the link between the presence and absence of microorganisms and the effect of washing with tighecht and camphor treatment. The results obtained are shown in <xref ref-type="table" rid="table-4">Table 4</xref>.</p>
<table-wrap id="table-4"><label>Table 4</label>
<caption>
<title>Count of microorganisms according to the kind of treatment</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Microorganisms</th>
<th>Raw wool</th>
<th>Wool washed with tighecht</th>
<th>Wool treated by tighecht and camphor</th>
</tr>
</thead>
<tbody>
<tr>
<td>FMAT (UFC&#x00B7;g<sup>&#x2212;1</sup>)</td>
<td>18.10<sup>5</sup></td>
<td>12.10<sup>4</sup></td>
<td>8.10<sup>4</sup></td>
</tr>
<tr>
<td>Yeast and Mildew (UFC&#x00B7;g<sup>&#x2212;1</sup>)</td>
<td>38.10<sup>2</sup></td>
<td>6.10<sup>2</sup></td>
<td>2.10<sup>2</sup></td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to <xref ref-type="table" rid="table-4">Table 4</xref>, the authors observe that concerning the method of aerobic mesophilic flora, the raw wool contains 18.10<sup>5</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>); however, by the treatment of Tighecht, this value decreased to 12.10<sup>4</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>), which represents a decrease of 93%; nonetheless, using Tighecht and camphor, the value of microorganisms decreased to 8.10<sup>4</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>), which represents a decrease of 95.5% compared to the raw materials. The study of the percentage of yeast and mildew in sheep wool indicates that the raw wool contains 38.10<sup>2</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>), but when the authors used the treatment Tighecht, this value decreased to 6.10<sup>2</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>), which represents a decrease of 84% of yeast and mildew, and finally, by adding Tighecht and camphor, this value decreased to 2.10<sup>2</sup> (UFC&#x00B7;g<sup>&#x2212;1</sup>) of yeast and mildew responsible for the degradation of wool, which represents a decrease of 94.73%. The analysis of those results proves the efficiency of this natural treatment to eliminate microorganisms from the sheep&#x2019;s wool. The authors conclude that the studied treatment of wool facilitates the building sector&#x2019;s use of a natural and ecological insulating material, sheep wool, in construction.</p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Fluorescence Method</title>
<p>The analysis of the fluorescence method as illustrated in <xref ref-type="table" rid="table-1">Tables 1</xref>&#x2013;<xref ref-type="table" rid="table-3">3</xref> proves that sheep wool is composed of carbon and oxygen in the majority of elements as an organic material; however, camphor is composed of CaO and SO<sub>3</sub> as illustrated in <xref ref-type="table" rid="table-2">Table 2</xref>, while silina folgariss is composed of oxygen, carbon, and a small percentage of calcium and silicon, which does not exceed 1%.</p>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Thermal Conductivity</title>
<p>The plot of Ts(t) &#x2013; Ts(t&#x003D;0) in function of ln(t) is a linear curve with a slope <inline-formula id="ieqn-3">
<mml:math id="mml-ieqn-3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03C6;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mn>4</mml:mn><mml:mi>&#x03C0;</mml:mi><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow><mml:mtext>&#x00A0;</mml:mtext><mml:mi>L</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</inline-formula>. By determining this value, the authors deduce the thermal conductivity of sheep&#x2019;s wool.</p>
<p><bold>&#x03BB; &#x003D; 0.05 W&#x00B7;m</bold><sup><bold>&#x2212;1</bold></sup><bold>&#x00B7; K</bold><sup><bold>&#x2212;1</bold></sup> <bold>&#x00B1; 0.01</bold></p>
<p><bold>&#x03BB; &#x003D; 0.046 W&#x00B7;m</bold><sup><bold>&#x2212;1</bold></sup><bold>&#x00B7;K</bold><sup><bold>&#x2212;1</bold></sup> <bold>&#x00B1; 0.01</bold></p>
<p>Results of thermal conductivity were presented according to <xref ref-type="fig" rid="fig-8">Figs. 8</xref> and <xref ref-type="fig" rid="fig-9">9</xref> using the hot wire method. The authors observe that the thermal conductivity for the first experiment, according to <xref ref-type="fig" rid="fig-8">Fig. 8</xref>, is 0.05 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>); however, concerning the second experiment, <xref ref-type="fig" rid="fig-9">Fig. 9</xref>, the authors remark that the value of thermal conductivity is 0.046 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>).</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title>The first experiment concerning the plot of sheep wool curve in function of time using hot wire method</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-8.tif"/>
</fig><fig id="fig-9">
<label>Figure 9</label>
<caption>
<title>The second experiment concerning the plot of sheep wool curve in function of time using hot wire method</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-9.tif"/>
</fig>
</sec>
<sec id="s3_4">
<label>3.4</label>
<title>Thermal Diffusivity</title>
<p>a (Degiovanni) &#x003D; 1.25.10<sup>&#x2212;06</sup> m&#x00B2;&#x00B7;s<sup>&#x2212;1</sup></p>
<p>a (Parker) &#x003D; 1.57.10<sup>&#x2212;06</sup> m&#x00B2;&#x00B7;s<sup>&#x2212;1</sup></p>
<p>a (Complete) &#x003D; 1.55.10<sup>&#x2212;06</sup> m&#x00B2;&#x00B7;s<sup>&#x2212;1</sup> &#x00B1; 0.02</p>
<p>The thermal diffusivity was evaluated using the complete model, and the authors found a value of 1.5580.10<sup>&#x2212;06</sup> m&#x00B2;.s<sup>&#x2212;1</sup>, which is confirmed by the Degiovanni and Parker models as shown in <xref ref-type="fig" rid="fig-10">Fig. 10</xref>.</p>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title>Thermogram of temperature in function of time using flash method</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-10.tif"/>
</fig>
<p>The results obtained were compared to the work of Zach et al. [<xref ref-type="bibr" rid="ref-5">5</xref>] and the work of Pennacchio et al. [<xref ref-type="bibr" rid="ref-2">2</xref>], the work of Jerman et al. [<xref ref-type="bibr" rid="ref-26">26</xref>] as represented in <xref ref-type="table" rid="table-5">Table 5</xref>, which seems to be comparable to those works at an ambient temperature of 20&#x00B0;C.</p>
<table-wrap id="table-5"><label>Table 5</label>
<caption>
<title>Comparison of thermal conductivity results with literature</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Physical properties</th>
<th>Characterized physical Parameter value</th>
<th>Literature value</th>
<th>Density (kg&#x00B7;m<sup>&#x2212;3</sup>)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Themal conductivity (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>)</td>
<td>0,046 &#x00B1; 0.01</td>
<td>0,044</td>
<td>20</td>
</tr>
<tr>
<td>Themal diffusivity (m<sup>2</sup>&#x00B7;s<sup>&#x2212;1</sup>)</td>
<td>1,55.10<sup>&#x2212;6</sup> &#x00B1; 0.02</td>
<td>1,1.10<sup>&#x2212;6</sup> &#x2212; 1,2.10<sup>&#x2212;6</sup></td>
<td>20</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3_5">
<label>3.5</label>
<title>Humidity Results</title>
<p><xref ref-type="table" rid="table-6">Tables 6</xref> and <xref ref-type="table" rid="table-7">7</xref> represent the results of measuring humid sheep wool samples in the summer season. The temperature is 30&#x00B0;C, and the authors observe that the combed sheep wool sample loses humidity more quickly than the compacted sample; the total weight lost is 26 g over three days.</p>
<table-wrap id="table-6"><label>Table 6</label>
<caption>
<title>Results of humidity for the compacted samples in the summer</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="3">Compacted sheep wool</th>
</tr>
<tr>
<th>Time (day)</th>
<th>Time (hour)</th>
<th>Weight of humid sample (g)</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>15</td>
</tr>
<tr>
<td>2</td>
<td>10</td>
<td>11</td>
</tr>
<tr>
<td>2</td>
<td>22</td>
<td>8</td>
</tr>
<tr>
<td>3</td>
<td>10</td>
<td>4</td>
</tr>
<tr>
<td>3</td>
<td>22</td>
<td>2</td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-7"><label>Table 7</label>
<caption>
<title>Results of humidity for the expanded samples in the summer</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="3">Expanded sheep wool</th>
</tr>
<tr>
<th>Time (day)</th>
<th>Time (hour)</th>
<th>Weight of humid combed sample (g)</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>14</td>
</tr>
<tr>
<td>2</td>
<td>10</td>
<td>10</td>
</tr>
<tr>
<td>2</td>
<td>22</td>
<td>7</td>
</tr>
<tr>
<td>3</td>
<td>10</td>
<td>4</td>
</tr>
<tr>
<td>3</td>
<td>22</td>
<td>2</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The authors observed, according to <xref ref-type="fig" rid="fig-11">Figs. 11</xref> and <xref ref-type="fig" rid="fig-12">12</xref>, that the combed sheep wool sample loses weight more quickly than the compacted sample in a total weight of both samples of 26 g, and the combed or expanded sheep wool always loses 1 g of water more than the compacted sheep wool in a period of three days during the summer.</p>
<fig id="fig-11">
<label>Figure 11</label>
<caption>
<title>Weight of humid samples for expanded sheep wool in summer</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-11.tif"/>
</fig><fig id="fig-12">
<label>Figure 12</label>
<caption>
<title>Weight of humid samples for compacted sheep wool in summer</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-12.tif"/>
</fig>
<p><xref ref-type="table" rid="table-8">Tables 8</xref> and <xref ref-type="table" rid="table-9">9</xref> represent the results of measuring humid sheep wool samples in the winter season, when the temperature is 18&#x00B0;C. The authors observe, according to <xref ref-type="fig" rid="fig-13">Figs. 13</xref> and <xref ref-type="fig" rid="fig-14">14</xref>, that the combed sheep wool sample loses humidity more quickly than the compacted one, and the total weight lost is 26 g during six days.</p>
<table-wrap id="table-8"><label>Table 8</label>
<caption>
<title>Results of humidity for the compacted samples in the winter</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="3">Compacted sheep wool</th>
</tr>
<tr>
<th>Time (day)</th>
<th>Time (hour)</th>
<th>Weight of humid sample (g)</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>28</td>
</tr>
<tr>
<td>1</td>
<td>22</td>
<td>25</td>
</tr>
<tr>
<td>2</td>
<td>10</td>
<td>24</td>
</tr>
<tr>
<td>2</td>
<td>22</td>
<td>21</td>
</tr>
<tr>
<td>3</td>
<td>10</td>
<td>19</td>
</tr>
<tr>
<td>3</td>
<td>22</td>
<td>16</td>
</tr>
<tr>
<td>4</td>
<td>10</td>
<td>14</td>
</tr>
<tr>
<td>4</td>
<td>22</td>
<td>11</td>
</tr>
<tr>
<td>5</td>
<td>10</td>
<td>8</td>
</tr>
<tr>
<td>5</td>
<td>22</td>
<td>6</td>
</tr>
<tr>
<td>6</td>
<td>10</td>
<td>3</td>
</tr>
<tr>
<td>6</td>
<td>22</td>
<td>2</td>
</tr>
</tbody>
</table>
</table-wrap><table-wrap id="table-9"><label>Table 9</label>
<caption>
<title>Results of humidity for the compacted samples in the winter</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th colspan="3">Expanded sheep wool</th>
</tr>
<tr>
<th>Time (day)</th>
<th>Time (hour)</th>
<th>Weight of humid combed sample (g)</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>28</td>
</tr>
<tr>
<td>1</td>
<td>22</td>
<td>24</td>
</tr>
<tr>
<td>2</td>
<td>10</td>
<td>21</td>
</tr>
<tr>
<td>2</td>
<td>22</td>
<td>18</td>
</tr>
<tr>
<td>3</td>
<td>10</td>
<td>15</td>
</tr>
<tr>
<td>3</td>
<td>22</td>
<td>11</td>
</tr>
<tr>
<td>4</td>
<td>10</td>
<td>8</td>
</tr>
<tr>
<td>4</td>
<td>22</td>
<td>5</td>
</tr>
<tr>
<td>5</td>
<td>10</td>
<td>3</td>
</tr>
<tr>
<td>5</td>
<td>22</td>
<td>2</td>
</tr>
<tr>
<td>6</td>
<td>10</td>
<td>2</td>
</tr>
<tr>
<td>6</td>
<td>22</td>
<td>2</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-13">
<label>Figure 13</label>
<caption>
<title>Comparison of humidity behavior of compacted sheep wool samples in winter</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-13.tif"/>
</fig><fig id="fig-14">
<label>Figure 14</label>
<caption>
<title>Comparison of humidity behavior of expanded sheep wool samples in winter</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-14.tif"/>
</fig>
</sec>
<sec id="s3_6">
<label>3.6</label>
<title>Analysis of Microstructure of the Sheep Wool Fiber Treated by Silini Folgariss and Camphor</title>
<p>The authors studied the microstructure of the sheep wool fiber before and after treatment to see the effect of the treatment used on its diameter. <xref ref-type="fig" rid="fig-15">Figs. 15</xref> and <xref ref-type="fig" rid="fig-16">16</xref> show the morphology of the fiber before and after treatment. According to <xref ref-type="fig" rid="fig-15">Fig. 15</xref>, the diameter of sheep&#x2019;s wool that is not treated is between 52.612 and 25.816 &#x03BC;m, and the length is between 3.5 and 6.5 cm. However, the diameter of sheep&#x2019;s wool after treatment represented in <xref ref-type="fig" rid="fig-16">Fig. 16</xref> is between 30.479 and 18.963 &#x03BC;m, and the length is between 3.5 and 6.5 cm, which means that the ecological treatment used reduces the diameter of sheep&#x2019;s wool because it eliminates the deposits of the lipid layer on the surface of the cortex. The results obtained have been confirmed by the literature concerning the work of Alyoussef et al. [<xref ref-type="bibr" rid="ref-27">27</xref>] and Moore et al. [<xref ref-type="bibr" rid="ref-28">28</xref>], which proves the efficiency of the ecological treatment used instead of the chemical treatments used by other researchers.</p>
<fig id="fig-15">
<label>Figure 15</label>
<caption>
<title>The diameters of sheep wool fibers before treatment using the scanning electron microscopy</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-15.tif"/>
</fig><fig id="fig-16">
<label>Figure 16</label>
<caption>
<title>The diameters of sheep wool fibers after treatment using the scanning electron microscopy</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-16.tif"/>
</fig>
</sec>
<sec id="s3_7">
<label>3.7</label>
<title>Study of the Energy Efficiency of Sheep Wool Applied to Buildings</title>
<sec id="s3_7_1">
<label>3.7.1</label>
<title>Thermal Transmittance</title>
<p>The thermal transmittance was calculated according to ISO 6949 [<xref ref-type="bibr" rid="ref-29">29</xref>,<xref ref-type="bibr" rid="ref-30">30</xref>], and the relation is shown in the <xref ref-type="disp-formula" rid="eqn-14">Eq. (14)</xref> below:<disp-formula id="eqn-14"><label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></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:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">h</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></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:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">h</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>+</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;&#x00A0;</mml:mtext></mml:mstyle></mml:mstyle></mml:mstyle></mml:mstyle></mml:math>
</disp-formula></p>
<p>&#x03A4;he composition of walls is described in <xref ref-type="table" rid="table-10">Table 10</xref> below:</p>
<table-wrap id="table-10"><label>Table 10</label>
<caption>
<title>Composition of walls</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Kind of walls</th>
<th>e (cm)</th>
<th>&#x03BB; (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>)</th>
<th>&#x03C1; (kg&#x00B7;m<sup>&#x2212;3</sup>)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Non isolated walls</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Cement-mortar</td>
<td>1</td>
<td>0.7</td>
<td>1400</td>
</tr>
<tr>
<td>Full brick</td>
<td>25</td>
<td>0.19</td>
<td>1700</td>
</tr>
<tr>
<td>Cement-mortar</td>
<td>1</td>
<td>0.7</td>
<td>1400</td>
</tr>
<tr>
<td>Isolated walls-sheep wool</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Cement mortar</td>
<td>1</td>
<td>0.7</td>
<td>1400</td>
</tr>
<tr>
<td>Full brick</td>
<td>25</td>
<td>0.19</td>
<td>1779</td>
</tr>
<tr>
<td>Sheep wool</td>
<td>3</td>
<td>0.044</td>
<td>12</td>
</tr>
<tr>
<td>Cement-mortar</td>
<td>1</td>
<td>0.7</td>
<td>1400</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to <xref ref-type="table" rid="table-10">Table 10</xref>, thermal transmittance was calculated for both kinds of walls. Concerning the non-isolated one, we obtained a value of 1.94 (W&#x00B7;m<sup>&#x2212;2</sup>&#x00B7;K<sup>&#x2212;1</sup>) and the isolated one of 1.06 (W&#x00B7;m<sup>&#x2212;2</sup>&#x00B7;K<sup>&#x2212;1</sup>), and the authors obtained a gain of 45% by insulating walls using sheep wool. The gain obtained is 45%.</p>
</sec>
<sec id="s3_7_2">
<label>3.7.2</label>
<title>Simulation Study</title>
<p>The building studied is a simple ground floor with 60 m<sup>2</sup> located in Marrakech, a city with arid weather whose altitude is 457 m, whose longitude is 7&#x00B0;59&#x2032;, and whose latitude is 31&#x00B0;38&#x2032;. The building contains one floor composed of four double-glazing windows built in full brick whose characteristics are &#x03BB; &#x003D; 0.19 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>); C &#x003D; 0.794 (KJ&#x00B7;K<sup>&#x2212;1</sup>); and &#x03C1; &#x003D; 1700 (kg&#x00B7;m<sup>&#x2212;3</sup>) as described in <xref ref-type="table" rid="table-9">Table 9</xref>. Simulation was conducted over a year, and data on cooling needs was calculated every hour during the year, results are illustrated in <xref ref-type="fig" rid="fig-17">Fig. 17</xref>.</p>
<fig id="fig-17">
<label>Figure 17</label>
<caption>
<title>Comparison of cooling need for both kinds of walls</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-17.tif"/>
</fig>
<p>The gain obtained was calculated according to the <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>.<disp-formula id="eqn-15"><label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:mi>g</mml:mi><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mtext>&#x00A0;&#x00A0;</mml:mtext></mml:mstyle></mml:math>
</disp-formula></p>
<p>An analysis of <xref ref-type="fig" rid="fig-17">Fig. 17</xref> concerning the building studied was conducted on both cases: the building without insulation and the building isolated by sheep wool demonstrate the cooling needs increasing in summer at 1.45 &#x00D7; 10<sup>4</sup> (KJ&#x00B7;h<sup>&#x2212;1</sup>) for the isolated building by sheep wool; however, for the building without insulation, it is at 3 &#x00D7; 10<sup>4</sup> (KJ&#x00B7;h<sup>&#x2212;1</sup>). We conclude that by using sheep&#x2019;s wool insulation, we gain 52%.</p>
<p><xref ref-type="fig" rid="fig-18">Histogram 1</xref> clearly shows the difference in cooling energy needs between the walls isolated by sheep wool and the ones without sheep wool.</p>
<fig id="fig-18">
<label>Histogram 1</label>
<caption>
<title>Comparison of cooling need concerning the kind of walls building studied</title></caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="JRM_49392-fig-18.tif"/>
</fig>
<p>Analysis of <xref ref-type="fig" rid="fig-18">Histogram 1</xref> was done concerning the cooling need for one year; the authors observe that the total cooling need concerning the isolated building by sheep wool is 2.8 &#x00D7; 10<sup>7</sup> (KJ&#x00B7;h<sup>&#x2212;1</sup>) during one year. However, concerning the non-isolated building, it is 5.45 &#x00D7; 10<sup>7</sup> (KJ&#x00B7;h<sup>&#x2212;1</sup>). We conclude that by using the insulating material sheep wool, we obtain a reduction of 48% in the cooling need during a year. The authors deduce that using sheep wool will significantly reduce the energy consumption of buildings, so by insulating the envelope, we will assure the best energy efficiency.</p>
<p>The results were compared with the work of Anjum et al. [<xref ref-type="bibr" rid="ref-31">31</xref>], who studied the thermophysical properties of bricks containing waste; the thermophysical properties of the rocks under the influence of moisture and temperature are reviewed; the construction of eco-friendly and thermally insulated bricks by adding waste materials is examined in depth in terms of energy savings; and the results prove that adding insulation to bricks permits a significant gain in terms of energy.</p>
</sec>
<sec id="s3_7_3">
<label>3.7.3</label>
<title>Study of the Economic Performance of the Treatment Studied</title>
<p>An economic study was conducted to evaluate the price of the proposed treatment and the <xref ref-type="table" rid="table-11">Table 11</xref> showed the data of this study.</p>
<table-wrap id="table-11"><label>Table 11</label>
<caption>
<title>The economic study of the treatment proposed</title></caption>
<table><colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Kind of materials</th>
<th>Quantity (g)</th>
<th>Minimum price</th>
<th>Maximum price</th>
</tr>
</thead>
<tbody>
<tr>
<td>Sheep wool</td>
<td>1000</td>
<td>3</td>
<td>5</td>
</tr>
<tr>
<td>Silini Folgariss</td>
<td>10</td>
<td>0.5</td>
<td>1</td>
</tr>
<tr>
<td>Camphor</td>
<td>2</td>
<td>0.25</td>
<td>0.5</td>
</tr>
<tr>
<td>Total price treatment (MAD)/kg (sheep wool treated)</td>
<td>6.5</td>
<td>3.75</td>
<td>6.5</td>
</tr>
<tr>
<td>Total price treatment (euro)/kg (sheep wool treated)</td>
<td></td>
<td>0.34</td>
<td>0.6</td>
</tr>
<tr>
<td>Total price treatment (American dollar)/kg (sheep wool treated)</td>
<td></td>
<td>1.02</td>
<td>0.65</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="table" rid="table-11">Table 11</xref> shows the price of the treatment proposed, which is a range between the minimum and the maximum price. According to the results, the minimum price per kg is 3.75 MAD in Moroccan dirhams, 0.34 in euro, and 1.02 in American dollar; however, for the maximum price per kg, it is 6.5 MAD in Moroccan dirhams, 0.6 in Euro, and 0.65 in American dollar.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Conclusions</title>
<p>This paper investigates the thermal, hygrothermal, and microbiological treatment of the raw material, sheep wool, as an insulating material in the building using a traditional treatment to remove microorganisms from it. The traditional treatment of sheep wool consists of using silini folgariss and camphor in order to wash and treat the sheep wool studied. Biological analyses were conducted, and the results prove the efficiency of the treatment. Thermal characterization show that the sheep&#x2019;s wool thermal conductivity is above 0.046 (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>), however, the thermal diffusivity is 1.55.10<sup>&#x2212;6</sup> m<sup>2</sup>&#x00B7;s<sup>&#x2212;1</sup>. Also, the hygrothermal study in the summer and winter was done for two kinds of sheep wool, combed and compacted, to study the impact of introducing air on the hygrothermal behavior of this material. The results prove that the combed wool removes humidity more quickly than the compacted wool. Besides, in winter, we need the double time compared to summer to remove the same quantity of water. Moreover, the study evaluates the impact of sheep wool on the building sector in terms of energy. Results show a reduction of 45% in terms of thermal transmittance. Furthermore, the research was extended to the scale of the building by simulating the cooling needs of an arid climate in both cases with and without sheep wool; the results show a gain of 48% during a year. This study encourages the industry to use and adopt an ecological method to treat and use sheep wool as an eco-friendly material that presents a lot of beneficial health aspects and to understand the hygrothermal behavior of this insulating material. From the perspective of this work, the authors estimate extending the biological study in order to specify the microorganisms that exist in sheep wool and what kind of microorganisms have been removed from sheep wool using the proposed traditional treatment.</p>
</sec>
</body>
<back>
<glossary content-type="abbreviations" id="glossary-1">
<title>Nomenclature</title>
<def-list>
<def-item>
<term>PCA</term>
<def>
<p>Plate count agar</p>
</def>
</def-item>
<def-item>
<term><inline-formula id="ieqn-4">
<mml:math id="mml-ieqn-4"><mml:mrow><mml:mi mathvariant="normal">&#x03BB;</mml:mi></mml:mrow></mml:math>
</inline-formula></term>
<def>
<p>Thermal conductivity (W&#x00B7;m<sup>&#x2212;1</sup>&#x00B7;K<sup>&#x2212;1</sup>)</p>
</def>
</def-item>
<def-item>
<term>A</term>
<def>
<p>Thermal diffusivity (m<sup>2</sup>&#x00B7;s<sup>&#x2212;1</sup>)</p>
</def>
</def-item>
</def-list>
</glossary>
<ack>
<p>The authors are thankful to the LEMTA-INPL NANCY for their help so as to realize this work.</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: study conception and design: S. Mounir, Y. Maaloufa, F.Z. Wardi, Y.A. Dodo, M. Slaoui; data collection: S. Mounir, F.Z. Wardi, Y. Maaloufa, S. Ibn Elhaj, M. Slaoui; analysis and interpretation of results: S. Mounir, A. Khabbazi; draft manuscript preparation: S. Mounir, Y. Maaloufa, Y.A. Dodo. 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 authors confirm that the data supporting the findings of this study are available within the article.</p>
</sec>
<sec sec-type="COI-statement">
<title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</sec>
<ref-list content-type="authoryear">
<title>References</title>
<ref id="ref-1"><label>1.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Jelle</surname> <given-names>BP</given-names></string-name></person-group>. <article-title>Traditional, state-of-the-art and future thermal building insulation materials and solutions&#x2013;Properties, requirements and possibilities</article-title>. <source>Energy Build</source>. <year>2011 Oct</year>;<volume>43</volume>(<issue>10</issue>):<fpage>2549</fpage>&#x2013;<lpage>63</lpage>.</mixed-citation></ref>
<ref id="ref-2"><label>2.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Pennacchio</surname> <given-names>R</given-names></string-name>, <string-name><surname>Savio</surname> <given-names>L</given-names></string-name>, <string-name><surname>Bosia</surname> <given-names>D</given-names></string-name>, <string-name><surname>Thiebat</surname> <given-names>F</given-names></string-name>, <string-name><surname>Piccablotto</surname> <given-names>G</given-names></string-name>, <string-name><surname>Patrucco</surname> <given-names>A</given-names></string-name>, <etal>et al</etal></person-group>. <article-title>Fitness: sheep-wool and hemp sustainable insulation panels</article-title>. <source>Enrgy Proced</source>. <year>2017 Mar 1</year>;<volume>111</volume>:<fpage>287</fpage>&#x2013;<lpage>97</lpage>.</mixed-citation></ref>
<ref id="ref-3"><label>3.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Corscadden</surname> <given-names>KW</given-names></string-name>, <string-name><surname>Biggs</surname> <given-names>JN</given-names></string-name>, <string-name><surname>Stiles</surname> <given-names>DK</given-names></string-name></person-group>. <article-title>Sheep&#x2019;s wool insulation: a sustainable alternatice use of renewable ressource</article-title>. <source>Ressour Conserv Recycl</source>. <year>2014</year>;<volume>86</volume>(<issue>C</issue>):<fpage>9</fpage>&#x2013;<lpage>15</lpage>.</mixed-citation></ref>
<ref id="ref-4"><label>4.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Patnaik</surname> <given-names>A</given-names></string-name>, <string-name><surname>Mvubu</surname> <given-names>M</given-names></string-name>, <string-name><surname>Muniyasamy</surname> <given-names>S</given-names></string-name>, <string-name><surname>Botha</surname> <given-names>A</given-names></string-name>, <string-name><surname>Anandjiwala</surname> <given-names>RD</given-names></string-name></person-group>. <article-title>Thermal and sound insulation materials from waste wool and recycled polyester fibers and their biodegradation studies</article-title>. <source>Energy Build</source>. <year>2015 Apr 1</year>;<volume>92</volume>:<fpage>161</fpage>&#x2013;<lpage>9</lpage>.</mixed-citation></ref>
<ref id="ref-5"><label>5.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Zach</surname> <given-names>J</given-names></string-name>, <string-name><surname>Korjenic</surname> <given-names>A</given-names></string-name>, <string-name><surname>Petr&#x00E1;nek</surname> <given-names>V</given-names></string-name>, <string-name><surname>Hroudov&#x00E1;</surname> <given-names>J</given-names></string-name>, <string-name><surname>Bednar</surname> <given-names>T</given-names></string-name></person-group>. <article-title>Performance evaluation and research of alternative thermal insulations based on sheep wool</article-title>. <source>Energy Build</source>. <year>2012 Jun 1</year>;<volume>49</volume>:<fpage>246</fpage>&#x2013;<lpage>53</lpage>.</mixed-citation></ref>
<ref id="ref-6"><label>6.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Tiza</surname> <given-names>TM</given-names></string-name>, <string-name><surname>Singh</surname> <given-names>SK</given-names></string-name>, <string-name><surname>Kumar</surname> <given-names>L</given-names></string-name>, <string-name><surname>Shettar</surname> <given-names>MP</given-names></string-name>, <string-name><surname>Singh</surname> <given-names>SP</given-names></string-name></person-group>. <article-title>Assessing the potentials of Bamboo and sheep wool fiber as sustainable construction materials: a review</article-title>. <source>Mater Today Proc</source>. <year>2021 Jan 1</year>;<volume>47</volume>:<fpage>4484</fpage>&#x2013;<lpage>9</lpage>.</mixed-citation></ref>
<ref id="ref-7"><label>7.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Ghermezgoli</surname> <given-names>ZM</given-names></string-name>, <string-name><surname>Moezzi</surname> <given-names>M</given-names></string-name>, <string-name><surname>Yekrang</surname> <given-names>J</given-names></string-name>, <string-name><surname>Rafat</surname> <given-names>SA</given-names></string-name>, <string-name><surname>Soltani</surname> <given-names>P</given-names></string-name>, <string-name><surname>Barez</surname> <given-names>F</given-names></string-name></person-group>. <article-title>Sound absorption and thermal insulation characteristics of fabrics made of pure and crossbred sheep waste wool</article-title>. <source>J Build Eng</source>. <year>2021 Mar 1</year>;<volume>35</volume>:<fpage>102060</fpage>.</mixed-citation></ref>
<ref id="ref-8"><label>8.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>D&#x00E9;nes</surname> <given-names>O</given-names></string-name>, <string-name><surname>Florea</surname> <given-names>I</given-names></string-name>, <string-name><surname>Manea</surname> <given-names>DL</given-names></string-name></person-group>. <article-title>Utilization of sheep wool as a building material</article-title>. <source>Procedia Manuf</source>. <year>2019 Jan 1</year>;<volume>32</volume>:<fpage>236</fpage>&#x2013;<lpage>41</lpage>.</mixed-citation></ref>
<ref id="ref-9"><label>9.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Mounir</surname> <given-names>S</given-names></string-name>, <string-name><surname>Maaloufa</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Abdelhamid</surname> <given-names>K</given-names></string-name>, <string-name><surname>El Harrouni</surname> <given-names>K</given-names></string-name></person-group>. <article-title>Characterization of thermal inertia and footprint carbon of clay-wool, clay-cork, and clay-plastic composites</article-title>. <source>Key Eng Mater</source>. <year>2021</year>;<volume>886</volume>:<fpage>213</fpage>&#x2013;<lpage>27</lpage>.</mixed-citation></ref>
<ref id="ref-10"><label>10.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Maaloufa</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Mounir</surname> <given-names>S</given-names></string-name>, <string-name><surname>Abdelhamid</surname> <given-names>K</given-names></string-name>, <string-name><surname>El Harrouni</surname> <given-names>K</given-names></string-name></person-group>. <article-title>Influence of the kind and the shape of insulating materials on the mechanical properties of the composites plaster-granular cork and plaster-fiber alpha</article-title>. <source>Key Eng Mater</source>. <year>2021</year>;<volume>886</volume>:<fpage>241</fpage>&#x2013;<lpage>55</lpage>.</mixed-citation></ref>
<ref id="ref-11"><label>11.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Alyousef</surname> <given-names>R</given-names></string-name>, <string-name><surname>Alabduljabbar</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mohammadhosseini</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mohamed</surname> <given-names>AM</given-names></string-name>, <string-name><surname>Siddika</surname> <given-names>A</given-names></string-name>, <string-name><surname>Alrshoudi</surname> <given-names>F</given-names></string-name>, <etal>et al</etal></person-group>. <article-title>Utilization of sheep wool as potential fibrous materials in the production of concrete composites</article-title>. <source>J Build Eng</source>. <year>2020 Jul 1</year>;<volume>30</volume>:<fpage>101216</fpage>.</mixed-citation></ref>
<ref id="ref-12"><label>12.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Parlato</surname> <given-names>MCM</given-names></string-name>, <string-name><surname>Porto</surname> <given-names>SMC</given-names></string-name>, <string-name><surname>Valenti</surname> <given-names>F</given-names></string-name></person-group>. <article-title>Assessment of sheep wool waste as new resource for green building elements</article-title>. <source>Build Environ</source>. <year>2022 Nov 1</year>;<volume>225</volume>:<fpage>109596</fpage>.</mixed-citation></ref>
<ref id="ref-13"><label>13.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Zormati</surname> <given-names>S</given-names></string-name>, <string-name><surname>Aloulou</surname> <given-names>F</given-names></string-name>, <string-name><surname>Sammouda</surname> <given-names>H</given-names></string-name></person-group>. <article-title>Effects of cationic surfactant on fresh and hardened properties of cement-based mortar</article-title>. <source>J Renew Mater</source>. <year>2023</year>;<volume>11</volume>(<issue>5</issue>):<fpage>2345</fpage>&#x2013;<lpage>65</lpage>.</mixed-citation></ref>
<ref id="ref-14"><label>14.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Alsamaraie</surname> <given-names>ARA</given-names></string-name>, <string-name><surname>Samin</surname> <given-names>PM</given-names></string-name>, <string-name><surname>Mazali</surname> <given-names>II</given-names></string-name>, <string-name><surname>Jadallah</surname> <given-names>AA</given-names></string-name>, <string-name><surname>Sultan</surname> <given-names>KF</given-names></string-name></person-group>. <article-title>Insulation materials based on recycled feather waste: a review</article-title>. <source>Tikrit J Eng Sci</source>. <year>2023 Mar 31</year>;<volume>30</volume>(<issue>1</issue>):<fpage>104</fpage>&#x2013;<lpage>11</lpage>.</mixed-citation></ref>
<ref id="ref-15"><label>15.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Aloulou</surname> <given-names>F</given-names></string-name>, <string-name><surname>Alila</surname> <given-names>S</given-names></string-name>, <string-name><surname>Sammouda</surname> <given-names>H</given-names></string-name></person-group>. <article-title>Stabilization and evaluation of modified nanofiber flour wood on the properties of cement-baszd mortar</article-title>. <source>J Renew Mater</source>. <year>2019</year>;<volume>7</volume>(<issue>8</issue>):<fpage>763</fpage>&#x2013;<lpage>74</lpage>. doi:<pub-id pub-id-type="doi">10.32604/jrm.2019.04071</pub-id>.</mixed-citation></ref>
<ref id="ref-16"><label>16.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Abdulmunem</surname> <given-names>AR</given-names></string-name>, <string-name><surname>Hamed</surname> <given-names>HM</given-names></string-name>, <string-name><surname>Samin</surname> <given-names>PM</given-names></string-name>, <string-name><surname>Mazali</surname> <given-names>II</given-names></string-name>, <string-name><surname>Sopian</surname> <given-names>K</given-names></string-name></person-group>. <article-title>Thermal management of lithium-ion batteries using palm fatty acid distillate as a sustainable bio-phase change material</article-title>. <source>J Energy Storage</source>. <year>2023 Dec 15</year>;<volume>73</volume>:<fpage>109187</fpage>.</mixed-citation></ref>
<ref id="ref-17"><label>17.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Abdulmunem</surname> <given-names>AR</given-names></string-name>, <string-name><surname>Samin</surname> <given-names>PM</given-names></string-name>, <string-name><surname>Sopian</surname> <given-names>K</given-names></string-name>, <string-name><surname>Hoseinzadeh</surname> <given-names>S</given-names></string-name>, <string-name><surname>Al-Jaber</surname> <given-names>HA</given-names></string-name>, <string-name><surname>Garcia</surname> <given-names>DA</given-names></string-name></person-group>. <article-title>Waste chicken feathers integrated with phase change materials as new inner insulation envelope for buildings</article-title>. <source>J Energy Storage</source>. <year>2022 Dec 1</year>;<volume>56</volume>:<fpage>106130</fpage>.</mixed-citation></ref>
<ref id="ref-18"><label>18.</label><mixed-citation publication-type="other"><person-group person-group-type="author"><collab>Camphor</collab></person-group>. <article-title>Wikipedia</article-title>. <comment>Available from:</comment> <ext-link ext-link-type="uri" xlink:href="https://en.wikipedia.org/w/index.php?title=Camphor&#x0026;oldid=1215167469">https://en.wikipedia.org/w/index.php?title=Camphor&#x0026;oldid=1215167469</ext-link>. <comment>[Accessed 2023]</comment>.</mixed-citation></ref>
<ref id="ref-19"><label>19.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><collab>Afnor EDITIONS</collab></person-group>. <article-title>NF EN ISO 4833-1</article-title>. <year>2013</year>. Available from: <ext-link ext-link-type="uri" xlink:href="https://www.boutique.afnor.org/fr-fr/norme/nf-en-iso-48331/microbiologie-des-aliments-methode-horizontale-pour-le-denombrement-des-mic/fa163727/42192">https://www.boutique.afnor.org/fr-fr/norme/nf-en-iso-48331/microbiologie-des-aliments-methode-horizontale-pour-le-denombrement-des-mic/fa163727/42192</ext-link>. <comment>[Accessed 2013]</comment>.</mixed-citation></ref>
<ref id="ref-20"><label>20.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Li</surname> <given-names>F</given-names></string-name>, <string-name><surname>Shang</surname> <given-names>F</given-names></string-name>, <string-name><surname>Cheng</surname> <given-names>S</given-names></string-name>, <string-name><surname>Ma</surname> <given-names>W</given-names></string-name>, <string-name><surname>Jin</surname> <given-names>H</given-names></string-name>, <string-name><surname>Zhang</surname> <given-names>X</given-names></string-name>, <etal>et al.</etal></person-group> <article-title>Thermal conductivity measurements of the H<sub>2</sub>/CO<sub>2</sub> mixture using the short-hot-wire method at 323.15&#x2013;620.05 K and 2.14&#x2013;9.37 MPa</article-title>. <source>Int J Hydrog Energy</source>. <year>2020 Nov 6</year>;<volume>45</volume>(<issue>55</issue>):<fpage>31213</fpage>&#x2013;<lpage>24</lpage>.</mixed-citation></ref>
<ref id="ref-21"><label>21.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Bobda</surname> <given-names>F</given-names></string-name>, <string-name><surname>Claude Damfeu</surname> <given-names>J</given-names></string-name>, <string-name><surname>Ngono Mvondo</surname> <given-names>RR</given-names></string-name>, <string-name><surname>Meukam</surname> <given-names>P</given-names></string-name>, <string-name><surname>Jannot</surname> <given-names>Y</given-names></string-name></person-group>. <article-title>Thermal properties measurement of two tropical wood species as a function of their water content using the parallel hot wire method</article-title>. <source>Constr Build Mater</source>. <year>2022 Feb 21</year>;<volume>320</volume>:<fpage>125974</fpage>.</mixed-citation></ref>
<ref id="ref-22"><label>22.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Jannot</surname> <given-names>Y</given-names></string-name>, <string-name><surname>Degiovanni</surname> <given-names>A</given-names></string-name>, <string-name><surname>Schick</surname> <given-names>V</given-names></string-name>, <string-name><surname>Meulemans</surname> <given-names>J</given-names></string-name></person-group>. <article-title>Apparent thermal conductivity measurement of anisotropic insulating materials at high temperature by the parallel hot-wire method</article-title>. <source>Int J Therm Sci</source>. <year>2021 Feb 1</year>;<volume>160</volume>:<fpage>106672</fpage>.</mixed-citation></ref>
<ref id="ref-23"><label>23.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Parker</surname> <given-names>WJ</given-names></string-name>, <string-name><surname>Jenkins</surname> <given-names>RJ</given-names></string-name>, <string-name><surname>Butler</surname> <given-names>CP</given-names></string-name>, <string-name><surname>Abbott</surname> <given-names>GL</given-names></string-name></person-group>. <article-title>Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity</article-title>. <source>J Appl Phys</source>. <year>1961 Sep 1</year>;<volume>32</volume>(<issue>9</issue>):<fpage>1679</fpage>&#x2013;<lpage>84</lpage>.</mixed-citation></ref>
<ref id="ref-24"><label>24.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Degiovanni</surname> <given-names>A</given-names></string-name>, <string-name><surname>Laurent</surname> <given-names>M</given-names></string-name>, <string-name><surname>Prost</surname> <given-names>R</given-names></string-name></person-group>. <article-title>Mesure automatique de la diffusivit&#x00E9; thermique</article-title>. <source>Rev Phys Appliqu&#x00E9;e</source>. <year>1979</year>;<volume>14</volume>(<issue>11</issue>):<fpage>927</fpage>&#x2013;<lpage>32</lpage>.</mixed-citation></ref>
<ref id="ref-25"><label>25.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Degiovanni</surname> <given-names>A</given-names></string-name>, <string-name><surname>Laurent</surname> <given-names>M</given-names></string-name></person-group>. <article-title>Une nouvelle technique d&#x2019;identification de la diffusivit&#x00E9; thermique pour la m&#x00E9;thode &#x00AB; flash &#x00BB;</article-title>. <source>Rev Phys Appliqu&#x00E9;e</source>. <year>1986</year>;<volume>21</volume>(<issue>3</issue>):<fpage>229</fpage>&#x2013;<lpage>37</lpage>.</mixed-citation></ref>
<ref id="ref-26"><label>26.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Jerman</surname> <given-names>M</given-names></string-name>, <string-name><surname>Palomar</surname> <given-names>I</given-names></string-name>, <string-name><surname>Ko&#x010D;&#x00ED;</surname> <given-names>V</given-names></string-name>, <string-name><surname>&#x010C;ern&#x00FD;</surname> <given-names>R</given-names></string-name></person-group>. <article-title>Thermal and hygric properties of biomaterials suitable for interior thermal insulation systems in historical and traditional buildings</article-title>. <source>Build Environ</source>. <year>2019 May 1</year>;<volume>154</volume>:<fpage>81</fpage>&#x2013;<lpage>8</lpage>.</mixed-citation></ref>
<ref id="ref-27"><label>27.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Alyousef</surname> <given-names>R</given-names></string-name>, <string-name><surname>Alabduljabbar</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mohammadhosseini</surname> <given-names>H</given-names></string-name>, <string-name><surname>Mohamed</surname> <given-names>AM</given-names></string-name>, <string-name><surname>Siddika</surname> <given-names>A</given-names></string-name>, <string-name><surname>Alrshoudi</surname> <given-names>F</given-names></string-name></person-group>. <article-title>Utilization of sheep wool as potential fibrous materials in the production of concrete composites</article-title>. <source>J Build Eng</source>. <year>2020 Jul</year>;<volume>30</volume>:<fpage>101216</fpage>.</mixed-citation></ref>
<ref id="ref-28"><label>28.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Moore</surname> <given-names>KE</given-names></string-name>, <string-name><surname>Mangos</surname> <given-names>DN</given-names></string-name>, <string-name><surname>Slattery</surname> <given-names>AD</given-names></string-name>, <string-name><surname>Raston</surname> <given-names>CL</given-names></string-name>, <string-name><surname>Boulos</surname> <given-names>RA</given-names></string-name></person-group>. <article-title>Wool deconstruction using a benign eutectic melt</article-title>. <source>RSC Adv</source>. <year>2016 Feb 16</year>;<volume>6</volume>(<issue>24</issue>):<fpage>20095</fpage>&#x2013;<lpage>101</lpage>.</mixed-citation></ref>
<ref id="ref-29"><label>29.</label><mixed-citation publication-type="book"><person-group person-group-type="author"><string-name><surname>Chahwane</surname> <given-names>L</given-names></string-name></person-group>. <source>Valorisation de l&#x2019;inertie thermique pour la performance &#x00E9;nerg&#x00E9;tique des b&#x00E2;timents [phdthesis]</source>. <publisher-loc>Universit&#x00E9; de Grenoble</publisher-loc>; <year>2011</year>. Available from: <ext-link ext-link-type="uri" xlink:href="https://theses.hal.science/tel-00701170">https://theses.hal.science/tel-00701170</ext-link>. <comment>[Accessed 2011]</comment>.</mixed-citation></ref>
<ref id="ref-30"><label>30.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Asdrubali</surname> <given-names>F</given-names></string-name>, <string-name><surname>Baldinelli</surname> <given-names>G</given-names></string-name></person-group>. <article-title>Thermal transmittance measurements with the hot box method: calibration, experimental procedures, and uncertainty analyses of three different approaches</article-title>. <source>Energy Build</source>. <year>2011 Jul</year>;<volume>43</volume>(<issue>7</issue>):<fpage>1618</fpage>&#x2013;<lpage>26</lpage>.</mixed-citation></ref>
<ref id="ref-31"><label>31.</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><surname>Anjum</surname> <given-names>F</given-names></string-name>, <string-name><surname>Yasin Naz</surname> <given-names>M</given-names></string-name>, <string-name><surname>Ghaffar</surname> <given-names>A</given-names></string-name>, <string-name><surname>Kamran</surname> <given-names>K</given-names></string-name>, <string-name><surname>Shukrullah</surname> <given-names>S</given-names></string-name>, <string-name><surname>Ullah</surname> <given-names>S</given-names></string-name></person-group>. <article-title>Sustainable insulating porous building materials for energy-saving perspective: stones to environmentally friendly bricks</article-title>. <source>Constr Build Mater</source>. <year>2022 Feb 7</year>;<volume>318</volume>:<fpage>125930</fpage>.</mixed-citation></ref>
</ref-list>
</back>
</article>