NUMERICAL INVESTIGATION OF HEAT AND MASS TRANSFER IN FLAX AND HEMP CONCRETE WALLS

Transcription

1 NUMERICAL INVESTIGATION OF HEAT AND MASS TRANSFER IN FLAX AND HEMP CONCRETE WALLS C. Maalouf 1, A.D. Tran Le 2, M.Q. T Knt 3, M. Lach 1, E. Wurtz 4, L. Mora 5, T.H. Ma 1 1 LTM. - Laboratore de Thermomécanque, GRESPI, Unversté de Rem BP. 139, Mouln de la Housse, F Rem Cedex 2, France. 2 Lafarge Center of Research, Technologcal pole of l Isle d Abeau, Sant Quentn Fallaver, France. 3 EPROAD, Ingénere des Matéraux et Procédé Unversté de Pcarde Jules Verne, 8 Amen France. 4 INES, Savoe Technolac, 5 Avenue du lac Leman, BP 332, Le Bourget du Lac, France. 5 I2M, Département TREFLE - UMR CNRS Ste ENSAM Esplanade des Arts et Méter F-3345 TALENCE Cedex ABSTRACT The purpose of ths paper s to study heat and mass transfer n two vegetal fbre materals: flax and hemp whch are known to have a low envronmental mpact. After presentng each of these materals and ther physcal properte we present equatons of the coupled heat and mosture transfer wthn smple layer walls. In ths model, mosture transport phenomenon s made through lqud and vapour phases. The lqud phase s supposed to move by capllarty whereas the vapour phase dffuses under vapour partal pressure gradent. Smulatons are done wth the smulaton envronment SPARK suted to complex problems. In ths case, we nvestgate the mpact of mosture transfer on heat dffuson wthn these two materals through the study of the dampng effect, tme lag and heat conducton loads and mosture transfer through a smple layer wall subjected to perodcal varaton of outdoor condtons. 1. INTRODUCTION The sustanable world s economc growth and people s lfe mprovement greatly depend on the use of alternatve products n the archtecture and constructon, such as vegetal fbres conventonally called green materals. Among these materal hemp and flax are wdely used n buldng constructon. Concernng the hemp case (a lme-hemp fbres and water mxture), the researches done untl ths day ((Collet, 24), (Cerezo, 25), (Tran Le, 21)) allowed us to determne ts physcal propertes and ts performances regardng the energy consumpton and hygrothermal comfort n buldngs. For the agro-composte based on flax-shaves (a mxture of the woody porton of the flax fbre stem and an agro-bnder from casen and vnegar treated by mcrowave radaton), ts mechancal, hygrothermal and acoustc propertes have been recently studed by (El Hajj N, 21). In comparson wth the agro-composte based on flaxshave the hemp has lower thermal conductvty whch s equal to.11 W/m.K compared to.145 W/m.K for the flax case. However, compared to other materals n constructon as the normal, the brck they have lower thermal conductvty, whch reduces heat dffuson, thus reducng wnter heat losses and protectng from summer heat waves. Though they have a low mass densty (415 and 57 kg/m 3 for hemp and flax s respectvely), whch reduces ther storage capacty, ther densty remans hgher than classcal nsulaton materals. Besde both are hygroscopc materal they have the capacty to store or to release mosture to ambent ar so they can moderate daly or seasonal humdty varatons of ndoor envronment. Regardng all that, hemp and flax-shaves can be consdered as a good compromse between nsulaton, energy effcency, bufferng capacty purpose and green materal. However the comparson of ther hygrothermal behavour based on ther physcal propertes s dffcult to quantfy and we rarely fnd n lterature studes comparng the use of these vegetable materals n constructon. The purpose of ths paper s to study performance of hemp and flax-shaves when they are used as buldng envelope. 2. MATHEMATICAL MODELS In order to reduce the energy consumpton and to ncrease the comfort n buldng, the study of heat and mass transfer through the wall s necessary because t s the man barrer that protects from the outsde weather or other condton such as cold n wnter, heat n summer, humdty, ran, wnd and

2 nose. Indeed, hgh mosture levels can damage constructon and nhabtant s health. Hgh humdty harms materal especally n case of condensaton and t helps moulds development ncreasng allergc rsks. Consequently, n ths secton, we present the mathematcal model for the heat and mosture transfer model (HAM) n a smple layer wall. Mechansms of mosture transport n a sngle buldng materal have been extensvely studed ((Künzel, 1995), (Mendes et al., 1997)). Most of the models have nearly the same orgn Phlp and de Vres model (Phlp and al., 1957). In ths artcle, we use the Umdus model (Mendes et al., 1997) n whch mosture s transported under lqud and vapour phases. Forms of mosture transport depend on the pore structure as well as envronmental condton. The lqud phase s transported by capllarty whereas the vapour phase s due to the gradents of partal vapour pressure. Wth these consderaton the mass conservaton equaton becomes: θ T θ = D + D t T θ Wth the boundary condtons (x= and x=l): (1) ( ρ ρ ) T θ ρl θ D T + D = hm, e ve, e ve, e x=, e (2) ( ρ ρ ) T θ ρl + θ = D T D hm, ve, ve, x= L, (3) The phase change occurrng wthn porous materals acts as a heat source or snk, whch results n the couple relatonshp between mosture and heat transfer. One dmensonal of the energy conservaton equaton wth coupled temperature and mosture for a porous meda s consdered, and the effect of the absorpton or desorpton heat s added. Ths equaton s wrtten as: T T T ρ Cpm = λ + Lvρl DT, v + t θ + Dθ, v (4) ρ Cp m =Cp +Cp l l θ (5) ρ Where Cp m s the average specfc heat whch takes nto account the dry materal specfc heat and the contrbuton of the specfc heat of lqud phase. λ s the thermal conductvty consdered as a functon of mosture content. T T θ ( T T ) λ Lvρl DT, v + Dθ, v = ht, e e x=, e L, e( ve, e ve, e) + Φray, e e + vh M ρ ρ (6) T T θ ( T T ) λ Lvρl DT, v + Dθ, v = ht, x= L, L vh M, ( ve, ve, ) + Φray, + ρ ρ (7) Boundary condtons take nto account radaton, heat and phase change. 3. OBJECT ORIENTED SIMULATION 3.1 Numercal resoluton In order to solve the prevous equaton system, the numercal soluton s based on the fnte dfference technque wth an mplct scheme. The numercal resoluton s shown n (Tran Le et al, 29). 3.2 Smulaton Envronment SPARK To solve ths system of equatons we used the Smulaton Problem Analyss and Research Kernel (SPARK), a smulaton envronment allowng to solve effcently dfferental equaton systems ((Sowell et al., 21), (Mendonça et al., 22). SPARK was developed by the Smulaton Research Group at Lawrence Berkeley Natonal Laboratory. Descrpton of a problem for SPARK soluton begns by breakng t down n an object-orented way. Ths means thnkng about the problem n terms of ts component s represented by a SPARK object. A model s than developed for ts component. Snce there may be several components of the same knd, SPARK object model equatons or group of equaton are defned n a generc manner called classes. Classes serve as templates any number of objects requred to formulate the whole problem. The problem model s then completed by lnkng objects together. Usng graph theoretc technque SPARK reduce the sze of the equaton system and use a Newton-Raphson teratve method to solve the reduced system and after convergence, solves for the remanng unknowns. We have just presented the physcal model used n smulaton n the next part we present model valdaton for the smple hemp wall. 3.3 Model valdaton In order to valdate the physcal model presented above, the experment has been done at laboratory of GRESPI/ LTM of Rems Unversty. It consders two samples whch surfaces are (1 cm x11 cm) and (12 cmx12 cm) and ther thcknesses are 3 cm and 6 cm respectvely. The test specmens are exposed to a perodcal step change n ambent relatve humdty chamber between 75% durng 24 hours and 35% durng 24 hours. The temperature s held constant at 2 C. In order to ensure one-dmensonal water vapour transfer between the specmen and ambent ar, fve faces of samples were sealed wth an alumnum tape

3 keepng only one face exposed to ndoor envronmental chamber condtons. The weght change of specmen was measured by a balance wth a resoluton of.1g. Intally, the specmen are n equlbrum state at 2 C temperature and 35% relatve humdty. The thermal and mass convecton coeffcents between the surface exposed and ndoor ar ambent of clmate chamber are equal to h=1 W/m²K and h=.8 m/s. Densty Thermal conductvty λ Heat capacty kg/m3 W/m.K J/kg.K Specmen weght (g) Modelsaton Experment Specmen 2 RH of ndoor clmate chamber 5 1 Temps (h) Relatve humdty 415,11 1 D Θ D T and D Tv D Θv m 2 /s m 2 /(s.k) m 2 /s 1,2E-9 1E-12 1E-9 Table 1 Propertes of hemp for valdaton The propertes and the sorpton sotherm of hemp for valdaton are shown n the table 1 and fgure 3. The comparson between the numercal results and the smulaton results s presented n Fgures 1 and 2. One can see n these fgures that predcted numercal results are n good agreement wth expermental data. In order to apprecate the result we use the root-meansquare crteron. The average dfference between the measured and predcted mosture content was expressed as a root-mean-square dfference, so: N ( mn) n= 1 δ RMS = (8) N where m s the nstantaneous dfference sample weght between the measured and predcted value and N s the number of values n the data set. Specmen weght (g) Smulaton 131 Experment_specmen 1 RH of ndoor clmate chamber Temps (h) Fgure 1 Numercal and smulated results for the specmen 1. Relatve humdty Fgure 2 Numercal and smulated results for the specmen 2. In our case theδ RMS values for specmen 1 and 2 are respectvely.14 g and.15 g, whch represent a very good agreement. The physcal model has been valdated and wll be used to nvestgate hygrothermal behavour of hemp and flax shave cases (other valdaton cases were run accordng to the exercses of the annex 41 of IEA). 3.4 Materal propertes Materal propertes (densty, thermal conductvty and specfc heat) are gven for the dry materal and are shown n Table 2 (Collet, 24; El Hajj, 21). Ths table presents also the thermal dffusvty a (m²/s) calculated by the rato λ/(ρ.c) and the thermal effusvty ( kρ C p ) whch ndcates the apttude of a materal to absorb and to restore heat energy. Table 2 Materal propertes n dry state (Collet, 24; El Hajj, 21). Flax shaves Hemp Densty (kg/m 3 ) Thermal conductvty (W/m.K) Specfc heat ( J/kg.K) Thermal dffusvty (*1-7 m²/s) Thermal effusvty (J/(m².K.s 1/2 )) The sorpton sotherm curves are shown n Fgure 3. We have neglected hysteress effect on the sorpton sotherm curves due to the lack of data. The smulaton s done by usng the straght forward lnk between mosture content (expressed by volume %) and the

4 relatve humdty. One can see n Fgure 1 that when the relatve humdty vares from to 43%, the mosture content of the both materals are very close and apart from ths value, the mosture content of flax-shaves case s much bgger than for the hemp case. Mosture content (vol %) Flax-shaves Hemp Relatve humdty (%) 4. NUMERICAL RESULTS 4.1 Physcal model Frstly, we present the physcal model n whch we study the behavour of a smple layer wall subjected to perodcal outdoor temperature and relatve humdty (Fgure 5). Indoor condtons are gven as (for x=l): T =24 C and T =2 C for summer and wnter condtons respectvely and the ndoor relatve humdty for both cases s 5%. External outdoor condtons are gven by snusodal functons. External and nternal thermal convecton coeffcents are equal to h T,e =16 W/m 2 K and h T, = 4 W/m 2 K. Fgure 3 Sorpton sotherms of studed materals (Collet, 24; El Hajj, 21). The thermal conductvty of both materals as functon of relatve humdty s shown n Fgure 4 n whch one can see that the thermal conductvty of hemp s smaller than that of flax-shaves. Indeed when the relatve humdty s bgger than 8%, the thermal conductvty n both cases ncreases dramatcally due to ther mosture sorpton sotherm. Thermal conductvty (W/m.K),2,18,15,13,1 Flax-shaves Hemp Relatve humdty (%) Fgure 4 Thermal conductvty of studed materals (Collet, 24; El Hajj, 21). Concernng the mass transport coeffcent assocated to a mosture content gradent (D θ ), for the same measurement condton (25 C of temperature and 9% of relatve humdty), ts value for the flaxshaves case s bgger than hemp case and t s equal to 6.65*1-9 (m²/s) compared to 1.18*1-1 (m²/s) respectvely. In the smulaton, the mass transport coeffcents for hemp case (D θ, D θv, D T, D θt ) are functons of water content as presented n (Tran Le, 21). Concernng the flaxshaves case, only the coeffcent assocated to a mosture content gradent (D θ ) s used because of lackng data (El Hajj, 21). Fgure 5 Physcal model for the smple layer wall. Indoor and outdoor mass transfer coeffcents were calculated usng the Lews number relaton for the ar: ht Le = = 1 (9) h ρc m Intal wall temperature and relatve humdty were consdered to be 2 C and 4 % respectvely through the wall. Wall thckness s 2 cm. The layer s dscretzed n 25 nodes and the tme step s 24 s. The smulatons are run for three months. 4.2 Computed results for summer condtons In ths secton, we study the behavour of a smple layer wall subjected to extreme summer condtons. External outdoor temperature and relatve humdty are gven by snusodal functons: T ext = 3-4* cos (w*t) HR ext =,5+.2* cos (w*t) where w=2*π/t and T= 24 hours. p (1) Fgure 6 shows the varaton of nternal surface temperature of the wall for the 6 th day and the numercal results are shown n Table 3. One can see that nternal surface temperature s dampened and phase shfted. We can notce that for the hemp envelope, ts temperature varaton s slghtly smaller than for the flax-shave case (about.12 C) and the average of nternal surface temperature of both cases are extremely close (about C). Regardng the tme lag whch explans the

5 materal capacty to dampen the outdoor temperature varaton, t s 1.8 h for the flax shave compared to 8.4 h for hemp case. Ths s due to the thermal dffusvty whch s slghtly hgher for the hemp than that of flax shave case (Maalouf et al., 211). Table 3 shows also the heat flux through the wall, t s postve when t s drected from outdoor to ndoor ar. Its values are always postve whch explans that the wall protects the ndoor from outdoor temperature varatons. The average value s 2.62 W/m² for the flax shave whch s slghtly hgher than that of hemp (2.54 W/m²). Internal surface temperature ( C) Ts_Flax Ts_Hemp Text Tme (day) Fgure 6 Varaton of nternal surface temperature of the wall for both cases. Table 3 Tme lag, extreme and average of nternal surface temperature and heat flux exchange between the wall and ndoor ar. Flax_shaves Outdoor temperature Text ( C) Hemp Tme lag (h) Mnmal nternal surface temperature ( C) Maxmal nternal surface temperature ( C) Average of nternal surface temperature ( C) Mnmal heat flux (W/m²) Maxmal heat flux (W/m²) Average heat flux (W/m²) The varatons of nternal surface relatve humdty of both cases are shown n Fgure7. We notce that ts value s mostly nfluenced by the nternal surface temperature varatons caused by the outdoor temperature fluctuatons (Fgure 6). The nternal surface relatve humdty of the flax shave case s more dampened and phase shfted. Its average values are very close n both cases and they are % for the hemp and % for the flax shave case. In the next secton, we wll study wall behavour under wnter condtons. Internal surface RH (%) RHs_Flax Ts_Flax Tme (day) RHs_Hemp Ts_Hemp Fgure 7 Varaton of nternal surface relatve humdty of the wall for the two studed cases. 4.3 Computed results for wnter condtons Outdoor temperature and relatve humdty varatons are descrbed by the snusodal functons gven by: T ext = -5* cos (w*t) HR ext =.8+.1* cos (w*t) Temperature C (1) We notce that ndoor temperature and relatve humdty are constant and equal to 2 C and 5 % respectvely. a. Effect of mosture transfer on thermal propertes of materals Snce both materals are porou the effect of mosture content on ther thermal conductvty and specfc heat s mportant and thus wll be extendly studed n ths part. The mosture content n the mddle layer of the wall s shown n Fgure 8. One can see n ths fgure that the mosture content for the hemp case s much smaller than that of flax shave case because of ther sorpton sotherm curves (Fgure 3). When the mosture content tends to the equlbrum value, t s 11.3% and 2.82% for the flax and the hemp cases respectvely. We notce also that the system needs three months to reach the equlbrum state, whch means that mosture content through the wall depends strongly on ntal mosture content (so ntal relatve humdty) and the smulaton tme (Maalouf et al., 211)

6 Mosture content (vol %) Teta_x=1cm_Hemp Teta_x=1cm_Flax Tme (day) Fgure 8 Varaton of the mosture content n mddle layer of the wall for the both cases. The varaton of the average thermal conductvty through the wall for both cases s shown n Fgure 9. Due to the mosture transfer through the materal, the thermal conductvty ncreases from.117 and.125 W/m K (6.8 %) for the hemp and from.154 to.174 W/m K (13%) for the flax shave case. Hgh mosture dffuson rate through the flax-shaves wall leads to hgher varatons n ts thermal conductvty. Thermal condutvty (W/mK) Flax Hemp Tme (day) Fgure 9 Varaton of average thermal conductvty through the wall for the both cases. Specfct heat (J/kg.K) Cp_Flax Cp_Hemp Tme (day) Fgure 1 Varaton of the average of specfc heat of the wall for the both cases. b. Mosture transfer between the wall and the ndoor ar Hygroscopc materals can be used to moderate the ampltude varaton of ndoor relatve humdty n buldngs thanks to ther vapour sorpton (absorpton and desorpton) capacty and thus they partcpate n the mprovement of the ndoor ar qualty and the reducton of energy consumpton. Therefore, n ths part we wll study the mosture transfer between the envelope and the ndoor ar. Water vapor flux (g/m².h) Hemp Flax Tme (day) The varatons of average specfc heat for both most materals are presented n Fgure 1. We notce that the effect of mass transfer on the specfc heat of flax s much more sgnfcant than the hemp case snce ts mosture content s hgher. In the begnnng of smulaton (the ntal relatve humdty of the wall was set at 4%), the specfc heat of hemp s 5.8 % bgger than that of flax-shaves and ther values are respectvely 1138 and 172 (J/kg.K). However, flax specfc heat ncreases fastly and becomes hgher after two days of smulaton. It can be seen that to reach the equlbrum value of the average of specfc heat, t takes approxmately three months. Here, at the equlbrum state, a sgnfcant ncrease of 67% of average specfc heat of flax was obtaned compared to 11.2 % for hemp case. Fgure 11 Water vapour flux exchange between the wall and ndoor ar. Fgure 11 shows the water vapour flux exchange expressed n g/m²h between the nsde wall surface and ndoor ar for a perod of three months. A negatve value means that water vapour flux s gong from ndoor ar to the wall. The equlbrum state s consdered when the dfference of two successve maxmum values of profle of water vapour flux s less than 1 %. For the studed case t takes 62 and 85 days for the hemp and flax respectvely to obtan equlbrum state. Ths result shows that n hygroscopc regon, materals wth low mosture storage capacty are reachng faster ther hygroscopc equlbrum. In addton, the flux of the water vapour s always negatve durng the frst 31 and 55 days for hemp and flax cases respectvely. That

7 can be explaned by the ntal relatve humdty whch was set to 4% through the wall and s smaller than ndoor relatve humdty. The results suggest that ntal condtons affect sgnfcantly materals sorpton capacty. Concernng the water vapour flux transfer between the ndoor ar and the wall when t reaches the equlbrum, the table 4 presents ts mnmal and maxmal values at the 9 th day. The maxmal value of hemp s 5% smaller than that of flax case due ts sorpton sotherm curve. Table 4 Mosture flux exchange between the wall and ndoor ar. Mnmal water vapour flux (g/m²h) Maxmal water vapour flux (g/m²h) Flax_shaves Hemp c. Heat exchange between nternal wall surface and ndoor ar. As shown n the boundary condton nternally, the wall s exposed to thermal convecton and phase change related to the water vapour transfer between the wall and ndoor ar. Regardng the heat loss due to the thermal convecton, Fgure 12 shows the varaton of heat loss flux through the wall n the equlbrum state durng fve days of the thrd month. The heat loss flux through the hemp wall s much smaller than that flax because t has a lower thermal conductvty. Hemps mean heat loss flux value s 1.4 W/m² compared to 13.7 W/m² for the flax-shaves showng a dfference of 31.7%. Energy heat loss through the wall for the three months s 11.7 and 15.8 kwh/m² respectvely for the hemp and flax cases showng that the use of hemp wll reduce energy consumpton about 35%. 15 Heat loss flux (W/m²) Flax Tme (day) Hemp Fgure 12 : Heat loss flux from the wall durng 5 days of the thrd month. Phase change heat (W/m²) 1,,5, -,5 Hemp Flax -1, Tme (day) Fgure 13 Heat exchange due to phase change between the wall and ndoor ar. Fgure 13 shows the varaton of the heat flux due to phase change between the nternal surface wall and ndoor ar for the two studed cases. Postve heat flux means that condensaton occurred whch corresponds to the case of mosture transfer from ndoor ar to the wall. In the second case, negatve heat flux s caused by the evaporaton phenomena n whch mosture transfers from the wall surface to ndoor ar. We notce that the mean value of ths heat flux s almost null whch s the same as for the mean value of water vapour flux exchange. In addton, the heat flux caused by phase change s small compared to heat loss due to thermal convecton. For hemp case, the maxmal heat flux related to phase change s.38 W/m² and represents 3.3% of the maxmal heat loss flux due to thermal convecton whch s 11.4 W/m². Concernng the flax case, ts value s 5 %. CONCLUSION AND PERSPECTIVES In ths paper, the hygrothermal behavour of hemp and flax s nvestgated at wall level. A one-dmenson model for heat and mosture transfer through a smple layer wall was used n the smulaton envronment SPARK. The computed results for summer condtons show that the nternal surface temperature of the flaxshaves wall s slghtly more dampened and ts tme lag s hgher than hemp case due to ts hgher thermal nerta. The results n wnter condtons show that the thermal propertes (thermal conductvty and specfc heat) of flax are much more affected by the mosture transfer n hygroscopc regon compared to hemp. Our results suggest that usng hemp may reduce conducton heat losses about 35 % for wnter condtons (at wall level). However, flax-shaves materal has a hgher apttude to nteract wth ndoor condtons meanng t has a hgher mosture bufferng capacty that could affect ts behavour at buldng level

8 For further work, we ntend to study the hygrothermal behavour of these materals for multlayered walls as usual n constructon desgn. In addton, the comparson of ther performances should be done n the whole buldng level wth dfferent ventlaton systems (senstve relatve humdty ventlaton for example). In ths way, t wll be possble to quantfy the effect of mosture bufferng capacty of these materals on hygrothermal comfort. NOMENCLATURE Symbol Defnton Unty C Specfc heat J.kg -1.K -1 C Specfc heat of dry materal J.kg -1.K -1 C l Specfc heat of water J.kg -1.K -1 D T D T,v D θ D θv h M h T Mass transport coeffcent assocated to a temperature gradent Vapor transport coeffcent assocated to a temperature gradent Mass transport coeffcent assocated to a mosture content gradent Vapor transport coeffcent assocated to a mosture content gradent Mass transfer convecton coeffcent Heat transfer convecton coeffcent m 2.s -1.K -1 m 2.s -1.K -1 m 2.s -1 m 2.s -1 m.s -1 W.m -2.K -1 L v Heat of vaporzaton J.kg -1 T Temperature K t Tme s x Abscssa m θ Mosture content m 3.m -3 λ Thermal conductvty W.m -1.K -1 ρ Mass densty of dry materal kg.m -3 ρ l Mass densty of water kg.m -3 ρ v Mass densty of vapor water kg.m -3 φ REFERENCES Relatve humdty % Cerezo V. 25. Proprétés mécanque thermques et acoustques d un matérau à base de partcules végétales : approche expérmentale et modélsaton théorque, Thèse de Doctorat, INSA & ENTPE de Lyon, 242 p. Collet F. 24. Caractérsaton hydrque et thermque de matéraux de géne cvl à fables mpacts envronnementaux, Thèse de Doctorat, INSA de Renne 22 p. El Hajj, N. 21. Contrbuton à la concepton et à l élaboraton d une âme multcouche multfonctonnelle agrosourcée pour panneau sandwch : étude expérmentale et modélsaton. Kunzel M Smultaneous heat and mosture transport n buldng component Fraunhofer Insttute of buldng physc Allemagne, 1995, dsponble sur: Maalouf, C., Tran Le, A D., Lach,M., Wurtz, E., Ma, T H Effect of mosture transfer on thermal nerta n smple layer wall Case of a vegetal fbre materal ; Internatonal Journal of Mathematcal Models and Methods n Appled Scences 5 (1), pp Mendes N Models for predcton of heat and mosture transfer through porous buldng element, Thèse de doctorat, 225, Federal Unversty of Santa Catarn Floranopol SC, Brésl. Mende N., Wnkelmann, F.C., Lambert R., Phlpp. 23. Mosture effects on conducton load Energy and Budng, v. 35, n. 7, p Mendonç K.C., Inard, C., Wurtz, E., Wnkelmann, F.C., Allard, F. 22. A zonal model for predctng smultaneous heat and mosture transfer n buldng Indoor Ar 22, 9th Internatonal Conference on Indoor Ar Qualty and Clmate, Monterey, USA, 22. Pedersen C.R Predcton of mosture transfer n buldng constructon Buldng and Envronment (3) (1992), p Phlp, J.R., De Vre D.A Mosture movement n porous materals under temperature gradent Transacton of Amercan Geophyscal Unon. V.38, n.2, p Sowell, E.F., Have P. 21. Effcent soluton strateges for buldng energy system smulaton, Energy and Buldng vol. 33, p Tran Le, A.D., Maalouf, C., Ma,T.H., Wurtz, E., Collet, F.21. Transent hygrothermal behavour of a hemp buldng envelope. Energy and Buldng vol. 42, p Tran Le, A.D., Maalouf, C., Mendonç K.C., Ma,T.H., Wurtz, E., Collet, F. 29. Study of mosture transfer n double layered wall wth mperfect thermal and hydraulc contact resstances. Journal of Buldng Performance Smulaton, vol. 2, n 4, p