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<article article-type="research-article" dtd-version="3.0" xml:lang="en" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
	<front>
		<journal-meta>
			<journal-id journal-id-type="publisher-id">MC</journal-id>
			<journal-title-group>
				<journal-title>Materiales de Construcci&#x00F3;n</journal-title>
			</journal-title-group>
			<issn pub-type="epub">0465-2746</issn>
			<publisher>
				<publisher-name>Consejo Superior de Investigaciones Cientificas</publisher-name>
			</publisher>
		</journal-meta>
		<article-meta>
			<article-id pub-id-type="publisher-id">MC201614_e096</article-id>
			<article-id pub-id-type="doi">10.3989/mc.2016.08115</article-id>
			<article-categories>
				<subj-group subj-group-type="heading">
					<subject>Articles</subject>
				</subj-group>
			</article-categories>
			<title-group>
				<article-title>Influence of the type of lightweight clay brick on the equivalent thermal transmittance of different types of fa&#x00E7;ades on buildings</article-title>
				<trans-title-group xml:lang="es">
					<trans-title>Influencia del tipo de bloque de arcilla aligerada en la transmitancia t&#x00E9;rmica equivalente de diferentes tipos de fachadas en edificios</trans-title>
				</trans-title-group>
				<alt-title alt-title-type="running-head">Influence of the type of lightweight clay brick</alt-title>
			</title-group>
			<contrib-group>
				<contrib contrib-type="author">
					<name>
						<surname>Morales</surname>
						<given-names>M.P.</given-names>
					</name>
					<xref ref-type="aff" rid="AF0001">a</xref>
					<xref ref-type="aff" rid="AF0002">b</xref>
				</contrib>
				<contrib contrib-type="author">
					<name>
						<surname>Mu&#x00F1;oz</surname>
						<given-names>P.</given-names>
					</name>
					<xref ref-type="aff" rid="AF0003">c</xref>
				</contrib>
				<contrib contrib-type="author" corresp="yes">
					<name>
						<surname>Ju&#x00E1;rez</surname>
						<given-names>M.C.</given-names>
					</name>
					<xref ref-type="aff" rid="AF0004">d</xref>
					<xref ref-type="corresp" rid="cor1">&#x002A;</xref>
				</contrib>
				<contrib contrib-type="author">
					<name>
						<surname>Mend&#x00ED;vil</surname>
						<given-names>M.A.</given-names>
					</name>
					<xref ref-type="aff" rid="AF0004">d</xref>
				</contrib>
				<contrib contrib-type="author">
					<name>
						<surname>Olasolo</surname>
						<given-names>P.</given-names>
					</name>
					<xref ref-type="aff" rid="AF0004">d</xref>
				</contrib>
			</contrib-group>
			<aff id="AF0001">
				<label>a</label>Facultad de Ingenier&#x00ED;a, Universidad Aut&#x00F3;noma de Chile, (Providencia, Santiago, Chile)</aff>
			<aff id="AF0002">
				<label>b</label>Research Group: MOdelaci&#x00F3;n Matem&#x00E1;tica Aplicada a la INgenier&#x00ED;a (MOMAIN), Universidad Internacional de La Rioja (UNIR),-(Logro&#x00F1;o, Spain)</aff>
			<aff id="AF0003">
				<label>c</label>Facultad de Ingenier&#x00ED;a Civil, Universidad Aut&#x00F3;noma de Chile, Talca- Chile</aff>
			<aff id="AF0004">
				<label>d</label>Escuela T&#x00E9;cnica Superior de Ingenier&#x00ED;a Industrial. Universidad de La Rioja,-(Logro&#x00F1;o, Spain)</aff>
			<author-notes>
				<corresp id="cor1"><label>&#x002A;</label><email xlink:href="manuel.juarez@unirioja.es">manuel.juarez@unirioja.es</email>
				</corresp>
			</author-notes>
			<pub-date pub-type="epub">
				<day>30</day>
				<month>09</month>
				<year>2016</year>
			</pub-date>
			<pub-date pub-type="collection">
				<year>2016</year>
			</pub-date>
			<volume>66</volume>
			<issue>323</issue>
			<elocation-id content-type="doi">10.3989/mc.2016.08115</elocation-id>
			<history>
				<date date-type="received">
					<day>18</day>
					<month>09</month>
					<year>2015</year>
				</date>
				<date date-type="accepted">
					<day>22</day>
					<month>02</month>
					<year>2016</year>
				</date>
				<date date-type="Available on line">
					<day>20</day>
					<month>07</month>
					<year>2016</year>
				</date>
			</history>
			<permissions>
				<copyright-statement>&#x00A9; 2016 CSIC</copyright-statement>
				<copyright-year>2016</copyright-year>
				<license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/3.0/es/deed.en">
					<license-p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) Spain 3.0.</license-p>
				</license>
			</permissions>
			<abstract>
				<title>ABSTRACT</title>
				<p>This paper compares the equivalent thermal transmittances of different fa&#x00E7;ades built using commercial clay bricks with three different thicknesses and fa&#x00E7;ades made using the same method but with ceramic bricks with optimized rhomboidal interior geometry.</p>
				<p>Equivalent thermal transmittances of 0.300 W/m<sup>2</sup>&#x00B7;K were recorded for the rhomboidal brick with a thickness of 0.290 m and a fa&#x00E7;ade with thermo-acoustic insulation and a large format brick on the interior, but the final thickness of the fa&#x00E7;ade was 0.445 m.</p>
				<p>For ventilated fa&#x00E7;ades made of the proposed rhomboidal brick with thicknesses of 0.290 and 0.240 m an 8&#x2013;9% improvement was found, with values of 0.312 W/m<sup>2</sup>&#x00B7;K and 0.339 W/m<sup>2</sup>&#x00B7;K, respectively.</p>
				<p>It can be concluded that in view of the small difference in thermal terms, the best option is to use a brick 0.240 m thick, as the overall thickness of the fa&#x00E7;ade will not then exceed 0.300 m.</p>
				</abstract>
				<trans-abstract xml:lang="es">
				<title>RESUMEN</title>
				<p><italic>Influencia del tipo de bloque de arcilla aligerada en la transmitancia t&#x00E9;rmica equivalente de diferentes tipos de fachadas en edificios</italic>. En el presente trabajo se comparan las transmitancias t&#x00E9;rmicas equivalentes de diferentes fachadas ejecutadas con bloques comerciales de tres espesores 0,290 m, 0,240 m y 0,190 m, con el mismo montaje pero con un bloque cer&#x00E1;mico optimizado con geometr&#x00ED;a interior romboidal.</p>
				<p>Se ha obtenido una transmitancia t&#x00E9;rmica equivalente de 0,300 W/m<sup>2</sup>&#x00B7;K para el ladrillo con geometr&#x00ED;a romboidal de 0,290 m de espesor y pared con aislamiento termoac&#x00FA;stico y gran formato en el interior, con un espesor total de fachada de 0,445 m.</p>
				<p>Para fachadas ventiladas con el ladrillo romboidal propuesto con espesores de 0,290 y 0,240 m, se obtiene una mejora de un 8%&#x2013;9%, con valores de 0,312 W/m<sup>2</sup>&#x00B7;K y 0,339 W/m<sup>2</sup>&#x00B7;K, respectivamente.</p>
				<p>Podemos concluir que, dada la peque&#x00F1;a diferencia en t&#x00E9;rminos t&#x00E9;rmicos, la mejor opci&#x00F3;n es el uso de ladrillos de 0,240 m de espesor, siempre y cuando el espesor total de fachada no exceda los 0,300 m.</p>
			</trans-abstract>
			<kwd-group xml:lang="en">
			<title>KEYWORDS</title>
				<kwd>Brick</kwd>
				<kwd>Ceramic</kwd>
				<kwd>Physical properties</kwd>
				<kwd>Thermal analysis</kwd>
				<kwd>Finite element method</kwd>
				</kwd-group>
				<kwd-group xml:lang="es">
				<title>PALABRAS CLAVE</title>
				<kwd>Ladrillo</kwd>
				<kwd>Cer&#x00E1;mica</kwd>
				<kwd>Propiedades f&#x00ED;sicas</kwd>
				<kwd>An&#x00E1;lisis t&#x00E9;rmico</kwd>
				<kwd>M&#x00E9;todo de los elementos finitos</kwd>
			</kwd-group>
		</article-meta>
	</front>
	<body>
		<sec id="S0001" sec-type="intro">
			<title>1. INTRODUCTION</title>
			<p>Improving the energy efficiency of machinery and premises is one of the most important ways of achieving global energy sustainability. Energy that is not used is the cheapest energy of all.</p>
			<p>Many buildings are ecologically unsustainable: they are not environmentally friendly, and may even be causing pollution by consuming large quantities of energy, with the substantial harmful atmospheric emissions that this entails (<xref ref-type="bibr" rid="CIT0001">1</xref>).</p>
			<p>Buildings are large consumers of thermal energy. In fact, the residential and services sectors account for around 27% of the total energy consumed in the EU-28, i.e. 275 MTEP (Million-Ton Equivalent of Petroleum) (<xref ref-type="bibr" rid="CIT0002">2</xref>). Much of this energy is used in air conditioning.</p>
			<p>One construction solution for outer envelopes that is now being implemented to improve the thermal efficiency of buildings and reduce energy losses is to use low-density, &#x201C;lightweight&#x201D; clay bricks.</p>
			<p>Recent studies have considered the impact of the cladding materials used on building walls on CO<sub>2</sub> emissions, and their influence on energy consumption (<xref ref-type="bibr" rid="CIT0003">3</xref>). Other studies have sought to further improve the materials used in building envelopes by showing how the porous nature of clay bricks can improve thermal characteristics (<xref ref-type="bibr" rid="CIT0004">4</xref>&#x2013;<xref ref-type="bibr" rid="CIT0006">6</xref>).</p>
			<p>Numerous studies have been conducted on the materials used in building envelopes. These studies have individually characterized the influence of the type of internal void in large format bricks (<xref ref-type="bibr" rid="CIT0007">7</xref>&#x2013;<xref ref-type="bibr" rid="CIT0013">13</xref>) and the type of tongue and groove system (<xref ref-type="bibr" rid="CIT0014">14</xref>, <xref ref-type="bibr" rid="CIT0015">15</xref>) as regards clay-air and clay-mortar cross-sections (see <xref ref-type="fig" rid="F0007">Fig. 7</xref>), along with the influence of the horizontal joint on the cross-section of the layer of bonding mortar itself (<xref ref-type="bibr" rid="CIT0016">16</xref>). Recent studies have shown that optimizing the internal geometry of bricks with a thickness of 0.290 m may lead to improvements of as much as 23% in the equivalent thermal transmittance of single-leaf walls (<xref ref-type="bibr" rid="CIT0017">17</xref>).</p>
			<p>Other studies have looked at reducing the thermal conductivity of clay by using additives, and have shown how those additives reduce thermal conductivity due to gas micropores generated in the volume of baked clay (<xref ref-type="bibr" rid="CIT0018">18</xref>&#x2013;<xref ref-type="bibr" rid="CIT0022">22</xref>). Industry manufacturers have added paper pulp to their clays, giving them conductivity levels of around 0.500 W/m&#x00B7;K. These clays are then used to make bricks called Termoarcilla<sup>TM</sup> in thicknesses of between 0.290 m and 0.140 m.</p>
			<p>The research reported here studies the possibility of improving the equivalent thermal transmittance of building fa&#x00E7;ades by using bricks available on the market with thicknesses of 0.290 m, 0.240 m and 0.190 m, and optimized internal geometry with rhomboidal internal voids (<xref ref-type="bibr" rid="CIT0007">7</xref>, <xref ref-type="bibr" rid="CIT0008">8</xref>, <xref ref-type="bibr" rid="CIT0009">9</xref>, <xref ref-type="bibr" rid="CIT0011">11</xref>, <xref ref-type="bibr" rid="CIT0012">12</xref>, <xref ref-type="bibr" rid="CIT0013">13</xref>) on different types of fa&#x00E7;ade. The focus is on single-leaf fa&#x00E7;ades, ventilated fa&#x00E7;ades, fa&#x00E7;ades with an outside thermal insulation system, and fa&#x00E7;ades with a thermo-acoustic insulation system with cladding made of large format bricks 0.070 m thick. As demonstrated below, these are the solutions that provide the best thermal results on today&#x0027;s market. This study also considers a continuous tongue and groove system, as propounded by several authors (<xref ref-type="bibr" rid="CIT0014">14</xref>, <xref ref-type="bibr" rid="CIT0015">15</xref>).</p>
			<p>Equivalent thermal transmittance, <italic>U</italic>
				<sub>
					<italic>eq</italic>
				</sub> [W/m<sup>2</sup>&#x00B7;K], is calculated in all cases in accordance with Spanish standards (<xref ref-type="bibr" rid="CIT0023">23</xref>, <xref ref-type="bibr" rid="CIT0024">24</xref>), EN European Standards (<xref ref-type="bibr" rid="CIT0025">25</xref>&#x2013;<xref ref-type="bibr" rid="CIT0030">30</xref>) and ISO International Standards (<xref ref-type="bibr" rid="CIT0031">31</xref>, <xref ref-type="bibr" rid="CIT0032">32</xref>). The thermal conductivity of each uncoated brick proposed is calculated using COMSOL Multiphysics software (<xref ref-type="bibr" rid="CIT0033">33</xref>).</p>
		</sec>
		<sec id="S0002" sec-type="materials|method">
			<title>2. MATERIALS AND METHOD</title>
			<sec id="S20003">
				<title>2.1. Bricks under study</title>
				<p>As its reference product, the study took commercially available Termoarcilla<sup>TM</sup> bricks with a herringbone internal geometry and three different thicknesses (with &#x201C;thickness&#x201D; taken to mean the dimension in the direction of which heat flows through the wall): 0.290 m, 0.240 m and 0.190 m, as shown in <xref ref-type="fig" rid="F0001">Fig. 1</xref>.</p>
				<fig id="F0001">
					<label>Figure 1</label>
					<caption>
						<p>Commercial Termoarcilla<sup>TM</sup> brick (<xref ref-type="bibr" rid="CIT0034">34</xref>).</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g001.tif"/>
				</fig>
				<p>The bricks proposed in this research had a rhomboidal internal geometry and a tongue and groove configuration with internal voids extending into them, referred to as a &#x201C;continuous tongue and groove system&#x201D; (<xref ref-type="bibr" rid="CIT0010">10</xref>). No changes were made in dimensions, so the height of 0.192 m, length of 0.307 m and thicknesses of 0.290, 0.240 and 0.190 m found in the commercial bricks were maintained. These bricks are shown in <xref ref-type="fig" rid="F0002">Fig. 2</xref>.</p>
				<fig id="F0002">
					<label>Figure 2</label>
					<caption>
						<p>Proposed bricks with rhomboidal internal voids.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g002.tif"/>
				</fig>
				<p>The study considered the same clays used by the commercial manufacturers, with paper pulp as an additive. Clay conductivity was 0.500 W/m&#x00B7;K, measured by the hot plate method as specified in (<xref ref-type="bibr" rid="CIT0035">35</xref>). This is a value reported by almost all the manufacturers of Termoarcilla<sup>TM</sup> bricks consulted. The same conductivity level was considered in all the bricks under study so that the thermal results could be compared.</p>
			</sec>
			<sec id="S20004">
				<title>2.2. Building solutions for the fa&#x00E7;ades under study</title>
				<p>Each different type of fa&#x00E7;ade involves the use of bonding mortars as horizontal joint, plaster renderings and other cladding materials. The conductivity for each material was standardized as per regulations or standard market specifications.</p>
				<p>Following the standard (<xref ref-type="bibr" rid="CIT0023">23</xref>), the horizontal joint is continuous for blocks 0.190 m thick, while for blocks 0.240 m and 0.290 m thick, mortar joint is discontinuous with 0.030 m air.</p>
				<p>This study examines the following types of fa&#x00E7;ade:<list list-type="alpha-lower">
						<list-item>
							<p>
								<bold><italic>Single-leaf fa&#x00E7;ade with a discontinuous joint and 0.030 m air space:</italic></bold> This consisted of clay bricks with a normal thickness of 0.290 m (referred to here as &#x201C;large format&#x201D;), and bricks 0.240 m thick. These bricks were in general clad with a 0.015 m plaster rendering on the inside face, the thermal conductivity of which was 0.57 W/m&#x00B7;K, as per the relevant standard (<xref ref-type="bibr" rid="CIT0023">23</xref>), and clad with mortar on the outside. In this case an ecological mortar consisting of lime, expanded perlite and hollow glass microspheres was used, with a thickness of around 0.025 m and a thermal conductivity of 0.068 W/m&#x00B7;K, according to the manufacturer (<xref ref-type="bibr" rid="CIT0036">36</xref>). An example of the arrangement is shown in <xref ref-type="fig" rid="F0003">Fig. 3</xref>.</p>
							<p>Single-leaf fa&#x00E7;ades provide suitable levels of thermal insulation, offset and shock absorbance, together with excellent thermal inertia. This ensures that they perform well in both summer and winter.</p>
						</list-item>
						<list-item>
							<p>
								<bold><italic>Ventilated fa&#x00E7;ades:</italic></bold> this refers to walls made of clay bricks with an outer insulating layer of rigid polyurethane foam (PUR) with hydrofluorocarbon (HFC) applied to a thickness of 0.040 m, with a thermal conductivity of 0.028 W/m&#x00B7;K, as per the relevant standard (<xref ref-type="bibr" rid="CIT0023">23</xref>), and interior cladding made of rendered plaster with a thickness of around 0.015 m and a thermal conductivity of 0.57 W/m&#x00B7;K, also as per the relevant standard (<xref ref-type="bibr" rid="CIT0023">23</xref>), plus an outer sheet that was not fully sealed (<xref ref-type="bibr" rid="CIT0037">37</xref>). The overall resistance of this outer sheet was calculated without taking into consideration the thermal resistance of the air space and all the other layers between that space and the outside atmosphere, but including an exterior surface resistance for still air conditions equal to the interior surface resistance of the same element, which for vertical fa&#x00E7;ades is 0.13 m<sup>2</sup>&#x00B7;K/W, in line with the relevant standard (<xref ref-type="bibr" rid="CIT0028">28</xref>). An example of the arrangement is shown in <xref ref-type="fig" rid="F0004">Fig. 4</xref>.</p>
							<p>Ventilated fa&#x00E7;ades are a high-performance design for building envelopes whose main feature is to separate the role of waterproofing from the role of thermal insulation. They comply with all requirements in terms of thermal protection, energy saving and environmental protection.</p>
						</list-item>
						<list-item>
							<p>
								<bold><italic>Fa&#x00E7;ade + ETICS</italic></bold> (External Thermal Insulation Composite System): this refers to a fa&#x00E7;ade with a thermal insulation system on the outside (<xref ref-type="bibr" rid="CIT0038">38</xref>, <xref ref-type="bibr" rid="CIT0039">39</xref>). It consisted of clay bricks, inside cladding made of rendered plaster around 0.015 m thick, with a thermal conductivity of 0.57 W/m&#x00B7;K, in line with the relevant standard (<xref ref-type="bibr" rid="CIT0023">23</xref>), and an ETICS outer sheet of insulating material attached to the wall mechanically, by adhesive or by a combination of the two. The insulation was protected by cladding made up of one or more layers applied on site, one of which contained a reinforcing mesh. This cladding was applied directly onto the insulating panel, with no air space or discontinuous layer. It was around 0.040 m thick and its thermal conductivity was 0.037 W/m&#x00B7;K (<xref ref-type="bibr" rid="CIT0040">40</xref>). There was also exterior cladding with a thermal resistance of 0.020 m<sup>2</sup>&#x00B7;K/W, compliant with the relevant standard (<xref ref-type="bibr" rid="CIT0029">29</xref>). An example of the arrangement is shown in <xref ref-type="fig" rid="F0005">Fig. 5</xref>.</p>
							<p>With the ETICS located on the outer face of the envelope, it contributes 90% of the envelope&#x0027;s mass to the building&#x0027;s thermal inertia. This outer insulation resolves any issues of thermal bridges, as the entire thickness of the insulating element is flush against the building envelope.</p>
						</list-item>
						<list-item>
							<p>
								<bold><italic>Fa&#x00E7;ade + ITAICS</italic></bold> (Internal Thermal Acoustic Insulation Composite System) <bold><italic>+LFB</italic></bold> (large format bricks): this consisted of clay with interior rendered plaster cladding around 0.015 m thick with a thermal conductivity of 0.57 W/m&#x00B7;K, compliant with the relevant Spanish standard (<xref ref-type="bibr" rid="CIT0024">24</xref>), an inner sheet consisting of a large format partition with a thickness of around 0.070 m and a thermal conductivity of 0.290 W/m&#x00B7;K, in line with the relevant standard (<xref ref-type="bibr" rid="CIT0024">24</xref>), then ITAICS consisting of glass wool around 0.050 m thick with a thermal conductivity of 0.036 W/m&#x00B7;K, in line with the relevant standard (<xref ref-type="bibr" rid="CIT0041">41</xref>), a layer of pneumatically applied mortar around 0.005 m thick with a thermal conductivity of 0.650 W/m&#x00B7;K (<xref ref-type="bibr" rid="CIT0042">42</xref>), and an outer sheet consisting of a Termoarcilla<sup>TM</sup> brick with an outside coating of mortar. In the case considered here standard mortar around 0.015 m thick was used, with a thermal conductivity of 1.300 W/m&#x00B7;K. An example of the arrangement is shown in <xref ref-type="fig" rid="F0006">Fig. 6</xref> (<xref ref-type="bibr" rid="CIT0043">43</xref>, <xref ref-type="bibr" rid="CIT0044">44</xref>).</p>
						</list-item>
					</list>
				</p>
				<fig id="F0003">
					<label>Figure 3</label>
					<caption>
						<p>Single-leaf fa&#x00E7;ade with blocks 0.290 m thick and discontinuous joint 0.030 m air, view from inside.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g003.tif"/>
				</fig>
				<fig id="F0004">
					<label>Figure 4</label>
					<caption>
						<p>Ventilated fa&#x00E7;ade with blocks 0.290 m thick and discontinuous joint 0.030 m air, view from outside.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g004.tif"/>
				</fig>
				<fig id="F0005">
					<label>Figure 5</label>
					<caption>
						<p>Fa&#x00E7;ade with blocks 0.290 m thick and discontinuous joint 0.030 m air, and external thermal insulation composite system, view from outside.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g005.tif"/>
				</fig>
				<fig id="F0006">
					<label>Figure 6</label>
					<caption>
						<p>Fa&#x00E7;ade with blocks 0.290 m thick and discontinuous joint 0.030 m air, and internal thermal acoustic insulation composite system, view from inside.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g006.tif"/>
				</fig>
			</sec>
			<sec id="S20005">
				<title>2.3. Thermal calculation method</title>
				<p>Thermal calculations were performed according to Spanish standards (<xref ref-type="bibr" rid="CIT0023">23</xref>, <xref ref-type="bibr" rid="CIT0024">24</xref>), EN European Standards (<xref ref-type="bibr" rid="CIT0025">25</xref>&#x2013;<xref ref-type="bibr" rid="CIT0030">30</xref>) and ISO International Standards (<xref ref-type="bibr" rid="CIT0031">31</xref>, <xref ref-type="bibr" rid="CIT0032">32</xref>). The heat flows for the new bricks proposed were resolved using the finite element method (<xref ref-type="bibr" rid="CIT0033">33</xref>), with the boundary conditions specified in the relevant standards.</p>
				<p>The brick cross-section featured vertical perforations referred to as voids. The equivalent conductivity of the air in these voids can only be calculated if they are rectangular, so for non-rectangular voids an equivalent rectangular void was created in accordance with the standard (<xref ref-type="bibr" rid="CIT0024">24</xref>). All the voids in the brick were considered as unventilated air spaces and the thermal conductivity of the air inside them was considered.</p>
				<p>The thermal conductivity of the uncoated clay bricks thus obtained was then used to calculate the equivalent thermal transmittances of the four different types of fa&#x00E7;ade proposed.</p>
				<p>The target model for analysis by numerical methods was the part of the wall represented by the assembly of two bricks as shown in <xref ref-type="fig" rid="F0007">Fig. 7</xref>, where the assembly&#x0027;s three characteristic cross-sections can be seen, along with the height of each one: that of the brick with the voids full of air, referred to as the clay/air cross-section (height <italic>h</italic> <sub>1</sub>), that of the brick with the voids full of binding mortar, referred to as the clay/mortar cross-section (height <italic>h</italic> <sub>2</sub>), and that of the horizontal joint (the &#x201C;tendel cross-section&#x201D;), composed of binding mortar, with height <italic>h</italic> <sub>3</sub>. These heights correspond to a type of standard assembly with binding mortar and penetration into the bricks.</p>
				<fig id="F0007">
					<label>Figure 7</label>
					<caption>
						<p>Part of the wall representing the assembly of two blocks and the heights of each characteristic cross-section.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g007.tif"/>
				</fig>
				<p>Using the finite element method, the first two characteristic cross-sections of each wall (the &#x201C;clay/air cross-section&#x201D; and the &#x201C;clay/mortar cross-section&#x201D;) were obtained with the boundary conditions specified by the aforementioned standards, as shown in <xref ref-type="fig" rid="F0008">Fig. 8</xref>. This gave the heat flow through each characteristic cross-section, <italic>Q<sub>i</sub></italic></p>
				<fig id="F0008">
					<label>Figure 8</label>
					<caption>
						<p>Boundary conditions for obtaining the heat flow, <italic>Q</italic><sub>1</sub>.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g008.tif"/>
				</fig>
				<p>Once the heat flow, <italic>Q<sub>i</sub></italic>, had been calculated it was then possible to find the thermal resistance, <italic>R<sub>i</sub></italic> by equation [<xref ref-type="disp-formula" rid="FD1">1</xref>].<disp-formula id="FD1">
						<alternatives>
						<mml:math id="M1">
							<mml:mrow>
								<mml:msub>
									<mml:mi>R</mml:mi>
									<mml:mi>i</mml:mi>
								</mml:msub>
								<mml:mo>=</mml:mo>
								<mml:mfrac>
									<mml:mrow>
										<mml:mi>L</mml:mi>
										<mml:mo>.</mml:mo>
										<mml:mi>&#x0394;</mml:mi>
										<mml:mi>T</mml:mi>
									</mml:mrow>
									<mml:mrow>
										<mml:msub>
											<mml:mi>Q</mml:mi>
											<mml:mi>i</mml:mi>
										</mml:msub>
									</mml:mrow>
								</mml:mfrac>
								<mml:mo>-</mml:mo>
								<mml:msub>
									<mml:mi>R</mml:mi>
									<mml:mrow>
										<mml:mi>i</mml:mi>
										<mml:mi>c</mml:mi>
									</mml:mrow>
								</mml:msub>
								<mml:mo>-</mml:mo>
								<mml:msub>
									<mml:mi>R</mml:mi>
									<mml:mrow>
										<mml:mi>e</mml:mi>
										<mml:mi>c</mml:mi>
									</mml:mrow>
								</mml:msub>
							</mml:mrow>
						</mml:math>
						<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq1.tif"/>
						</alternatives>
					</disp-formula>
				</p>
				<p>
					<italic>R</italic><sub>1</sub> is the resistance of the clay/air cross-section and <italic>R<sub>i</sub></italic> is that of the clay/mortar cross-section.</p>
				<p>For the horizontal joint, (the &#x201C;tendel cross-section&#x201D;), the data on the conductivity of the bonding mortar and the size of the air joint served immediately to calculate the resistance to the passage of heat:<list list-type="bullet">
						<list-item>
							<p>For a joint with standard mortar and a 0.030 m air gap resistance is given by equation [<xref ref-type="disp-formula" rid="FD2">2</xref>].<disp-formula id="FD2">
									<alternatives>
									<mml:math id="M2">
										<mml:mrow>
											<mml:msub>
												<mml:mi>R</mml:mi>
												<mml:mn>3</mml:mn>
											</mml:msub>
											<mml:mo>=</mml:mo>
											<mml:mfrac>
												<mml:mrow>
													<mml:mi>e</mml:mi>
													<mml:mo>-</mml:mo>
													<mml:mn>0</mml:mn>
													<mml:mo>,</mml:mo>
													<mml:mn>03</mml:mn>
												</mml:mrow>
												<mml:mrow>
													<mml:msub>
														<mml:mi>&#x03BB;</mml:mi>
														<mml:mi>m</mml:mi>
													</mml:msub>
												</mml:mrow>
											</mml:mfrac>
											<mml:mo>+</mml:mo>
											<mml:mfrac>
												<mml:mrow>
													<mml:mn>0.03</mml:mn>
												</mml:mrow>
												<mml:mrow>
													<mml:msub>
														<mml:mi>&#x03BB;</mml:mi>
														<mml:mrow>
															<mml:mi>a</mml:mi>
															<mml:mi>i</mml:mi>
															<mml:mi>r</mml:mi>
														</mml:mrow>
													</mml:msub>
												</mml:mrow>
											</mml:mfrac>
										</mml:mrow>
									</mml:math>
									<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq2.tif"/>
									</alternatives>
								</disp-formula>
							</p>
						</list-item>
						<list-item>
							<p>Whereas for a thin joint resistance is given by equation [<xref ref-type="disp-formula" rid="FD3">3</xref>].<disp-formula id="FD3">
									<alternatives>
									<mml:math id="M3">
										<mml:mrow>
											<mml:msub>
												<mml:mi>R</mml:mi>
												<mml:mn>3</mml:mn>
											</mml:msub>
											<mml:mo>=</mml:mo>
											<mml:mfrac>
												<mml:mi>e</mml:mi>
												<mml:mrow>
													<mml:msub>
														<mml:mi>&#x03BB;</mml:mi>
														<mml:mi>m</mml:mi>
													</mml:msub>
												</mml:mrow>
											</mml:mfrac>
										</mml:mrow>
									</mml:math>
									<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq3.tif"/>
									</alternatives>
								</disp-formula>
							</p>
						</list-item>
					</list>
				</p>
				<p>Where &#x3BB;<sub>m</sub> is the conductivity of the bonding mortar, &#x3BB;<sub>air</sub> is the conductivity of the air, and <italic>e</italic> is the size of the air joint.</p>
				<p>Based on the resistance value for each specific section, <italic>R<sub>i</sub></italic>, the overall resistance for the uncoated wall was determined, depending on the height of each specific section, <italic>h<sub>i</sub></italic>, using equation [<xref ref-type="disp-formula" rid="FD4">4</xref>].<disp-formula id="FD4">
						<alternatives>
						<mml:math id="M4">
							<mml:mrow>
								<mml:msub>
									<mml:mi>R</mml:mi>
									<mml:mrow>
										<mml:mi>U</mml:mi>
										<mml:mi>W</mml:mi>
									</mml:mrow>
								</mml:msub>
								<mml:mo>=</mml:mo>
								<mml:mfrac>
									<mml:mrow>
										<mml:msub>
											<mml:mi>h</mml:mi>
											<mml:mn>1</mml:mn>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>h</mml:mi>
											<mml:mn>2</mml:mn>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>h</mml:mi>
											<mml:mn>3</mml:mn>
										</mml:msub>
									</mml:mrow>
									<mml:mrow>
										<mml:mfrac>
											<mml:mrow>
												<mml:msub>
													<mml:mi>h</mml:mi>
													<mml:mn>1</mml:mn>
												</mml:msub>
											</mml:mrow>
											<mml:mrow>
												<mml:msub>
													<mml:mi>R</mml:mi>
													<mml:mn>1</mml:mn>
												</mml:msub>
											</mml:mrow>
										</mml:mfrac>
										<mml:mo>+</mml:mo>
										<mml:mfrac>
											<mml:mrow>
												<mml:msub>
													<mml:mi>h</mml:mi>
													<mml:mn>2</mml:mn>
												</mml:msub>
											</mml:mrow>
											<mml:mrow>
												<mml:msub>
													<mml:mi>R</mml:mi>
													<mml:mn>2</mml:mn>
												</mml:msub>
											</mml:mrow>
										</mml:mfrac>
										<mml:mo>+</mml:mo>
										<mml:mfrac>
											<mml:mrow>
												<mml:msub>
													<mml:mi>h</mml:mi>
													<mml:mn>3</mml:mn>
												</mml:msub>
											</mml:mrow>
											<mml:mrow>
												<mml:msub>
													<mml:mi>R</mml:mi>
													<mml:mn>3</mml:mn>
												</mml:msub>
											</mml:mrow>
										</mml:mfrac>
									</mml:mrow>
								</mml:mfrac>
							</mml:mrow>
						</mml:math>
						<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq4.tif"/>
						</alternatives>
					</disp-formula>
				</p>
				<p>The data on the conductivity of the component material enabled the resistance to the passage of heat of all the other layers that made up the fa&#x00E7;ade to be calculated immediately via equation [<xref ref-type="disp-formula" rid="FD5">5</xref>].<disp-formula id="FD5">
						<alternatives>
						<mml:math id="M5">
							<mml:mrow>
								<mml:msub>
									<mml:mi>R</mml:mi>
									<mml:mi>n</mml:mi>
								</mml:msub>
								<mml:mo>=</mml:mo>
								<mml:mfrac>
									<mml:mi>e</mml:mi>
									<mml:mrow>
										<mml:msub>
											<mml:mi>&#x03BB;</mml:mi>
											<mml:mi>n</mml:mi>
										</mml:msub>
									</mml:mrow>
								</mml:mfrac>
							</mml:mrow>
						</mml:math>
						<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq5.tif"/>
						</alternatives>
					</disp-formula>
				</p>
				<p>Finally, the equivalent thermal transmittance of the envelope cladding was obtained for each of the four types of fa&#x00E7;ade using equation [<xref ref-type="disp-formula" rid="FD6">6</xref>].<disp-formula id="FD6">
						<alternatives>
						<mml:math id="M6">
							<mml:mrow>
								<mml:msub>
									<mml:mi>U</mml:mi>
									<mml:mi>i</mml:mi>
								</mml:msub>
								<mml:mo>=</mml:mo>
								<mml:mfrac>
									<mml:mn>1</mml:mn>
									<mml:mrow>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mi>T</mml:mi>
										</mml:msub>
									</mml:mrow>
								</mml:mfrac>
								<mml:mo>=</mml:mo>
								<mml:mfrac>
									<mml:mn>1</mml:mn>
									<mml:mrow>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mrow>
												<mml:mi>i</mml:mi>
												<mml:mi>c</mml:mi>
											</mml:mrow>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mrow>
												<mml:mi>U</mml:mi>
												<mml:mi>W</mml:mi>
											</mml:mrow>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mrow>
												<mml:mi>n</mml:mi>
												<mml:mn>1</mml:mn>
											</mml:mrow>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:mn>&#x2026;</mml:mn>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mrow>
												<mml:mi>n</mml:mi>
												<mml:mi>i</mml:mi>
											</mml:mrow>
										</mml:msub>
										<mml:mo>+</mml:mo>
										<mml:msub>
											<mml:mi>R</mml:mi>
											<mml:mrow>
												<mml:mi>e</mml:mi>
												<mml:mi>c</mml:mi>
											</mml:mrow>
										</mml:msub>
									</mml:mrow>
								</mml:mfrac>
							</mml:mrow>
						</mml:math>
						<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-eq6.tif"/>
						</alternatives>
					</disp-formula>
				</p>
				<p>Where <italic>R<sub>ic</sub></italic> and <italic>R<sub>ec</sub></italic> are the thermal resistance of the internal and external cladding, <italic>R<sub>UW</sub></italic> is the thermal resistance of the uncoated wall and <italic>R<sub>n</sub></italic> is the thermal resistance of each layer of insulating materials, air spaces, etc. in the wall.</p>
				<p>For the sake of clarity, a schematic of the thermal network is shown in <xref ref-type="fig" rid="F0009">Fig. 9</xref>.</p>
				<fig id="F0009">
					<label>Figure 9</label>
					<caption>
						<p>Thermal network.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g009.tif"/>
				</fig>
			</sec>
		</sec>
		<sec id="S0006" sec-type="results|discussion">
			<title>3. RESULTS AND DISCUSSION</title>
			<sec id="S20007">
				<title>3.1. Thermal results for commercial Termoarcilla<sup>TM</sup> bricks with herringbone voids, used as a reference</title>
				<p>To compare the results for the new bricks proposed, we sought to characterize the four types of wall assemblies with commercial bricks with herringbone voids, referred to as type 29, 24 and 19 Termoarcilla<sup>TM</sup> bricks.</p>
				<p>As mentioned above, several manufacturers that market these bricks certify a thermal transmittance of around 0.500 W/m&#x00B7;K (<xref ref-type="bibr" rid="CIT0044">44</xref>) for their uncoated bricks based on the thermal conductivity of the clays used in them. The thermal resistances of the uncoated bricks are shown in <xref ref-type="table" rid="T0001">Table 1</xref>.</p>
				<table-wrap id="T0001">
					<label>Table 1</label>
					<caption>
						<p>Properties of Termoarcilla<sup>TM</sup> bricks</p>
					</caption>
					<table frame="hsides" rules="groups">
						<thead>
							<tr>
								<th align="left">Name</th>
								<th align="center">THICKNESS (m)</th>
								<th align="center">THERMAL CONDUCTIVITY (W/m&#x00B7;k)</th>
								<th align="center">THERMAL RESISTANCE UNCOATED (m<sup>2</sup>&#x00B7;K/W)</th>
							</tr>
						</thead>
						<tbody>
							<tr>
								<td align="left">Termoarcilla<sup>TM</sup> 29</td>
								<td align="center">0.290</td>
								<td align="center">0.240</td>
								<td align="center">1.208</td>
							</tr>
							<tr>
								<td align="left">Termoarcilla<sup>TM</sup> 24</td>
								<td align="center">0.240</td>
								<td align="center">0.240</td>
								<td align="center">1.000</td>
							</tr>
							<tr>
								<td align="left">Termoarcilla<sup>TM</sup> 19</td>
								<td align="center">0.190</td>
								<td align="center">0.280</td>
								<td align="center">0.679</td>
							</tr>
						</tbody>
					</table>
				</table-wrap>
				<p>It should be noted that the walls with 0.290 m and 0.240 m bricks considered were made with a discontinuous joint with a 0.030 m air space, in compliance with the relevant standards (<xref ref-type="bibr" rid="CIT0023">23</xref>&#x2013;<xref ref-type="bibr" rid="CIT0032">32</xref>). However the standards do not permit discontinuous joints with the 0.190 m brick, so in that case a continuous mortar joint was used. This means that there were major differences in the thermal conductivity of the bricks.</p>
				<p>The data for the thermal resistance of each brick enabled the equivalent thermal transmittance for each type of fa&#x00E7;ade under study to be obtained. <xref ref-type="table" rid="T0002">Table 2</xref> shows the values for each layer in the building arrangement used for the fa&#x00E7;ade for each assembly using Termoarcilla<sup>TM</sup> 29 bricks, thereby providing the equivalent thermal transmittance.
</p>
				<table-wrap id="T0002">
					<label>Table 2</label>
					<caption>
						<p>Values of each layer in the different types of fa&#x00E7;ades made from a main brick of Termoarcilla<sup>TM</sup> 29, and equivalent thermal transmittance obtained</p>
					</caption>
					<table frame="hsides" rules="groups">
						<thead>
							<tr>
								<th align="left">LAYER No.</th>
								<th align="center">NAME</th>
								<th align="center">THICKNESS (m)</th>
								<th align="center">CONDUCTIVITY (W/m&#x00B7;K)</th>
								<th align="center">RESISTANCE (m<sup>2</sup>&#x00B7;K/W)</th>
							</tr>
						</thead>
						<tbody>
							<tr>
								<td colspan="5" align="center">
									<bold>SINGLE-LEAF FA&#x00C7;ADE</bold>
								</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td align="left">INTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.130</td>
							</tr>
							<tr>
								<td align="left">1</td>
								<td align="left">PLASTER RENDER</td>
								<td align="center">0.015</td>
								<td align="center">0.570</td>
								<td align="center">0.026</td>
							</tr>
							<tr>
								<td align="left">2</td>
								<td align="left">Termoarcilla<sup>TM</sup> 29</td>
								<td align="center">0.290</td>
								<td align="center">0.240</td>
								<td align="center">1.208</td>
							</tr>
							<tr>
								<td align="left">3</td>
								<td align="left">THERMOCAL</td>
								<td align="center">0.025</td>
								<td align="center">0.068</td>
								<td align="center">0.368</td>
							</tr>
							<tr>
								<td align="left">EXTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.040</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left">WALL THICKNESS</td>
								<td align="center">0.330</td>
								<td align="center">RESISTANCE =</td>
								<td align="center">1.772</td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left"/>
								<td align="center"/>
								<td align="center">
									<bold>U</bold>
									<sub>
										<bold>eq</bold>
									</sub>
									<bold>(W/m</bold>
									<sup>
										<bold>2</bold>
									</sup>
									<bold>&#x00B7;K) =</bold>
								</td>
								<td align="center">0.564</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td colspan="5" align="center">
									<bold>VENTILATED FA&#x00C7;ADE</bold>
								</td>
							</tr>
							<tr>
								<td colspan="5">
									<hr/>
								</td>
							</tr>
							<tr>
								<td align="left">INTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.130</td>
							</tr>
							<tr>
								<td align="left">1</td>
								<td align="left">PLASTER RENDER</td>
								<td align="center">0.015</td>
								<td align="center">0.570</td>
								<td align="center">0.026</td>
							</tr>
							<tr>
								<td align="left">2</td>
								<td align="left">Termoarcilla<sup>TM</sup> 29</td>
								<td align="center">0.290</td>
								<td align="center">0.240</td>
								<td align="center">1.208</td>
							</tr>
							<tr>
								<td align="left">3</td>
								<td align="left">POLYURETHANE INSUL</td>
								<td align="center">0.040</td>
								<td align="center">0.028</td>
								<td align="center">1.429</td>
							</tr>
							<tr>
								<td align="left">4</td>
								<td align="left">WELL VENTILATED CHAMBER.</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center"/>
							</tr>
							<tr>
								<td align="left">5</td>
								<td align="left">OUTER SKIN</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center"/>
							</tr>
							<tr>
								<td align="left">EXTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.130</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left">WALL THICKNESS</td>
								<td align="center">0.345</td>
								<td align="center">RESISTANCE =</td>
								<td align="center">2.923</td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left"/>
								<td align="center"/>
								<td align="center">
									<bold>U</bold>
									<sub>
										<bold>eq</bold>
									</sub>
									<bold>(W/m</bold>
									<sup>
										<bold>2</bold>
									</sup>
									<bold>&#x00B7;K) =</bold>
								</td>
								<td align="center">0.342</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td colspan="5" align="center">
									<bold>FA&#x00C7;ADE + ETICS</bold>
								</td>
							</tr>
							<tr>
								<td colspan="5">
									<hr/>
								</td>
							</tr>
							<tr>
								<td align="left">INTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.130</td>
							</tr>
							<tr>
								<td align="left">1</td>
								<td align="left">PLASTER RENDER</td>
								<td align="center">0.015</td>
								<td align="center">0.570</td>
								<td align="center">0.026</td>
							</tr>
							<tr>
								<td align="left">2</td>
								<td align="left">Termoarcilla<sup>TM</sup> 29</td>
								<td align="center">0.290</td>
								<td align="center">0.240</td>
								<td align="center">1.208</td>
							</tr>
							<tr>
								<td align="left">3</td>
								<td align="left">SATEN PROPAM AISTERM</td>
								<td align="center">0.040</td>
								<td align="center">0.037</td>
								<td align="center">1.081</td>
							</tr>
							<tr>
								<td align="left">4</td>
								<td align="left">CLADDING</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.020</td>
							</tr>
							<tr>
								<td align="left">EXTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.040</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left">WALL THICKNESS</td>
								<td align="center">0.345</td>
								<td align="center">RESISTANCE =</td>
								<td align="center">2.506</td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left"/>
								<td align="center"/>
								<td align="center">
									<bold>U</bold>
									<sub>
										<bold>eq</bold>
									</sub>
									<bold>(W/m</bold>
									<sup>
										<bold>2</bold>
									</sup>
									<bold>&#x00B7;K) =</bold>
								</td>
								<td align="center">
									<bold>0.399</bold>
								</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td colspan="5" align="center">
									<bold>FA&#x00C7;ADE + ITAICS + LFB</bold>
								</td>
							</tr>
							<tr>
								<td colspan="5">
									<hr/>
								</td>
							</tr>
							<tr>
								<td align="left">INTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0,130</td>
							</tr>
							<tr>
								<td align="left">1</td>
								<td align="left">PLASTER RENDER</td>
								<td align="center">0.015</td>
								<td align="center">0.570</td>
								<td align="center">0.026</td>
							</tr>
							<tr>
								<td align="left">2</td>
								<td align="left">TGF-7</td>
								<td align="center">0.070</td>
								<td align="center">0.290</td>
								<td align="center">0.241</td>
							</tr>
							<tr>
								<td align="left">3</td>
								<td align="left">GLASS WOOL</td>
								<td align="center">0.050</td>
								<td align="center">0.036</td>
								<td align="center">1.389</td>
							</tr>
							<tr>
								<td align="left">4</td>
								<td align="left">PNEUM. APPL. MORTAR</td>
								<td align="center">0.005</td>
								<td align="center">0.650</td>
								<td align="center">0.008</td>
							</tr>
							<tr>
								<td align="left">5</td>
								<td align="left">Termoarcilla<sup>TM</sup> 29</td>
								<td align="center">0.290</td>
								<td align="center">0.240</td>
								<td align="center">1.208</td>
							</tr>
							<tr>
								<td align="left">6</td>
								<td align="left">SINGLE-LAYER MORTAR</td>
								<td align="center">0.015</td>
								<td align="center">1.300</td>
								<td align="center">0.012</td>
							</tr>
							<tr>
								<td align="left">EXTERIOR</td>
								<td align="left">SURFACE CHANGE</td>
								<td align="center"/>
								<td align="center"/>
								<td align="center">0.040</td>
							</tr>
							<tr>
								<td colspan="5"><hr/></td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left">WALL THICKNESS</td>
								<td align="center">0.445</td>
								<td align="center">RESISTANCE =</td>
								<td align="center">3.054</td>
							</tr>
							<tr>
								<td align="left"/>
								<td align="left"/>
								<td align="center"/>
								<td align="center">
									<bold>U</bold>
									<sub>
										<bold>eq</bold>
									</sub>
									<bold>(W/m</bold>
									<sup>
										<bold>2</bold>
									</sup>
									<bold>&#x00B7;K) =</bold>
								</td>
								<td align="center">0.327</td>
							</tr>
						</tbody>
					</table>
				</table-wrap>
				<p>Once the reference assembly had been characterized for each type of fa&#x00E7;ade, the next step was to compare the thermal results for the fa&#x00E7;ades made with the different thicknesses of commercial bricks proposed for the study.</p>
				<p>
					<xref ref-type="table" rid="T0003">Table 3</xref> shows the equivalent thermal transmittances of the different types of fa&#x00E7;ade and the thicknesses of the walls in question, indicating by how much each type of fa&#x00E7;ade reduced the useful surface area of the housing unit.
</p>
				<table-wrap id="T0003">
					<label>Table 3</label>
					<caption>
						<p>Equivalent thermal transmittance of the envelope for each type of fa&#x00E7;ade with commercial bricks and thicknesses affecting the useful surface area of the housing unit</p>
					</caption>
					<table frame="hsides" rules="groups">
						<thead>
							<tr>
								<th align="left" rowspan="3"/>
								<th align="center" colspan="3">THICKNESSES (m)</th>
								<th align="center" colspan="3">Ueq (W/m<sup>2</sup>&#x00B7;K)</th>
							</tr>
							<tr>
								<th colspan="3"><hr/></th>
								<th colspan="3"><hr/></th>
							</tr>
							<tr>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
							</tr>
						</thead>
						<tbody>
							<tr>
								<td align="left">SINGLE-LEAF FA&#x00C7;ADE</td>
								<td align="center">0.330</td>
								<td align="center">0.280</td>
								<td align="center">0.230</td>
								<td align="center">0.564</td>
								<td align="center">0.639</td>
								<td align="center">0.805</td>
							</tr>
							<tr>
								<td align="left">VENTILATED FA&#x00C7;ADE</td>
								<td align="center">0.345</td>
								<td align="center">0.295</td>
								<td align="center">0.245</td>
								<td align="center">0.342</td>
								<td align="center">0.368</td>
								<td align="center">0.418</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ETICS</td>
								<td align="center">0.345</td>
								<td align="center">0.295</td>
								<td align="center">0.245</td>
								<td align="center">0.399</td>
								<td align="center">0.435</td>
								<td align="center">0.506</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ITAICS + LFB</td>
								<td align="center">0.445</td>
								<td align="center">0.395</td>
								<td align="center">0.345</td>
								<td align="center">0.327</td>
								<td align="center">0.370</td>
								<td align="center">0.396</td>
							</tr>
						</tbody>
					</table>
				</table-wrap>
				<p>As can be seen, a single-leaf fa&#x00E7;ade made of Termoarcilla<sup>TM</sup> 29 brick was found to comply with the strict standard that specifies 0.570 W/m<sup>2</sup>&#x00B7;K as the most restrictive value in the most climatically adverse regions (<xref ref-type="bibr" rid="CIT0023">23</xref>, <xref ref-type="bibr" rid="CIT0024">24</xref>), whereas the other two bricks proved unacceptable for such regions. By contrast, all the other types of fa&#x00E7;ade showed very good thermal values, regardless of the brick.</p>
				<p>The best solution found here was clearly the ventilated fa&#x00E7;ade with a type 24 or 29 brick, with an equivalent thermal transmittance of around 0.350 W/m<sup>2</sup>&#x00B7;K and a reduction of less than 0.350 m in the useful area of the housing unit. This thickness may however be considered excessive for housing units. Depending on the thermal requirements in each building, the fa&#x00E7;ade + ITAICS+ LFB with a Termoarcilla<sup>TM</sup> 19 brick could be considered as acceptable.</p>
			</sec>
			<sec id="S20008">
				<title>3.2. Thermal results for the proposed Termoarcilla<sup>TM</sup> bricks with rhomboidal internal voids</title>
				<p>This study involved a proposed brick with the same dimensions as the commercial Termoarcilla<sup>TM</sup> bricks with rhomboidal voids to optimize its internal geometry (<xref ref-type="bibr" rid="CIT0010">10</xref>). The design consisted of rhomboidal voids that extended to the tongue and groove area, thus giving the brick a thermal break at the vertical joint, as shown above (<xref ref-type="bibr" rid="CIT0014">14</xref>&#x2013;<xref ref-type="bibr" rid="CIT0017">17</xref>).</p>
				<p><xref ref-type="fig" rid="F0010">Fig. 10</xref> displays the cross-sections of the three bricks under study, showing that the 0.290 m brick has three tongues and three grooves, while the 0.240 m and 0.190 m bricks have only two grooves and two tongues. This arrangement is required in order to extrude the pieces by resting the brick on the grooved face. If they were extruded on the faces without tongue and grooving there would be a bellows effect.</p>
				<fig id="F0010">
					<label>Figure 10</label>
					<caption>
						<p>Cross-section of the proposed bricks under study.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g010.tif"/>
				</fig>
				<p>An analysis of the specific cross-sections of each type of wall showed that the 0.290 m and 0.240 m thick bricks had a discontinuous horizontal joint with an air space 0.030 m wide, while the 0.190 m brick had a continuous joint. Finite element software (<xref ref-type="bibr" rid="CIT0033">33</xref>) was used, with the boundary conditions specified in the standards, to obtain the heat flows passing through the clay/air cross-section, the clay/mortar cross-section, and the horizontal joint. Considering the height of each specific section, these heat flows enabled the resistance of the uncoated wall for each brick under study to be obtained.</p>
				<p>
					<xref ref-type="fig" rid="F0011">Fig. 11</xref> shows the heat flow diagram for the specific clay/air cross-sections (a clay cross-section with air-filled voids) for the proposed brick with a thickness of 0.240 m.</p>
				<fig id="F0011">
					<label>Figure 11</label>
					<caption>
						<p>Heat flow of the specific clay/air cross-section for the proposed brick with a thickness of 0.240 m.</p>
					</caption>
					<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="MC201614_e096-g011.tif"/>
				</fig>
				<p>
					<xref ref-type="table" rid="T0004">Table 4</xref> shows the figures for the equivalent thermal transmittance of the different types of fa&#x00E7;ade and the thicknesses of the walls in question, to indicate by how much each type of fa&#x00E7;ade reduces the useful surface area of the housing unit.
</p>
				<table-wrap id="T0004">
					<label>Table 4</label>
					<caption>
						<p>Equivalent thermal transmittance of the envelope for each type of fa&#x00E7;ade with the proposed Termoarcilla<sup>TM</sup> bricks with rhomboidal internal voids and thicknesses affecting the useful surface area of the housing unit</p>
					</caption>
					<table frame="hsides" rules="groups">
						<thead>
							<tr>
								<th align="left" rowspan="3"/>
								<th align="center" colspan="3">THICKNESSES (m)</th>
								<th align="center" colspan="3">U<sub>eq</sub> (W/m<sup>2</sup>&#x00B7;K)</th>
							</tr>
							<tr>
								<th colspan="3"><hr/></th>
								<th colspan="3"><hr/></th>
							</tr>
							<tr>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
							</tr>
						</thead>
						<tbody>
							<tr>
								<td align="left">SINGLE-LEAF FA&#x00C7;ADE</td>
								<td align="center">0.330</td>
								<td align="center">0.280</td>
								<td align="center">0.230</td>
								<td align="center">0.486</td>
								<td align="center">0.556</td>
								<td align="center">0.767</td>
							</tr>
							<tr>
								<td align="left">VENTILATED FA&#x00C7;ADE</td>
								<td align="center">0.345</td>
								<td align="center">0.295</td>
								<td align="center">0.245</td>
								<td align="center">0.312</td>
								<td align="center">0.339</td>
								<td align="center">0.407</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ETICS</td>
								<td align="center">0.345</td>
								<td align="center">0.295</td>
								<td align="center">0.245</td>
								<td align="center">0.358</td>
								<td align="center">0.395</td>
								<td align="center">0.491</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ITAICS + LFB</td>
								<td align="center">0.445</td>
								<td align="center">0.395</td>
								<td align="center">0.345</td>
								<td align="center">0.299</td>
								<td align="center">0.325</td>
								<td align="center">0.387</td>
							</tr>
						</tbody>
					</table>
				</table-wrap>
				<p>The results provided by the bricks proposed revealed that for single-leaf fa&#x00E7;ades, 0.290 m and 0.240 m thick bricks met the standards applicable in the most restrictive Spanish regions, where an equivalent thermal transmittance of less than 0.570 W/m<sup>2</sup>&#x00B7;K is required.</p>
				<p>Equivalent thermal transmittances below 0.300 W/m<sup>2</sup>&#x00B7;K were also observed: such figures were not obtained with any of the wall types using the commercial herringbone bricks.</p>
			</sec>
			<sec id="S20009">
				<title>3.3. Comparative analysis</title>
				<p>A joint analysis of the figures in <xref ref-type="table" rid="T0003">Tables 3</xref> and <xref ref-type="table" rid="T0004">4</xref> served to compare the percentage improvements between the commercial herringbone bricks and the rhomboidal bricks proposed here. The results are shown in <xref ref-type="table" rid="T0005">Table 5</xref>.
</p>
				<table-wrap id="T0005">
					<label>Table 5</label>
					<caption>
						<p>Comparison in % of improvement in types of fa&#x00E7;ade between the bricks proposed and commercial bricks</p>
					</caption>
					<table frame="hsides" rules="groups">
						<thead>
							<tr>
								<th align="left" rowspan="5"/>
								<th align="center" colspan="6">U<sub>eq</sub> (W/m<sup>2</sup>&#x00B7;K)</th>
								<th align="center" colspan="3">% IMPROVEMENT</th>
							</tr>
							<tr>
								<th colspan="6"><hr/></th>
								<th colspan="3"><hr/></th>
							</tr>
							<tr>
								<th align="center" colspan="3">HERRINGBONE</th>
								<th align="center" colspan="3">RHOMBOIDAL</th>
								<th align="center" colspan="3">RHOMB/HERRINGBONE</th>
							</tr>
							<tr>
								<th colspan="3"><hr/></th>
								<th colspan="3"><hr/></th>
								<th colspan="3"><hr/></th>
							</tr>
							<tr>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
								<th align="center">TA-29</th>
								<th align="center">TA-24</th>
								<th align="center">TA-19</th>
							</tr>
						</thead>
						<tbody>
							<tr>
								<td align="left">SINGLE-LEAF FA&#x00C7;ADE</td>
								<td align="center">0.564</td>
								<td align="center">0.639</td>
								<td align="center">0.805</td>
								<td align="center">0.486</td>
								<td align="center">0.556</td>
								<td align="center">0.767</td>
								<td align="center">&#x2212;14%</td>
								<td align="center">&#x2212;13%</td>
								<td align="center">&#x2212;5%</td>
							</tr>
							<tr>
								<td align="left">VENTILATED FA&#x00C7;ADE</td>
								<td align="center">0.342</td>
								<td align="center">0.368</td>
								<td align="center">0.418</td>
								<td align="center">0.312</td>
								<td align="center">0.339</td>
								<td align="center">0.407</td>
								<td align="center">&#x2212;9%</td>
								<td align="center">&#x2212;8%</td>
								<td align="center">&#x2212;2%</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ETICS</td>
								<td align="center">0.399</td>
								<td align="center">0.435</td>
								<td align="center">0.506</td>
								<td align="center">0.358</td>
								<td align="center">0.395</td>
								<td align="center">0.491</td>
								<td align="center">&#x2212;10%</td>
								<td align="center">&#x2212;9%</td>
								<td align="center">&#x2212;3%</td>
							</tr>
							<tr>
								<td align="left">FA&#x00C7;ADE + ITAICS + LFB</td>
								<td align="center">0.327</td>
								<td align="center">0.370</td>
								<td align="center">0.396</td>
								<td align="center">0.299</td>
								<td align="center">0.325</td>
								<td align="center">0.387</td>
								<td align="center">&#x2212;9%</td>
								<td align="center">&#x2212;12%</td>
								<td align="center">&#x2212;2%</td>
							</tr>
						</tbody>
					</table>
				</table-wrap>
				<p>The 0.290 m and 0.240 m bricks showed improvements of more than 13% for single-leaf fa&#x00E7;ades, which we consider to be a very important result. For 0.190 m bricks the improvement in such walls was not so great.</p>
				<p>In general the 0.190 m brick showed no significant differences for almost any type of fa&#x00E7;ade, which means that it is not worth changing the internal geometry of bricks of that specific thickness.</p>
				<p>By contrast, the thermal improvements for the 0.290 m and 0.240 m bricks were significant for all the types of fa&#x00E7;ade proposed here, ranging between 8% and 14%. These improvements can be considered important in terms of the thermal insulation of fa&#x00E7;ades.</p>
				<p>As shown in <xref ref-type="table" rid="T0004">Tables 4</xref> and <xref ref-type="table" rid="T0005">5</xref>, assuming an acceptable fa&#x00E7;ade thickness of 0.300 m, single-leaf, ventilated and ETICS fa&#x00E7;ades would be acceptable for similar fa&#x00E7;ade thicknesses only with 0.240 and 0.190 m bricks. As mentioned above, little difference was found between commercial herringbone bricks and rhomboidal ones in the 0.190 m case.</p>
				<p>The 0.240 m rhomboidal brick proposed here showed an improvement of between 8% and 13%, and can therefore be considered as recommendable.</p>
				<p>The best value recorded for equivalent thermal transmittance was 0.299 W/m<sup>2</sup>&#x00B7;K, for the rhomboidal brick on the fa&#x00E7;ade + ITAICS + LFB, where there was a 9% improvement on the performance of the commercial herringbone brick for the same type of wall. However this type of fa&#x00E7;ade is 0.445 m thick, which may be considered somewhat high as it reduces the useful surface area of the housing unit. Its use would therefore depend on the thermal requirements of each building.</p>
			</sec>
		</sec>
		<sec id="S0010" sec-type="conclusions">
			<title>4. CONCLUSIONS</title>
			<p>The use of clay bricks in fa&#x00E7;ades provides building envelopes with good thermal performance levels. This paper reports a study comparing the equivalent thermal transmittances of fa&#x00E7;ades for two kinds of brick: one that is commercially available and another proposed by the authors, using three different brick thicknesses and four types of fa&#x00E7;ade: single-leaf fa&#x00E7;ades, ventilated fa&#x00E7;ades, fa&#x00E7;ades with an exterior thermal insulation system and fa&#x00E7;ades with internal thermo-acoustic insulation and a large format brick on the inside.</p>
			<p>Commercial Termoarcilla<sup>TM</sup> bricks with herringbone internal voids were used as a baseline reference, but the study focused on bricks with rhomboidal internal voids. All the bricks used had the same outside face measurements. Thicknesses of 0.290 m, 0.240 m and 0.190 m were studied.</p>
			<p>It can be concluded that the 0.190 m thick rhomboidal brick proposed offers little improvement on the 0.190 m brick already commercially available: the improvement is less than 5% in the best of cases. This type of brick has a continuous horizontal joint, while the other two types have discontinuous joints with a 0.030 m air space. By contrast, the thermal performances of the 0.290 m and 0.240 m rhomboidal bricks proposed were between 8% and 14% better than those of the commercially available bricks for all the types of wall studied.</p>
			<p>For single-leaf fa&#x00E7;ades the thermal performances recorded for the 0.290 m and 0.240 m bricks proposed were better by a highly significant 13%&#x2013;14%, with a thermal transmittance of 0.486 W/m<sup>2</sup>&#x00B7;K for the 0.290 m brick.</p>
			<p>If fa&#x00E7;ades must not exceed 0.350 m in thickness, only 0.190 m thick bricks can feasibly be used on multilayer fa&#x00E7;ades with thermo-acoustic insulation and a large format brick on the inside. In this case, the equivalent thermal transmittance would be close to 0.400 W/m<sup>2</sup>&#x00B7;K. For either of the other two bricks the fa&#x00E7;ade thickness would exceed 0.400 m.</p>
			<p>Equivalent thermal transmittances of 0.300 W/m<sup>2</sup>&#x00B7;K were recorded for the 0.290 m thick rhomboidal brick on fa&#x00E7;ades with thermo-acoustic insulation and a large format brick on the inside, but the final thickness of the wall was 0.445 m.</p>
			<p>For ventilated fa&#x00E7;ades the 0.290 m and 0.240 m thick rhomboidal bricks proposed gave 8%&#x2013;9% improvements, with values of 0.312 W/m<sup>2</sup>&#x00B7;K and 0.339 W/m<sup>2</sup>&#x00B7;K, respectively. In view of the small difference in thermal terms, the best option would therefore be to use 0.240 m bricks, as the overall thickness of the fa&#x00E7;ade would not then exceed 0.300 m.</p>
		</sec>
	</body>
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