NUMERICAL SIMULATION OF COUPLED HEAT AND MASS TRANSFER IN HYGROSCOPIC POROUS MATERIALS CONSIDERING THE INFLUENCE OF ATMOSPHERIC PRESSURE Li FengzhiDepartment of Engineering Mechanics,Dalian University of Technology,Dalian,China and Institute of Textiles and Clothing,The Polytechnic University of Hong Kong,Hung Hom,Hong KongLi YiInstitute of Textiles and Clothing,The Polytechnic University of Hong Kong,Hung Hom,Hong KongLiu YingxiDepartment of Engineering Mechanics,Dalian University of Technology,Dalian,ChinaLuo ZhongxuanDepartment of Applied Mathematics,Dalian University of Technology,Dalian,ChinaA model of simultaneous transport in hygroscopic porous materials was developed.Water in fabrics is considered to be present in three forms:liquid water in the void space between fibers,bound water in the fibers,and vapor.It is assumed that the heat and mass transport mechanisms include movement of liquid water due to the capillarity and atmospheric pressure gradient,diffusion of vapor within interfibers due to the partial pressure gradient of vapor and total gas pressure gradient,diffusion of vapor into fiber,evaporation,and condensation of water.The moisture diffusion process into hygroscopic porous materials such as wool fabrics was simulated.At normal atmospheric pressure,the results were compared with experimental data on the temperature and water content changes reported in the literature.The distribution of temperature,moisture concentration,liquid water saturation,and atmospheric pressure in the void space between fibers at different boundary conditions are numerically computed and compared.The conclusion is that atmospheric pressure gradient has significant impact on heat and mass transport processes in hygro-scopic porousmaterials.Received 13March 2003;accepted 16July 2003.We would like to thank The Hong Kong Polytechnic University for funding this research throughprojects T612and A188in the ASD in Fashion,Design and Technology Innovation.Address correspondence to Li Yi,Institute of Textiles and Clothing,The Polytechnic University ofHong Kong,Hung Hom,Hong Kong.E-mail:tcliyi@.hkNumerical Heat Transfer,Part B ,45:249–262,2004Copyright #Taylor &Francis Inc.ISSN:1040-7790print/1521-0626online DOI:10.1080/104077904902688142491.INTRODUCTIONThe clothing system plays a very important role in determining the human body core temperature and other human thermal responses because it determines how much of the heat generated in the human body can be exchanged with the environment.With the development of new technology,it is becoming important to know how the human body will behave thermally under different environmental conditions with various clothing systems.In order to obtain a comfortable micro-climate for human body,it is necessary to understand the thermal and moisture transport behavior of the clothing.The first clothing model that describes the mechanism of transient diffusion of heat and moisture transfer into an assembly of hygroscopic textile materials was introduced and analyzed by Henry [1].He developed a set of two differential coupled governing equations for the mass and heat transfer in a small flat piece of clothingNOMENCLATUREc v volumetric heat capacity of the fabric,J =m 3Kc vf volumetric heat capacity of fiber,J =m 3KC fwater vapor concentration in the fibers of the fabric,kg =m 3div divergenceDdiffusivity of vapor,m 2=sD f ðw c ;t Þdiffusion coefficient of water vapor in the fibers grad gradienth c convection mass transfer coefficient,m =sh l $g mass transfer coefficient,m =sh t convection heat transfer coefficient,J =m 2Kh vap latent heat of evaporation =condensation,J =kgk mix thermal conductivity of the fabric,W =m KK intrinsic permeability,m 2K rg relative permeability of water vapor K rw relative permeability of liquid water L thickness of fabricm a mass flux of dry air under gas pressure gradient driving m v mass flux of vapor under gas pressure gradient drivingm D v diffusion mass flux of water vapor m w diffusion mass flux of liquid water M w mole mass of water vapor,kg =mol p a dry air partial pressure,kg =m s 2p c capillary pressure,kg =m s 2p g pressure of gas phase,kg =m s 2p v water vapor partial pressure,kg =m s 2rradius,mS liquid water volumetric saturation (liquid volume =pore volume)S v specific area of the fabric,l =m T temperature of the fabric,K T 1environmental temperature,KWevaporation or condensation flux of water in interfiber void space of fabric,kg =m 3sw c water content of the fibers in the fabric,kg =kg G boundarye porosity of fabricl heat of sorption or desorption water or vapor by fibers,J =kgm g dynamic viscosity of gas,kg =m s m w dynamic viscosity of water,kg =m s r a density of dry air,kg =m 3r w density of liquid water,kg =m 3r vwater vapor concentration in the air filling the interfiber void space,kg =m 3r vs saturated water vapor concentration,kg =m 3r v ?environmental water vapor concentration,kg =m 3Superscripts n previous time n þ1present time Subscripts 0initial value 1left boundary N right boundary ?environment250L.FENGZHI ET AL.SIMULATION OF COUPLED HEAT AND MASS TRANSFER251 material.The analysis of Henry was based on a simplified analytical solution. Downes and Mackay[2]and Watt[3]found experimentally that the sorption of water vapor by wool is a two-stage process.In order to describe the complicated process of the two-stage adsorption behavior in textile materials,Nordon and David [4]presented a model in terms of experimentally adjustable parameters appropriate for thefirst and second stages of moisture sorption.However,their model did not take into account the physical mechanisms of the process.For this reason,Li and Holcombe[5]introduced a new two-stage absorption model to better describe the coupled heat and moisture transport in fabrics.Li and Luo[6]improved the sorption rate equation by assuming that the moisture sorption by a woolfiber can be generally described as a uniform-diffusion equation for both stages of sorption.Luo et al.[7]presented a dynamic model of heat and moisture transfer with sorption and condensation in porous clothing assemblies.Their model considers the effect of water content in the porousfibrous batting on the effective thermal conductivity as well as radiative heat transfer.However,the above-mentioned models ignore the effect of liquid water movement.Fan and Wen[8]reported a model,in which eva-poration and mobile condensates are considered.Li and Zhu[9]reported a new model that takes into account the condensation=evaporation and liquid diffusion by capillary action,which is a function offiber surface energy,contact angle,and fabric pore size distributions.Furthermore,they investigate the effects of the pore size distribution,fiber diameter[10],thickness and porosity[11]on the coupled heat and moisture transfer in porous textiles.Wang Zhong et al.[12]reported a model con-sidering the radiation and conduction heat transfer coupled with liquid water transfer,moisture sorption,and condensation in porous polymer materials.How-ever,in the above references[1–12],the models were based on the mass diffusion due only to the concentration gradient;the effect of the atmospheric pressure gradient on heat and moisture transfer in porous materials was ignored.For example,when a person runs,the atmospheric pressure between the inside and the outside of clothing is different,which may have significant impact on the thermal comfort and protec-tion of clothing.Although the effects of the atmospheric pressure gradient on mass transfer in porous media were considered by previous researchers[13,16],these models are established for nonhygroscopic materials.In order to investigate the influence of atmospheric pressure gradient on heat and mass transfer within hygroscopic textile materials,and to provide insights into the functional design of clothing for windy conditions and active sportswear outdoors,we report a new model by introducing new equations=terms and integrating them.2.MATHEMATICAL FORMULATIONA schematic diagram of the physical mechanisms within fabric is shown in Figure1.To obtain the governing equation,we have made the following assump-tions.First,the clothing is isotropic,and the gas phase is considered to be an ideal gas composed of dry air and water vapor,which are regarded as two miscible species. Second,local thermal equilibrium exists among all phases.This is reasonable,as the pore dimension in the textile material is small.Third,volume changes of thefibers due to changing moisture content are neglected.Fourth,diffusion within thefiber is considered to be so slow that the moisture content at thefiber surface is always insorptive equilibrium with that of the surrounding air.Fifth,water in fabrics is considered to be present in three forms:free liquid water in the void space of interfibers,bound water in the fibers,and water vapor.The mass transport mechanisms are movement of free liquid water due to the capillarity and atmo-spheric pressure gradient,diffusion of vapor in the space between fibers due to the partial pressure gradient of vapor and total gas pressure gradient,and diffusion of vapor in the fiber due to sorption =desorption.Based on the above assumptions,we can establish the following mathematical equations for the coupled heat and mass transfer in the clothing according to the conservation of masses and heat energy:q E ð1ÀS Þr v ½ ½ q t þq C f 1ÀE ðÞÂÃq t ÀE ð1ÀS ÞS v h l $g r vs ðT ÞÀr v ½ ¼div ðÀm D v Þþdiv ðÀm v Þq ½E S r wq t þE ð1ÀS ÞS v h l $g r vs ðT ÞÀr v ½ ¼div ðÀm w Þq E ð1ÀS Þr a ½ ½ q t ¼div ðm D v Þþdiv ðÀm a ÞC v q T q t Àl ð1ÀE Þq C f q t þh vap E ð1ÀS ÞS v h l $g r vs ðT ÞÀr v ½ ¼div ½k mix ðgrad T Þ :8>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>:ð1ÞHere,E is porosity;S is saturation of free liquid water;S v is the specific area of thefabric;r v is water vapor concentration;r a is the concentration of dry air;r w is the density of liquid water;C f is the water vapor concentration in the fibers;h l $gisFigure 1.Schematic diagram of the physical model.252L.FENGZHI ET AL.the mass transfer coefficient;r vsðTÞis the concentration of saturated water vapor at T;h vap is the latent heat of evaporation=condensation;l is the sorption heat of thefiber;m v is the massflux of vapor under total atmospheric pressure gradient;m Dv isthe diffusion massflux of water vapor;m a is the massflux of dry air under total atmospheric pressure gradient;m w is the diffusion massflux of liquid water;c v is the effective volume heat capacity;and k mix is the effective thermal conductivity of the fabric.Thefirst equation in(1)represents the mass balance of water vapor.Thefirst term on the left side represents vapor storage within the void space of the interfiber; the second term represents water vapor accumulation rate within thefiber,i.e.,the sorption rate offibers;whereas the third term is evaporation or condensationflux of the water in the interfiber void space.The right side of the equation represents water-vapor diffusion.Thefirst term denotes the effect of the vapor diffusion under vapor partial pressure gradient,whereas the second term represents the effect of the vapor diffusion under total gas pressure gradient driving.Similarity,the second equation represents the mass balance of liquid water,and the third equation represents the mass balance of dry air.The fourth equation in(1)represents the energy balance. Thefirst term on the left side of the fourth equation represents energy storage, whereas the second and third terms represent sorption latent heat of water vapor by fibers and the latent heat of liquid water within interfibers,respectively.The right side represents the heat conduction.Sorption and desorption of moisture by thefibers obey the Fickian Law[6]:q C f q t ¼1rqq rrD fðw c;tÞq C fq r!ð2Þwhere D fðw c;tÞis the diffusion coefficient,which has different presentation at dif-ferent stages of moisture sorption;C f is the moisture concentration in thefiber; w c is the bound water content in thefibers.The boundary condition around thefiber is determined by assuming that the moisture concentration at thefiber surface is instantaneously in equilibrium with the surrounding air.Hence,the moisture concentration at thefiber surface is determined by the relative humidity of the surrounding air and temperature,i.e.,[6]C fðR fÞ¼fðRH;TÞð3Þwhere f is the moisture sorption isotherm of thefibers,which can be determined experimentally for differentfibers.The pore sizes infibrous materials are generally small,so that the diffusion of flow is governed by Darcy’s law[1].In the pores formed betweenfibers,we have the massflux of water vapor and dry air under total atmospheric pressure gradient, respectivelym v¼Àr v KK rgm ggradðp gÞÂÃð4Þm a¼Àr a KK rgm ggradðp gÞÂÃð5ÞSIMULATION OF COUPLED HEAT AND MASS TRANSFER253where p g is the atmospheric pressure,K is intrinsic permeability,K rg is relative permeability of water vapor,and m g is the gas-phase dynamic viscosity.For the free liquid water phase,Darcy’s law is expressed as[13]m w¼Àr w KK rwm wgradðp gÀp cÞð6Þwhere K rw is the relative permeability of liquid water,m w is the dynamic viscosity of the liquid water,and p c is the capillary pressure.For the water-vapor phase,diffusion massflux under partial pressure gradient is expressed as[13]m Dv ¼À1:952Â10À7eð1ÀSÞÂT0:8p agradðp vÞð7Þwhere p a is the partial pressure of dry air and p v is the partial pressure of water vapor.In order to generate a solution to the equations mentioned above,we need to specify an initial condition and boundary conditions on the fabric surfaces in terms of concerntration,saturation,temperature,and atmospheric pressure.Initially,a fabric is equilibrated to a given atmospheric pressure,temperature,saturation,and humidity;the temperature,atmosphere,saturation,and concentration are uniform throughout the clothing at known value.T¼T0r v¼r v0S¼S0p g¼p g0C f¼fðRH0;T0Þð8ÞThe boundary conditions arem DvÁ n j GþmÁ n j G1¼h cðr vÀr v1ÞS jG1¼S B;m wÁ n j g12¼qð9ÞK mix grad TÁ n j G¼h tðTÀT1Þp g j G¼p g Gwhere G denotes the boundary,h c is the mass transfer coefficient,h t is the convective heat transfer coefficient,and the subscript1denotes the environment.3.DISCRETIZATION OF THE CONTINUUM EQUATIONTo derive a numerical solution for Eqs.(1),(8),and(9)by using thefinite-volume method,we select a well-distributed control volume with D x,as shown in Figure2.For example,thefirst equation of(1)can be rewritten as follows:A qr vq tþBq Sq tþCþD¼qq xEqr vq xþqq xFq Tq xþqq xGq p gq xð10ÞwhereA¼eð1ÀSÞB¼Àer v C¼e f q C fq tD¼Àeð1ÀSÞh lg S v r vsðTÞÀr v½254L.FENGZHI ET AL.E ¼ð1:952e À7Þe ð1ÀS ÞT 0:8p a RTM wF ¼ð1:952e À7Þe ð1ÀS ÞT 0:8p a R r vM wG ¼r vKK rg m gIf the control volume P is located in the inner of zone,integration of Eq.(10)over the control volume givesZ Or A qr v q t þB q S q t þC þDdx ¼Z Orq q x E qr v q x þq q x F q T q x þq q x G q p gq x !dxð11ÞThenA n p r n þ1vp Àr n v D t D x þB n p S n þ1vp ÀS n vp D t D x þC n pD x þD np D x ¼E qr v q x eÀE qr v w þF q T e ÀF q T w þG q p g e ÀGq p gwð12ÞNow the right-hand side of Eq.(12)can be written asE qr v q x e ÀE qr v q x w þF q T q x e ÀF q T q x w þG q p g q x e ÀGq p g q xw¼E n e r n þ1v E Àr n þ1v pD xÀE n wr n þ1v p Àr n þ1v WD xþF n eT n þ1EÀT n þ1p D xÀF n wT n þ1p ÀT n þ1W D x þG n e p n þ1gE Àp n þ1gp D x ÀG n wp n þ1gpÀp n þ1gW D xð13ÞWith the new symbols,Eq.(12)becomesK w v r n þ1v W þK wt T n þ1W þK wg p n þ1gW ÀK p v r n þ1v P ÀK ps S n þ1P ÀK pt T n þ1P ÀK pg p n þ1gPþK e v r n þ1v EþK et T n þ1EþK eg p n þ1gE¼RRð14ÞFigure 2.Schematic map of control volume.SIMULATION OF COUPLED HEAT AND MASS TRANSFER 255where K wv¼m E n w,K wt¼m F n w,K wg¼m G n w,K pv¼m E n wþm E n eþA n p,K pt¼m F nw þm F n e,K ps¼B n p,K pg¼m G n wþm G n e,K cv¼m E n e,K et¼m F n e,K eg¼m G n e,RR¼ÀA np r nvpÀB n p S n pþC n p D tþD n p D t.If control volume P is located on the left boundary,we consider that the integration area is half of the inner volume andE qr vq xþFq Tq xþGq p gq xP ¼h cl r nþ1vpÀr vp1ð15ÞThen,we can obtainÀK pv r nþ1vP ÀK ps S nþ1PÀK pt T nþ1PÀK pg p nþ1gPþK ev r nþ1vEþK et T nþ1EþK eg p nþ1gE¼RRð16Þwhere m¼D t=D x2,Z¼D t=D x,K pv¼2m E n eþA n pþ2Z h cl,K pt¼2m F n e, K ps¼B n p,K pg¼2m G n e;K ev¼2m E n e,K et¼2m F n e,K eg¼2m G n e,RR¼ÀA n p r n vpÀB n p S n pþC n pD tþD npD tÀ2Z h el r vp1.Similarly,if control volume P is located on the right boundary:K w v r nþ1n W þK wt T nþ1WþK wg p nþ1gWÀK p v r nþ1n PÀK ps S nþ1PÀK pt T nþ1PÀK pg p nþ1gP¼RRð17Þwhere m¼D t=D x2,Z¼D t=D x,K w v¼2m E n w,K wt¼2m F n w,K wg¼2m G n w, K p v¼2m E n wþA n pþ2Z h cN,K pt¼2m F n w,K ps¼B n p,K pg¼2m G n w;RR¼ÀA n p r n n pÀB n p S npþC n p D tþD n p D tÀ2Z h cN r n p1N,where h cN is the mass transfer coefficient in theright boundary,and r n p1N is the concentration of right environment water vapor.Following the same procedure as for the water-vapor mass conservation,we can derive the discretization equations for liquid water,energy,and dry air.By specifying initial conditions we can calculate the coefficient of the discretization and its right term,the values of water-vapor concentration,liquid water saturation, temperature,and atmospheric pressure at next time,can be obtained.The dis-cretization errors of these schemes are O½ðD xÞ2þðD tÞ2 .And the full implicit scheme is stable without any restriction on D t=D x2.In order to obtain grid independence of the solution,we selected grids of different sizes and did computations.The difference in solution betweenfine and coarse grids with increase of size by2is less than2%.4.NUMERICAL SIMULATION AND DISCUSSIONFor computation,the values of the main parameters are listed as Table1.parison between Theoretical Predictions and Experimental MeasurementsAs reported previously by Li Yi et al.[5],a wool fabric sample measuring 3cm615cm62.96mm was suspended in a cell from an electronic balance,which can measure the weight change of fabric during the sorption process.In the cell the temperature was controlled at293.12Æ2K,and the atmospheric pressure was controlled at1atm.The relative humidity was produced by aflow-divider humidity 256L.FENGZHI ET AL.generator,which can change the relative humidity (RH)from 0%to 99%in 1%steps to an accuracy of Æ0.1%of total flow.Fabric was equlibriated in the cell at 0%RH for 90min,then the RH in the cell was rapidly changed from 0%to 99%at time zero,and this RH was maintained for 90min.The surface temperature of the specimen was measured by using a fine thermocouple wire attached to fabric surface.The mean water content of the fabric was calculated on the basis of the weight recorded by a balance.The detailed information on experimental measurements and uncertainty analysis for experimental data was reported previously [5].Table 1.Parameter values for computation ParameterSymbol Unit Value and referenceDensity of a fiber r f kg =m 31,300[14]Volumetric heat C vf kJ =m 3K 373.3þ4661W c þ4.221T [14]capacity of fabric Thermal conductivity of fabricK fab W =m 2K (38.49370.72w c þ0.113w c 270.002w c 3)61073[14]Head of sorption of water vapor by fibers l kJ =kg 1602.5exp(711.72w c )þ2522.0[14]Diffusion coefficientof water vapor in fiberD f ðw c ;t Þm 2=s(1.04þ62.8w c 71342.59w c 2)610714t <540s [14]1:6164f 1Àexp ½À18:16exp ðÀ28:0w c Þ g t !540s [14]Dynamic viscosity of gasm g kg =m s 1.8361075[15]Dynamic viscosity of liquid waterm w kg =m s 1.061073[15]Intrinsic permeability of fabricKm 21.5610713[16]Figure parison of the temperature between theoretical predictions and experimental measurements.SIMULATION OF COUPLED HEAT AND MASS TRANSFER257The new model described in Section2is applied to this experimental condition by specifying corresponding boundary conditions.The comparisons of temperature and bound water content between theoretical prediction and experimental mea-surements[10]are shown in Figures3and4,respectively.Figure3shows tem-perature changes at the surface of the fabric during the dynamic-moisture diffusion process.Since the temperature of surroundings was kept constant at293.15K,in the testing conditions,no external heatflow was provided to the fabric.Hence the temperature rise in the fabric was due purely to the heat released during the moisture-sorption process.The mean error between theoretical prediction and experimental measurements on temperature is0.13%.Figure4shows the mean moisture uptake of the fabric during humidity transient.The mean error on water content of fabric is4.6%.The diameter of thefiber significantly affects its sorption rate.The difference between measured and actual diameter of thefiber and porosity of fabric may be the main sources of paring the predicted temperature and mean moisture uptake with the experimental results,it is obvious that the models are able to predict the moisture sorption of thefibers with satisfactory accuracy.4.2.Influence of Atmospheric Pressure GradientIn order to investigate the effect of the pressure gradient on heat and mass transfer in porous materials,we carried out a series of computational experiments; two cases are selected to show the trends.In the computations,the fabric sample is assumed to be made of woolfiber with thickness L¼3.0mm,and the initial and boundary conditions were specified as follows.The initial conditions wereT0¼298:15K r v0¼0:01kg=m3S0¼0p g0¼1:0135e5PaAt the left (x ¼0)boundary,T 1¼298:15K r v 1¼0:02kg =m 3m w j G ¼0p g G ¼1:0135e 5PaAnd at the right (x ¼L)boundary,T 1¼298:15K ;r v 1¼0:02kg =m 3S ¼0:4p g G ¼2:0135e 5Pa in Case 11:0135e 5Pa in Case 2(The difference between case 1and case 2is the pressure boundary condition at the location x ¼L .Other conditions are the same.The corresponding numerical simu-lations and comparisons are shown in Figures 5–9.Figure 5a shows the atmospheric pressure variation in the fabric with time under the pressure boundary condition of case 1.We can see that the atmospheric pressure is uniform constant initially,then the atmospheric pressure redistributes with the new boundary pressures.The pressure at x ¼L reaches 2atm.Figure 5bFigure 5.Distribution of atmosphericpressure.Figure 6.Distribution of water-vapor concentration.SIMULATION OF COUPLED HEAT AND MASS TRANSFER 259represents the pressure distribution under the condition of case 2.The pressure is uniform because of the same initial and boundary conditions.Figure 6a shows the distribution of the water-vapor concentration in case 1:the water vapor concentration at x ¼0is higher than that at x ¼L .This is because of the effect of atmospheric pressure.The atmospheric pressure gradient,which is the main driving force of water-vapor movement,makes the water vapor diffuse from high pressure (location x ¼L )to low pressure (location x ¼0).Figure 6b shows dis-tribution of the water-vapor concentration in case 2.The water vapor diffuses due to the driving force of water vapor partial pressure gradient only,when the total pressure gradient does not exist.Because of the water-vapor diffusion,the water-vapor concentration in the fabric increases from 0.01to 0.02kg =m 3with time.Then,the concentration of the water vapor reaches equilibrium.Figure 7shows the distribution of water content in fiber.Since the hygro-scopicity of wool is high,water vapor is absorbed.The different water vapor con-centration affects the relative humidity of the water vapor,and then affects the amount of water absorbed by the fiber.From Figures 7a and 7b we can see that the distributions of water content in the fiber agree with the water-vapor concentration in Figures 6a and 6b ,respectively.Figure 7.Water content distribution offiber.Figure8shows the predicted temperature distribution in the wool fabric during the vapor diffusion process.From Figure8,we can see that the temperature rises in the middle layer of the fabric because of the heat released during moisture sorption. At the beginning,the temperature rises quickly,due to the large sorption rate of fiber.Then the temperature decreases gradually,with time reaching equilibrium with the environmental temperature because of much lower sorption rate and heat exchange with environment.At the beginning,the temperature in case1is lower than that in case2.The reason is that the atmosphere pressure gradient affects the dis-tribution of the water-vapor concentration.The different water-vapor concentration affects the amount of water absorbed by thefiber,which leads to different sorption heat.Most of the water content of thefibers in the fabric,except at the boundary x¼L in case1,is lower than that in case2(see Figure7),so the temperature in case1 is lower than that in case2.From Figures8a and8b we also can see the temperature at location x¼L is larger than that at location x¼0in thefirst stage.This is because there is much more liquid water at location x¼L than that at x¼0,and the conductivity of liquid water is greater than that of fabric.Figure9shows the distribution of liquid water saturation during the process of liquid water diffusion into the wool fabric by capillary action.We can see that the liquid water diffuses from side x¼L to x¼0.The reason is that the diffusion potential of the liquid water is liquid water pressure,which equals the difference between atmospheric pressure and capillary pressure.The capillary pressure in the region of high saturation of liquid water(x¼L)is lower than that in the region of low saturation of liquid water(x¼0).In case1,the atmospheric pressure at x¼L is higher than that at x¼0.And in case2,the atmospheric pressure at x¼0is equal to that at x¼L.So the total liquid water driving potential at location x¼L is higher than that at location x¼0in both case1and case2.From Figures9a and9b we can see that the difference in the distributions of liquid water saturation between case1 and case2is not large in this computational condition.5.CONCLUSIONIn this article,we report a new model of heat and moisture transfer inhygroscopic porous textile materials,considering the influence of the atmospheric。
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