Study of heat and moisture migration properties in porous building materials

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<ul><li><p>environmental characteristic, heat and moisture transport in the porous building materials is quitecomplex. Richards [1] rstly established the equation of unsaturated ow in porous materials,which is on the basis of Darcys law and the principle of continuous motion. Philip and Vries [2]* Corresponding author. Tel.: +86-25-8620-5393; fax: +86-25-5771-4489.Department of Power Engineering, Southeast University, No. 2 Si Pai Lou, Nanjing 210096, Jiangsu Province, PR China</p><p>Received 25 December 2003; accepted 6 May 2004</p><p>Available online 13 August 2004</p><p>Abstract</p><p>Based on the non-equilibrium thermodynamic theory, the thermal driving forces and the uxes in heat</p><p>and moisture migration process for unsaturated porous building materials are analyzed. The mechanisms of</p><p>heat and moisture migration in unsaturated porous building materials are discussed and the pheno-</p><p>menological equations to describe the immigrating process in unsaturated porous building materials areestablished. By means of the diusion law and the equation of state for ideal gas, the expressions of</p><p>coecients in the phenomenological equations are deduced. The eects of temperature, water content or</p><p>partial vapour pressure on the phenomenological coecients are also discussed.</p><p> 2004 Elsevier Ltd. All rights reserved.</p><p>Keywords: Heat and moisture migration; Phenomenological coecients; Non-equilibrium thermodynamics; Porous</p><p>building materials</p><p>1. Introduction</p><p>Problems involving heat and moisture migration in porous building materials arise in a numberof engineering interests, such as wall drying, the solar house designing, cooling load calculating ofair conditioning, etc. Aected by porous structure, temperature gradients, moisture gradients andStudy of heat and moisture migration propertiesin porous building materials</p><p>Z.Q. Chen *, M.H. Shi</p><p>Applied Thermal Engineering 25 (2005) address: (Z.Q. Chen).</p><p>1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2004.05.001</p></li><li><p>migrmigrandcomporderapprmentporo</p><p>element was investigated by Taylor et al. [13]. More recently, real-time thermal and moistureparameters in buildings were studied theoretically and experimentally [14,15]. All these previous</p><p>62 Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171works are very instructive, but the migration phenomenological coecients are still not to bedecided owing to the complexity of heat and moisture migration processes in porous materials.This paper will present a method to predict the phenomenological coecients with considerationof heat and moisture migration mechanisms, in which a non-equilibrium approach is employed toexplain combined heat transfer and water, including liquid and vapour, movement.</p><p>2. Linear phenomenological equations of heat and moisture migration</p><p>Heat and moisture migration in porous building materials is the process aected by theinteractions of temperature eld, moisture eld, and partial vapour pressure eld. Generally, thecoupled heat and moisture migration can be described in linear non-equilibrium thermodynamictheory [16]. According to the Curies principle, the thermal driving forces and the uxes in heatand mass transfer process are coupled. So the linear phenomenological equations of heat andmoisture migrations in porous building materials can be described as</p><p>~Jq LqqT 2 rT LqLT</p><p>rh LqvTrPV 1</p><p>~JL LLqT 2 rT LLLT</p><p>rh qLK~g 2</p><p>~JV LVqT 2 rT LVVT</p><p>rPV 3where,~Jq,~JL and~JV are heat ux, liquid mass ux and vapour mass ux, respectively. T , h and PVvolume moisture content were studied by Shah et al. [6]. The steady-ux measurements ofmoisture diusivity in unsaturated porous media were studied by Richards [7]. In a paper seriesWilson, Hall and coworkers [811] studied the water movement in porous building materials byuse of unsaturated ow theory and obtained some experimental verications of capillaryabsorption of water for dierent building materials and structures. The dierent moisturetransport mechanisms and some interfacial phenomena in porous materials were investigated byFreitas et al. [12] using the theory of Luikov [3] and Philip and Vries [2]. Based on a one-dimensional steady model, the dynamic and diusive behavior of a three-layer building envelopeare thation aected by temperature gradient was taken over. In the process of heat and moistureation, the gradients of temperature, moisture and pressure, the main driving forces of heatmoisture migration in unsaturated porous media, inuence one another [3]. Due to thelicated structure of porous building materials, it is dicult to consider micro-phenomena. Into describe the continuity of porosity and other parameters in unsaturated porous media</p><p>oximately, unsaturated models were developed by using the method of representative ele-ary volume [4,5]. Because of water evaporation, phase-change is taking place in unsaturatedus materials. To decide the transport properties, migration coecients vs. temperature anddeveloped a moisture migration model at inhomogeneous temperature proles, in which moisturee temperature, water content and partial vapour pressure. qL and K are liquid water density</p></li><li><p>coedius</p><p>Inmigr</p><p>Moisture migration in unsaturated porous building materials includes diusive migration andinltdius</p><p>3.2.1Li</p><p>cause</p><p>Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171 63liquid ow ~JLC can be described as</p><p>~JLC qLDhLrh DTLrT K~g 8where, DhL K o/oh</p><p> , DTL K o/oT , / is hydraulic potential.In non-isothermal conditions, surface diusion uid ow ~JLD caused by adsorption anddesorration uid ow. The diusive migration has the forms of molecular diusion, Knudsenion and surface diusion.</p><p>. Liquid water mass uxquid ux in porous building materials consists of inltration ow and surface diusiond by the gradients of moisture and temperature. According to Darcy law [17], the inltration3.1. Mechanism of heat migration</p><p>Heat transfer in unsaturated building materials under temperature gradient covers heat con-duction, inltration convection heat transfer, radiation heat transfer and phase-change heattransfer. They are interactive. For there is no large temperature dierence in unsaturated buildingmaterials, so radiation heat transfer is ignored.According to the analysis above, the heat ux is consisted of heat conduction heat ux ~Jqd</p><p>and convection heat ux ~Jqc caused by inltration uid ow.</p><p>~Jq ~Jqd ~Jqc kerT ~JLhL ~JVhV ~J aha 7</p><p>3.2. Mechanism of moisture migrationorder to describe the linear phenomenological coecients, the mechanisms of heat, moistureation and thermodynamic ux are analyzed below.So, Eqs. (1)(3) can be written as</p><p>~Jq krT k1mrh k1PrPV 4</p><p>~JL k11mrT kmrh qLK~g 5</p><p>~JV k11P rT kPrPV 6</p><p>3. Analysis of thermodynamics uxcient; km T , mass diusivity; km T , mass thermal diusivity; km T 2 , thermomassivity.and unsaturated hydraulic conductivity. We assume, k LqqT 2 , apparent thermal conductivity;k1P LqVT , migration coecient; kP LVVT , inltration coecient; k11P </p><p>LVqT 2 , thermal inltration</p><p>LLL 1 LqL 11 LLqption is [18]</p></li><li><p>3.2.2Th</p><p>Knudthat</p><p>4. Phenomenological coecients</p><p>Ac</p><p>4.2. V</p><p>64 Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171~J a ~0 15In the unsaturated porous building materials, comparing to vapour ux, air ux is very small[19], so the net transfer of air is zeroapourkm qLDhL qLK oh 13</p><p>k11m qLDTL DTD qL Ko/oT</p><p> DTD</p><p>14o/ menological coecients are deduced below.</p><p>4.1. Liquid water</p><p>The phenomenological coecients include mass diusivity km and thermomass diusivity k11m .</p><p>Comparing Eqs. (5) and (10), they are respectively described ascording to the analysis of thermodynamic ux and ideal gas state equation, the pheno-where, De and qV are eective diusion coecient and vapour density, respectively.</p><p>3.2.3. Air uxThe total air ux also includes air convection ux and diusion ux. For the convection</p><p>velocity of air is the same as that of vapour [19], so the air ux is</p><p>~J a qa~V Derqa 12where, qV is air density.. Vapour uxe total vapour ux includes the vapour convection ux, general molecular diusion andsen diusion ux under the gradients of temperature and vapour partial pressure. Assumingthe vapour convection velocity is ~V , so vapour ux ~JV is [19]</p><p>~JV qV~V DerqV 11where, DTD CqLT is the coecient of adsorption-diusion.So, the liquid ux ~JL is</p><p>~JL ~JLC ~JLD qLDhLrh DTL DTDrT K~g 10~JLD qLDTDrT 9</p></li><li><p>Usin</p><p>Com</p><p>Asmaterials, therefore the vapour ux is described as [19]</p><p>e</p><p>Therscrib</p><p>D P</p><p>where, D is the eective diusion coecient, R is general gas constant, P and P are total gas</p><p>4.3. H</p><p>Th</p><p>Combining Eq. (7) and Eqs. (21)(23) the heat ux is</p><p>Comcond</p><p>Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171 65k1m kmCLT 27k1P kPCPVT HC 26k ke k11m CLT 25pared Eqs. (4) and (24), the phenomenological coecients of heat uxapparent thermaluctivity k, migration coecient k1P and mass thermal diusivity k</p><p>1m are~Jq ke k11m CLT rT kmCLTrh kPHC CPVT rPV qLCLTK~g 24ha CPaT 23hL CLT 21hV CPVT HC 22eat</p><p>e enthalpies of liquid water, vapour and air in unsaturated porous building materials aree V V</p><p>pressure and partial vapour pressure, respectively.kP eRVT P PV 19</p><p>k11P 0 20~JV RVT P PVrPV 18</p><p>efore, by using Eqs. (12) and (18), the phenomenological coecients of vapour ux is de-ed asD Psuming that the air and vapour obey the ideal gas law in the unsaturated porous building~JV DeqVrqaqa</p><p>rqVqV</p><p>17g Eq. (15) to (12) the vapour convection velocity ~V is described as</p><p>~V Derqa=qa 16bined Eqs. (11) and (16), the vapour ux is </p></li><li><p>5. E</p><p>5.1.1</p><p>wher</p><p>5.1.3</p><p>66 Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171The eective thermal conductivity in unsaturated porous building materials can be describedapproximately as</p><p>ke kS1 e kLh kge h 31where, kS, kL and kg are the thermal conductivity of solid, liquid and gas (vapour and air),respectively.</p><p>5.1.4. Eective diusion coecient DeThe eective diusion is the combination of general modular diusion and Knudsen diusion.</p><p>So, its coecient is</p><p>De DatmDKn 32PV PS exp g/RVT</p><p> 30</p><p>e, PS is the saturated vapour partial pressure and g is the acceleration to gravity.</p><p>. Eective thermal conductivity kewhere, e, /S, KS and c are porosity, saturated hydraulic potential, saturated hydraulic conductivityand surface extended coecient, respectively. For sandy block with mean pore diameter of 0.3mm, e, /S, KS and c are 0.39, )0.0315 m, 1.76 105 m/s and 2.189 103 C1 [20].</p><p>5.1.2. Partial vapour pressure PVIn the unsaturated porous building materials, vapour partial pressure obeys the following</p><p>thermodynamic relation [19]:K KS /S/ 2:75</p><p>29The hydraulic potential and conductivity are functions of temperature and water content. Theycan be described by Eq. (28) [20] and Eq. (29) respectively [23].</p><p>/ /She</p><p> 4expcT 28. Hydraulic potential / and conductivity KAccording to the analysis above, the phenomenological coecients of heat and moisturemigrations are functions of temperature and moisture or partial vapour pressure. For sandybuilding block, the eects of temperature and moisture on the phenomenological coecients areanalyzed below.</p><p>5.1. Thermodynamic and thermal physical parametersects of temperature and moisture on the phenomenological coecientsDatm DKn</p></li><li><p>General modular diusion coecient [21]</p><p>Datm 4:942 104eT 1:5=Pf0 33Knudsen diusion coecient [22]</p><p>DKn 8e2</p><p>3f0Sg</p><p>2RVTpMV</p><p> 0:534</p><p>where s, S and M are tortuosity factor, specic area for BET and molecular weight of watervapour. For sandy block with mean particle diameter of 0.3 cm, the coecient of adsorption-diusion is very small and it can be neglected.</p><p>5.2. Eects of temperature and moisture on phenomenological coecients</p><p>For sandy block with mean particle diameter of 0.3 mm and porosity of 0.39, the eectivecurves of temperature and moisture on phenomenological coecientsapparent thermal con-ductivity k, mass thermal diusivity k1 , mass diusivity k and thermomass diusivity k11 are</p><p>3.5</p><p>ah</p><p>n10</p><p>ath</p><p>nx1</p><p>0</p><p>0</p><p>3.5</p><p>10.5</p><p>0.3</p><p>Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171 670.05 0.25 0.45 0 50 100 150App</p><p>AppT=10</p><p>rent</p><p> t</p><p>rent</p><p> 7.0</p><p>40</p><p>erm</p><p>al c</p><p>o</p><p>erm</p><p>al c</p><p>o</p><p>=0.110.570</p><p>duct</p><p>ivity</p><p> x</p><p>duct</p><p>ivity</p><p>7.0m m mshowed in Figs. 14 respectively. As shown, the phenomenological coecients increase with theincreasing of temperature and water content. But the mass thermal diusivity k1m, mass diusivitykm and thermomass diusivity k</p><p>11m are closed to zero when the water content is very small. So when</p><p>the water content is below 0.1, the liquid water immigration, the eect of heat on liquid watermigration and eect of liquid water migration on heat transfer are very small. The relations ofmigration coecient and inltration coecient with temperature and vapour partial pressure arein Figs. 5 and 6. As shown, the eects of temperature on migration coecient and inltrationcoecient are larger than the eects of vapour partial pressure.</p><p>14.0</p><p>100</p><p>a</p><p>4 (k</p><p>W/m</p><p> C)</p><p>4 (kW</p><p>/m C</p><p>)</p><p>14.0b</p><p>0.39Water content Temperature T (C)</p><p>Fig. 1. Apparent thermal conductivity curve.</p></li><li><p>68 Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 61714a</p><p>/m)</p><p>4b</p><p>)These calculated values are used in the numerical simulation of heat and moisture transfer inunsaturated soil. The predicted results are compared with the experimental data obtained fromone-dimensional column of soil and the agreement is satisfactory [18].</p><p>-1</p><p>0</p><p>1</p><p>2</p><p>3</p><p>0.05 0.25 0.45</p><p>100</p><p>70</p><p>40</p><p>T=10</p><p>Water content </p><p>Mas</p><p>s th</p><p>erm</p><p>al d</p><p>iffus</p><p>ivity</p><p> 1 m</p><p> (kW</p><p>-1</p><p>0</p><p>1</p><p>2</p><p>3</p><p>0 50 100 150</p><p>0.39</p><p>0.3</p><p>=0.1</p><p>Temperature T (C)M</p><p>ass </p><p>ther</p><p>mal</p><p> diff</p><p>usiv</p><p>ity </p><p>1 m (k</p><p>W/m</p><p>Fig. 2. Mass thermal diusivity curve.</p><p>0</p><p>2.5</p><p>5.0</p><p>7.5</p><p>10.0</p><p>0.05 0.25 0.45</p><p>a</p><p>1007040</p><p>T=10</p><p>-1.0</p><p>1.4</p><p>3.8</p><p>6.2</p><p>8.6</p><p>11.0</p><p>0 50 100 150</p><p>b</p><p>0.39</p><p>0.3</p><p>=0.1</p><p>Temperature T (C)</p><p>Mas</p><p>s di</p><p>ffudi</p><p>vity</p><p> x</p><p>103 (</p><p>kg/m</p><p>s)m</p><p>Water content </p><p>Mas</p><p>s di</p><p>ffusi</p><p>ty </p><p>mx1</p><p>03 (k</p><p>g/m</p><p>s)</p><p>Fig. 3. Mass diusivity curve.</p></li><li><p>Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171 692</p><p>1007040</p><p>a</p><p>(kg/</p><p>ms</p><p>C)</p><p>2</p><p>0.39</p><p>b</p><p>(kg/</p><p>ms</p><p>C)6. Conclusions</p><p>The phenomenological equation to describe the immigration process of heat and mass inunsaturated porous building material is established. The phenomenological coecients of heatand moisture are deduced. The phenomenological coecients of heat and moisture migration are</p><p>-1</p><p>0</p><p>1</p><p>0.05 0.25 0.45</p><p>T=10</p><p>Watercontent </p><p>Ther</p><p>mo-</p><p>mas</p><p>s di</p><p>ffusi</p><p>vity</p><p> x</p><p> 106</p><p>m</p><p>-1</p><p>0</p><p>1</p><p>0 50 100 150</p><p>0.3=0.1</p><p>TemperatureT(C)Th</p><p>erm</p><p>o-m</p><p>ass </p><p>diffu</p><p>sivi</p><p>ty </p><p> x 1</p><p>06m" "</p><p>Fig. 4. Thermomass diusivity curve.</p><p>6.0</p><p>6.5</p><p>7.0</p><p>7.5</p><p>8.0</p><p>0 600 1200 1800</p><p>100</p><p>70</p><p>40</p><p>T=10</p><p>a</p><p>Partialvapor pressure Pv (Pa)</p><p>Mig</p><p>ratio</p><p>n co</p><p>effic</p><p>ient</p><p> 1 x </p><p>108 (k</p><p>W/m</p><p>C)</p><p>p</p><p>6.0</p><p>6.5</p><p>7.0</p><p>7.5</p><p>8.0</p><p>8.5</p><p>0 50 100 150</p><p>0.390.3</p><p>=0.1</p><p>b</p><p>Temparature T (C)</p><p>Mig</p><p>ratio</p><p>n co</p><p>effic</p><p>ient</p><p> 1 p</p><p> x10</p><p>8 (kW</p><p>/mC</p><p>)</p><p>Fig. 5. Migration coecient curve.</p></li><li><p>T=10</p><p>filtra</p><p>ti</p><p>filtra</p><p>ti</p><p>Fig. 6. Inltration coecient curve.</p><p>70 Z.Q. Chen, M.H. Shi / Applied Thermal Engineering 25 (2005) 6171very useful for simulation of the heat and moisture migration process in porous building mate-rials. The eects of temperature, water content or partial vapour pressure on the phenomeno-logical coecients are also discussed. For sa...</p></li></ul>