AND MOISTURE TRANSFER THROUGH

Conrad Voelker1, Sabine Hoffmann1, Oliver Kornadt1, Edward Arens2, Hui Zhang2 and Char- lie Huizenga2 1Bauhaus-Universität Weimar, Germany 2University of California, Berkeley, USA

ABSTRACT INTRODUCTION The UC Berkeley Comfort Model is a helpful simula- The task of clothing is, besides fashionable tion tool for the assessment of in embodiment and expression, the protection against non-uniform environments. A major element of the harmful environmental stresses including the climatic model is the implementation of a clothing node, conditions. On this account, well being, health and which considers both heat and moisture capacitance productivity of humans largely depends on clothing. of clothing. of the clothing has been Humans usually wear clothing all day long - even in demonstrated to be important when considering tran- bed we are surrounded by textiles - therefore it is sient effects. Moisture capacitance is important to often characterized as a “second skin”. Except in correctly model evaporative heat loss from the body tropical latitudes, a person needs constant protect to through clothing. The moisture model uses the regain avoid simply freezing. But protection against cold is approach to calculate the amount of moisture that a only one aspect of the physiological function of specific fabric will absorb at a given . clothing. When the human body rises above a certain level, an effective is provided NOMENCLATURE by the of sweat coming out of the glands. A area (m²) The type of clothing has a major impact on this c specific heat capacity (J/kgK) process, since it is responsible for the diffusion of C heat capacity (J/K) water vapor. Hence, clothing strongly influences the fcl clothing surface area factor physiological operations including the temperature F view factor control of the human body. Detailed knowledge of h coefficient (W/m²K) the exact process, the importance of which should not hfg heat of vaporization of water (kJ/kg) be underestimated, is necessary to determine thermal i clothing vapour permeation efficiency comfort. I (clo) The human body converts the provided by Lr Lewis ratio (K/kPa) food into and heat, depending mainly on the m mass (g) level of activity. To guarantee a constant body p vapor (kPa) temperature within a narrow range, the heat has to be Q heat (W) released to the environment. This process is R regain content (%) controlled by signals, which are sent by the t time (s) thermoreceptors of the skin and the hypothalamus, T temperature (K) managing heat production and heat exchange using v velocity (m/s) four different mechanisms: vasodilation, vaso- w skin wettedness constriction, perspiration and shivering. The main α absorption coefficient part of the heat release occurs through the skin, only ε emission coefficient a small percentage accounts for the heat transfer via φ relative humidity respiration. Since the skin is usually largely covered 2 4 σ Stefan-Boltzmann constant (W/m K ) with clothing, the heat release of the human body is θ temperature (°C) strongly influenced by the heat and moisture transfer Suffix through clothing. a air Heat release via skin can be divided into dry heat cl clothing losses and losses through evaporation. The former c convective can be split into , conduction, and, e evaporation additionally, the radiative exchange with the m mean surrounding surfaces. Dry losses depend largely on n nude the insulation of the clothing, which includes the r radiative insulation of the clothing itself and the insulation of s solar

IBPSA Building Simulation 2009, University of Strathclyde, Glasgow, Scotland, July 27 – 30. page 1 of 7 the air layer between skin and clothing and of heat loss. First, the nude skin is exposed to the respectively the air between different clothing layers. surrounding air. Second, the skin is covered with The second, the evaporative heat exchange with the clothing influencing the thermophysiological environment, is the removal of heat from the human behavior of the human being. And third, the human is body by the evaporation of sweat from the skin. This in direct contact to other materials such as a chair. process is mainly driven by the thermoregulatory However, this paper only deals with heat loss through system, the permeation efficiency of the clothing and clothing. the surrounding air’s water vapour pressure. If the It is assumed that there is no transfer ratio of evaporated and produced perspiration is low, occurring directly between the skin and the moisture accumulates in the clothing layer. This environment. The latent heat exchange always occurs process influences the thermal characteristics of the first between skin and clothing, and then, as the garment due to swelling of the fibres causing changes clothing’s partial changes, there is a in the size, shape and stiffness. latent heat exchange between the clothing and the (Henry 1939) developed one of the first theories of environment. Furthermore, we assume that the coupled heat and moisture transfer through clothing garment features isotropic properties, which includes considering accumulation effects. (Ogniewicz et al., an equilibrium between the moisture content at the 1981) proceeded with a steady-state model, which surface of the fibres and the surrounding air. included both the convective and the diffusive Additionally, we have left out the change of the transport mechanisms in the garment, along with properties due to swelling of the fibres resulting from phase change due to and evaporation. the absorption process, meaning that no change of Since time-dependent modelling is necessary due to occurs. Since the temperature does not water accumulation, (Farnworth 1986) developed a strongly influence the characteristics of clothing, it is rather simple dynamic model that included heat not observed. transport by conduction and as well as moisture transport by diffusion. Detailed dynamic HEAT AND MOISTURE TRANSFER modelling, including a comparison with experimental THROUGH CLOTHING results, was later done by ( et al., 2005). (Wu et The human body converts the energy provided by al., 2008; Wissler et al., 2009) presented food into work and heat, depending mainly on the mathematical models for heat and moisture transport level of activity. For example, when doing office through multi-layer clothing. Nowadays the heat and work, the human body has a metabolic rate of moisture transfer is a factor for the international approximately 70 W/m² (1,2 met), which is standards (ISO 11092 1993; ASHRAE 2005; ISO equivalent to about 130 W for an average male 7730 2006; ISO 9920 2009). person. To keep the body temperature at a constant In combination with the thermal interaction of the level, heat is released via evaporation, radiation, human body, (Shitzer et al., 1985) observed the heat convection, conduction and finally respiration. Since exchange with clothing, even considering - the latter affects only the core layer of the chest it is cooled garments. Both (Jones et al., 1992) and (Li et not taken into further consideration in this paper al., 1998) later introduced dynamic models of heat which only deals with heat transfer through the outer and moisture characteristics in interaction with two- layer, from the skin through clothing to the node human thermoregulation model of (Gagge et al., environment. In the UCB thermal comfort model 1971). (de Dear et al., 1993) created a very detailed each segment of the human body can be completely skin and clothing model by dividing skin and nude, partly nude and partly clothed or fully clothed. clothing into 40 layers. (Fiala et al., 1999) and (Xu et The algorithms describing the sensible and latent heat al., 1997) developed their own human thermo- transfer through the clothing apply only to the regulation models including heat and moisture clothed fraction. The heat balance of the clothing transfer through clothing including accumulation node can be described as follows: effects. With a sweating thermal manikin, (Celcar et al., 2008) investigated the characteristics of clothing. . . . dθcl C = Q −clskin,c + Q −clskin,e − Q −envcl,c In order to determine thermal comfort it is necessary cl dt (1) to understand the thermal behavior of the clothing . . . (Voelker et al., 2009a). This present paper focuses on Q −envcl,e Q −envcl,r +−− Q −envcl,s the thermal characteristics of clothing, dealing with heat and from the skin through the clothing to the environment. The introduced clothing This heat balance contains the heat transfer from the model is part of the UC Berkeley comfort model, skin to the clothing through convection (Qc,skin-cl) and with a supplementary node in every segment of the through evaporation (Qe,skin-cl). The heat exchange existing 65 node model (Huizenga et al., 2001; with the environment is described by the heat losses Hoffmann et al., 2008; Voelker et al., 2009b). The through convection (Qc,cl-env), evaporation (Qe,cl-env), UC Berkeley comfort model considers different ways radiation (Qr,cl-env) and possible gains due to solar

IBPSA Building Simulation 2009, University of Strathclyde, Glasgow, Scotland, July 27 – 30. page 2 of 7 radiation (Qs,cl-env). Ccl indicates the heat capacity of decreased clothing insulation can be determined the clothing and is calculated by according to (ISO 7730 2006). The outer surface of a clothed part is calculated using the factor f , which ⋅= cmC (2) cl cl clcl augments the skin surface according to the type of clothing by with mcl as the clothing mass (for exemplary values see also table 1). However, depending on the level of cl = ⋅ fAA clskin , (5) insulation, the mass of clothing is roughly estimable according to (McCullough et al., 1985) with 0.74 clo/kg. Finally, ccl expresses the specific heat whereas the parameter fcl represents the clothing area capacity of the garment. factor, which is the ratio of the projected surface area of the clothed body to the projected surface area of the nude. It is possible to determine the clothing area transfer from skin to clothing node factor exactly by using photographic methods, but a The sensible heat transfer from the skin node to the rough estimate is feasible according to (McCullough clothing node can be calculated using the equation et al., 1985) using the following equation:

. A 1 f cl ⋅+≈= I31.00.1 . (6) Q −clskin,c = A ()skincl θ−θ⋅⋅ cl cl cl + II An cla , (3)

with θskin describing the skin temperature calculated Latent heat transfer from skin to clothing node by the 65 node model and the clothing temperature The amount of latent heat being released from the θclo. Ia describes the insulation of the air layer, while skin is influenced by two issues. Firstly, it depends Icl is the summation of the effective insulation of the on the body’s heat balance. Only under warm worn garments of every single segment of the human ambient conditions or high exercise levels will body. It can be roughly calculated by accumulating significant sweating occur. The human body’s heat the number of overlaying clothing layers covering balance determines whether or not to release heat via one body segment (Olesen 1985). evaporation. The principle of the control system which is applied to the thermal comfort model is described, amongst others, in (Hoffmann et al., cl = ∑II i,clu 2008). Two control signals, called SWEAT and i (4) WARM, based on (Stolwijk 1971), are determined based on the temperature differences between the Generally, the unit of the insulation is typically speci- calculated skin and core and their set fied using the unit clo (1 clo = 0.155 m²K/W). Aver- points. By using the coefficient sweatfac, the age values of the effective insulation of several following equation also takes into account the fact garments can be seen in table 1. that different body parts are unequally able to sweat. In the model, the evaporative heat transfer is firstly calculated as Table 1

Garment insulation and mass (McCullough et al., 1985; ASHRAE 2005) WARM * 10 Q& −clskin,e = sweatfac ⋅⋅ 2SWEAT . (7) GARMENT m Iclu [kg] [clo] Second, the environment’s vapour pressure limits the Briefs 0.065 0.04 Shirt 0.196 0.28 ability of evaporation. The maximum evaporation of Trousers 0.459 0.24 the human body is limited to the surrounding vapour Socks 0.049 0.03 pressure. Once the partial vapour pressure of the Suit jacket 0.652 0.48 clothing node is known, the difference between the Shoes 0.186 0.04 saturated vapour pressure on the skin’s surface (assuming the skin being completely sweat covered) and the partial vapour pressure of the air / clothing However, the insulation of the clothing and the determines the maximum evaporative heat loss. additional layer of air are influenced by air velocity as well as by human movement. This may result in a & −⋅⋅= ppAhQ decrease of the clothing’s insulation value, which max,e ( skin,satcle cl ) (8) may be corrected. The corrected factor for the

IBPSA Building Simulation 2009, University of Strathclyde, Glasgow, Scotland, July 27 – 30. page 3 of 7 In case the skin is not completely covered by sweat, being absorbed in the clothing node can be expressed (Eq. 10) using the skin wettedness w modifies the as following evaporation rate between skin and clothing. As it is . difficult to determine the evaporative heat transfer . Q m = −clskin,e coefficient h [W/Pa·m²], a simplified equation is OH abs2 e hfg used for the calculation: (12)

⋅ iLR The parameter hfg is the heat of vaporization of water h = m and is equal to 2.43 · 103 J/g at 30°C according to e ⋅ 155.0I cl (9) (ASHRAE 2005). The absorption of water has a major impact on the heat and mass transfer through the clothing layer. First of all, absorbed water in the The Lewis relation (LR) simply describes the clothing layer increases both heat capacity and relationship between convective heat transfer and . Therefore, the sensible heat mass transfer coefficients and equals, at typical transfer through the clothing layer changes. With an indoor conditions, 16.5 K/kPa (ASHRAE 2005). The increased water content more heat can be stored in parameter im describes the total vapour permeation the tissue, while at the same time the heat conduction efficiency, which shows the evaporative to the outer surface increases as well. Due to the of the clothing system (Woodcock 1962). It is the absorption process, the heat capacity of the clothing ratio of the actual evaporative heat flow capability is modified by between the skin and the environment to sensible heat flow capability to Lewis ratio (ASHRAE 2005). It is a , which does not include ⋅+⋅= cmcmC abs2 2OHOHclclcl insulation or thickness value. A value of zero means (13) completely impermeable, the maximum is equal to 1 and stands for ideally permeable clothing. In Secondly, the vapour pressure of the clothing node opposition to the parameter icl, it includes the increases with increasing water content and might resistance of the air layer surrounding the human even reach the level of saturation. An increasing va- body. According to (McCullough et al., 1989; pour pressure limits at the same time the ability to ASHRAE 2005), an average value of im = 0.4 can be sweat. In order to determine the new vapour in the used. Additional values are provided in table 2. clothing node the so called regain approach is used. Table 2 The first scientific approach to investigate regain was Moisture permeability index for clothing done by (Schloesing 1893), who investigated the (McCullough et al., 1989) hygroscopicity of several fabrics. Further compre- hensive research on water absorption and desorption in clothing was carried out by (Urquhart et al., 1924; ENSEMBLE im Men’s business suit 0.37 Speakman et al., 1936). According to (Morton et al., Men’s summer casual 0.43 1997), the regain is calculated by Jeans & shirt 0.40 Insulated coverall 0.39 . m OH R abs2 Δ⋅= t m Even under low activity conditions or a cold climate cl . (14) without obvious sweating, the skin is still covered by a 6 % sweating rate of the maximum sweating However, a garment’s moisture regain is not only possible (Arens et al., 2006). Therefore the actual controlled by the human being’s perspiration or the evaporative heat loss from skin to clothing can be air humidity, but also depends on the garment’s past. expressed as following: Illustrated in figure 1, the plot of regain against rela- tive air humidity shows two main curves describing a * Q& −clskin,e path-dependent hysterese loop. The lower curve of += 94.006.0w (10) the plot is called the absorption isotherm and shows & Q max,e the equilibrium regain of a garment which was at the beginning absolutely dry and was exposed to gradu- ally higher . Q& * ⋅= Qw & (11) −clskin,e max,e The upper curve is generated when the garment was initially soaked and is then exposed to gradually lower humidities. This curve is called the desorption Water absorption in the clothing node isotherm. One can observe, that both curves show a When moisture is transferred from skin to clothing sigmoidal characteristic. At low relative air humidity, the humidity in the tissue will increase. The water the curves are quite steep, followed by a linear course

IBPSA Building Simulation 2009, University of Strathclyde, Glasgow, Scotland, July 27 – 30. page 4 of 7 at medium humidities. At high humidities, finally, and the short wave absorption of solar radiation. The the course is extremely steep again, which has an convective term can be expressed as imprecise effect during measurements. Between the two curves, additional intermediate . curves exist. For example, if the absorption process Q Ah −envcl,c ()θ−θ⋅⋅= aclclc , (15) begins at approximately 10 % on the desorption curve, it will not join the absorption curve before a relative air humidity of 60 % is reached. The same depending on the difference of the temperature of the phenomenon applies for the opposite direction: If clothing node and the temperature of the surrounding desorption starts at 90 % humidity on the absorption air. As in the case of the sensible heat transport from curve, it will not meet the desorption curve before the skin to the clothing, the dry heat loss is calculated 30 %. To get on either the absorption curve or the using a heat transfer coefficient. These were derived desorption curve it is therefore essential to start at from experiments with thermal manikins in climate either absolutely dry or absolutely wet conditions. chambers and depend strongly on the air velocity and the observed segment (table 3). 24

R [%] Table 3 Convective heat transfer coefficients [W/m²K] (de 20 Dear et al., 1997)

n 16 SEGMENT hc hc = a·v (v ≤ 0.1 m/s) (v > 0.1 m/s) a n 12 Head 3.7 11.75 0.625 Chest 3.0 9.1 0.59 8 Back 2.6 8.9 0.63 Pelvis 2.8 8.2 0.65

4 Shoulder 3.4 11.4 0.64 Arm 3.8 11.75 0.625 Hand 4.5 14.45 0.6 0 Thigh 3.7 8.9 0.6 0 20 40 60 80 φ 100[%] Figure 1 Adsorption/desorption of water by cotton Leg 4.0 13.15 0.57 (Urquhart et al., 1930) Foot 4.2 12.9 0.545

However, such conditions rarely occur in reality, The radiation heat exchange with the environment is beyond the lab. Therefore, this model ignores the based on the Stefan-Boltzmann law. For each body difference regain between the two processes, using segment and the surrounding environmental surfaces for the sake of simplicity only the absorption curve including other body parts, view factors are by regression. At beginning of a simulation, the calculated. The radiation heat exchange depends on model assumes that the clothing reaches its the surface area, the surface temperature, the equilibrium with the environment. Knowing the emission ratio and, finally, the position. relative humidity of the air, it is possible to determine the regain of the fabric by the first regression. After & 4 4 calculating the mass transfer between the skin and Q −envcl,r = ∑ → AF clmcl ()clcl ⋅ε−⋅ε⋅σ⋅⋅ TT mm the clothing, the new regain can be calculated. From =1m this new calculated regain, the relative humidity of (16) the garment will be assessed by the second regression. Once the clothing temperature and its Additionally, the human body is not only exposed to relative humidity is known, the calculation of the the long-wave heat exchange with the environmental partial vapour pressure of the clothing p is realized. surfaces, but also to short-wave solar radiation. cl Taking solar altitude, azimuth and direct radiation HEAT TRANSFER ON THE OUTER into consideration, the incident radiation qs on a SURFACE specific oriented surface is calculated. The clothing node absorbs the short-wave radiation depending on Sensible heat loss the absorption coefficient of the clothing. In the The sensible heat exchange between the surface of model a value of α = 0.6 is considered. the clothing and the environment comprises the convective heat transfer with the ambient air, the . long wave radiation exchange with the environment Q Aq −envcl,s α⋅⋅= clcls (17)

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