Rational design of sun and wind shaded evaporative cooling vests for enhanced personal cooling in hot and dry climates

Applied Thermal Engineering 171 (2020) 115122

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Rational design of sun and wind shaded evaporative cooling vests for enhanced personal cooling in hot and dry climates

T

Konrad Rykaczewski School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe 85287, USA

H I GH L IG H T S

cooling garments can provide heatwave relief to dry climate populations. • Evaporative and convective heating lead to excessive water loss from cooling garments. • Solar simulation of evaporative cooling is developed and validated. • Multiphysics evaporation temperature and humidity have competing effect of air buoyancy. • During • Model-based design of a collapsible shade enables sun and wind independent cooling.

A R T I C LE I N FO

A B S T R A C T

Keywords: Personal cooling Multiphysics modeling Model-based design Evaporation Natural convection

As heatwaves become more frequent and intense, personal cooling becomes increasingly important for maintaining outdoor activities and for individuals without access to air conditioning. For about one-third of the current global population living in drylands, evaporating water from clothing is the simplest method of augmenting natural thermoregulation. To cool off, one can simply wear a water-soaked cotton shirt or a highly water-absorbing commercial cooling garment. However, of the stored water, the vast majority is wasted if such apparel is exposed to solar radiation or even slow air flow. Here I show that this issue can be mostly mitigated by incorporating sun and wind shading elements over surface of the cooling garment. First, to enable rational design of these multifunctional shading elements, I develop and benchmark a comprehensive multiphysics finite element model. This model couples conductive, convective, evaporative, and radiative heat transfer with mass transport in natural or forced laminar flow. In the case of natural convection, the model accounts for air buoyancy induced by both temperature and water vapor concentration, which in conditions of interest have a competing effect that can induce flow reversal. Second, I use the model to quantify the impact of geometry and radiative properties of louver and slitted shades on the performance of an evaporative cooling vest in hot and arid conditions. Under natural convection conditions, wearer cooling and water usage efficiency are optimized by introducing about 1.5 cm ventilation gap between the vest surface and the shading structures. In forced convection conditions, however, such a gap results in excessive evaporation rates that are highly wind-speed dependent. Based on these results, I propose a slitted shade design with a collapsible ventilation gap that can provide nearly sun and wind independent moderate cooling rate. If required due to high wearer exertion rate, the intelligently shaded evaporative vest could also provide a higher cooling rate by maintaining the gap. This shaded evaporative vest design concept can minimize the weight of the water stored in the garment and/or significantly increase its cooling period.

1. Introduction As anyone getting out of an outdoor swimming pool during Arizona summer can attest to, it is possible to be “freezing cold” even when the air temperature exceeds 45 °C. The large water vapor concentration difference between our skin and the environment drives rapid

evaporation of water and cools our bodies [1,2]. Employing the same physical principle, I can soak a cotton shirt in water prior to leaving work and bike relatively comfortably home in the afternoon desert heat. Since the latent heat of vaporization of water is about seven times higher than that for its fusion [2], letting the liquid evaporate from my shirt should cool me for significantly longer time than equivalent

E-mail address: [email protected]. https://doi.org/10.1016/j.applthermaleng.2020.115122 Received 28 October 2019; Received in revised form 8 January 2020; Accepted 22 February 2020 Available online 24 February 2020 1359-4311/ © 2020 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

amount of ice or any other material undergoing solid-to-liquid phase change. However, my shirt is completely dry when I get home, a short 10-minute ride away. Intriguingly, I will show below that the majority of the evaporated water did little to cool me and was wasted due to solar heating and excessive convection. Mitigating of these two effects could not only enable me to take longer bike rides in the summer but, by far more importantly, help millions of people cope with increasingly frequent and intensive heatwaves [3–6]. Specifically, around a third of the world’s population lives in areas classified as drylands [7] where evaporative cooling should be effective. Owing to climate change the extent of these areas will likely increase to around half of the global land surface in the coming decades [8]. The expanding drylands are expected sustain 50% of the projected global population growth from 2000 to 2025 with half of that growth occurring in developing countries [8]. Further, in hyper-arid and arid drylands population is projected to increase even more, by around two-thirds. In many developing countries, access to air conditioning is limited and water resources are scarce [8], further highlighting the need for affordable personal cooling [9–12] that minimizes water use. Many have studied evaporative thermoregulation and factors that influence efficiency of the process [1,13,22,23,14–21] as well as textile designs that could improve it [24–29]. In contrast, augmenting the evaporative cooling process of garments using macroscopic texturing to reduce the impact of the sun and wind has received limited attention [30,31]. Notably, Hes et al. and Bal et al. [30,31] proposed that enhanced cooling in hot arid climates can be achieved by attaching inclined sun-shading fabric elements onto clothing. However, in such environmental conditions relying solely on sweat evaporation can cause severe dehydration while preventive overhydration can cause hyponatremia [32]. In addition, to provide more than just the feeling of being cooled, evaporation must occur over substantial body area (i.e. not just the neck) [33–35]. As such, in this work I focus on the macroscopic exterior design a thicker upper body evaporative vest that incorporates a presoaked extremely water-absorbing polymer (see schematics in Fig. 1a and 1b). Such superabsorbent polymers can soak up an order of magnitude more water than common fabrics [1] and are already commonly employed in cooling garments [36,37,46–48,38–45]. If in hot and arid conditions such a water-soaked vest is exposed to sun and wind, the wearer either experiences heating or mild cooling equivalent to evaporation of only a small fraction of used water. I quantified these effects by comparing the performance of a vest that is either shaded from or exposed to sun in various wind speeds using a one-dimensional (1D) resistive network model (see Fig. 1b). With a representative air temperature (Tair ) of 40 °C and a fractional relatively humidity (ϕair ) of 0.1, such a vest is heated by the body (qbody " ), by convection (qc"), by solar radiation (qsolar " ) and, by far-infrared (FIR) radiation (qrad " ). Owing to emissions from the surroundings or the shade structure itself, the latter heat source is likely to be present in all cases. The air flow responsible for the convective heating also controls the water evaporation rate, which in turn provides the overall latent heat sink for the system (qeva " ). By treating the convective heat transfer coefficient (hc ) as an input parameter, I can iteratively solve the steadystate one-dimensional model (see Methods Section and Appendix A formulation details). Demonstrating that air flow is detrimental to effective water use, the plot in Fig. 1c shows that with hc greater than about 10 Wm−2 °C−1 the wearer experiences cooling equivalent to evaporation of only one-third to half of the used water, even without exposure to the sun. In other terms, out of 1 kgm−2 hr−1 of used water the wearer experiences a cooling equivalent to the evaporation of only 0.33–0.5 kgm−2 hr−1 (i.e. water use efficiency η = qbody " / qeva " of 0.3 to 0.5). If the vest is also exposed to solar radiation, qbody decreases " markedly despite a significant increase in qeva " . Moreover, in natural convection conditions (hc below 5 Wm−2 °C−1) the vest wearer is −2 substantially heated (qbody " of −100 to −200 Wm ) despite nearly doubling of the evaporation flux over the sun-shaded case (qeva " increase from 250 to 450 Wm−2). With a higher air flow, the wearer experiences

Fig. 1. (a) Schematic of an individual wearing an evaporative cooling vest, (b) corresponding cross-sectional schematic and thermal resistance network indicating various heat and mass transfer processes involved in evaporative cooling of the wearer. (c) A plot of body cooling, convective loss, and evaporative heat fluxes as function of heat transfer coefficient (air speed) for an evaporative vest with total, hemispherical absorptivity (αT ) of 0.7 that is surrounded by air with a temperature of 40 °C and a fractional relative humidity of 0.1 and is either exposed to or shaded from early afternoon sun whose direct and diffusive components provide a heat source of 600 Wm−2; (d–e) schematic of evaporative vests with the (d) louver and (e) slitted shading structures.

a moderate level of cooling (i.e. 50 to 100 Wm−2) but at the expense of a very low η of around 0.2. In this work, I propose that this issue can be mostly mitigated by incorporating macroscopic sun and wind shading elements over the surface of an evaporative vest. I will focus on louver and slitted shades that, in essence, correspond to horizontal ruffles and slashes (see schematics in Fig. 1d–e). Since the 1D model cannot capture augmentation of transport processes by these elements, I develop and benchmark a comprehensive multiphysics finite element model of these processes. This model couples conductive, convective, evaporative, and 2

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

must decreased below 34 °C. Consequently, in order correctly capture evaporation driven by natural convection both the temperature and the water vapor concentration effects on air density are captured in the coupled FEM developed in COMSOL Multiphysics v5.4. I considered laminar flow to model the vapor transport from the vest surface to the air because, with a representative temperature difference of 10 °C and vest height of 40 cm, the Rayleigh number for completely dry air is order of magnitude lower than the critical transition value of 109 [2] (the Rayleigh number is further decreased if humidity is taken into account). In order to account for the possibility of the flow reversal, I simulated transient transport in the natural convection case (steadystate was achieved with a simulation time of 4000 s). In turn, for the forced convection simulations, I imposed a uniform flow that is normal to the surface of the vest. Since the imposed flows had velocities (1 ms−1 and more) an order of magnitude higher than that in natural convection simulations (~0.1 ms−1), I neglected buoyancy and transient effects in the forced convection simulations. Since the surrounding air is hotter than the surface of the evaporative vest, the shading elements should minimize both solar and FIR radiative heat transfer to the vest. In other words, for best results the exterior surface of the shade should be highly reflective throughout the entire spectrum, while the interior side should have a low emissivity in far infrared region (see inset schematic in Fig. 1d). Specifically, I simulated opaque shades with a very low, wavelength-independent absorptivity of 0.05 (a high reflectivity of 0.95) that reflect and emit in a diffuse manner. The value of the selected reflectivity corresponds roughly to spectral average of normal, spectral properties of aluminum [52] and can, at least in large fraction of the visible to far infrared spectrum, be mostly attained using metalized mylar blanket or nanoengineered fabrics [25,26,53,54]. In selected cases, I also simulated shading elements with higher absorptivity/emissivity corresponding to, for example, white (αT of 0.5) or black cotton fabrics (αT of 0.7, see Supplemental Material for further discussion of radiative properties). In all cases, I assumed that the other thermophysical properties of the shades are equivalent to those of cotton. For simplicity, I also assumed that the shades are impermeable to moisture and air (as would be a metalized mylar blanket). Additionally, since it is shaded from direct solar radiation and is predominantly exposed to FIR radiation, I assumed the wet surface of the vest to have αT = 1. I approximated early afternoon solar radiation in June in Phoenix, Arizona as a source with intensity of 1000 Wm−2 that is incident at 30° from the vertical axis (see also discussion in Appendix A). For brevity, Appendix B presents further details of the mathematical formulation of the FEM model, which is validated using literature data and compared against the 1D model in next sub-sections.

radiative heat transfer with mass transport in natural or forced laminar flow. In the case of natural convection, the model accounts for air buoyancy induced by both temperature and water vapor concentration, which in conditions of interest have a competing effect that can induce flow reversal. Next, I use the model to quantify the impact of geometry and radiative properties of these two categories of shades on the performance of the evaporative cooling vest model shown in Fig. 1. The simulations reveal that under natural convection conditions the qbody " and η are optimized by introducing about 1.5 cm ventilation gap between the vest surface and the shading structures. In forced convection conditions, however, such a gap results in an excessive and highly wind-speed dependent rate of water evaporation from the vest surface. Based on these results, I propose a slitted shade design with a collapsible ventilation gap that can provide a nearly sun and wind independent moderate cooling rate. If required due to high wearer exertion rate, the intelligently shaded evaporative vest could also provide a higher cooling rate by maintaining the gap. 2. Formulation and validation of the models 2.1. Overview of the model formulations To provide a first order estimate of the factors controlling the performance of an evaporative vest without shading elements, I employed a 1D steady-state analysis of the coupled heat and mass transfer model with the convective heat transfer coefficient treated as an input parameter. The thermal circuit in Fig. 1b highlights that I modeled the body resistance with representative layers of fat (thermal conductivity kfat = 0.16 Wm−1 °C−1 and thickness Lfat = 5 mm) and skin (kskin= 0.47 Wm−1 °C−1 and Lskin= 2 mm) [1]. Further, I assumed that the skin surface is covered by a fully swollen superabsorbent polymer (SAP) with properties approximately equal to that of water (k water = 0.6 Wm−1 °C−1 and L vest = 5 mm). It is worth pointing out that due to the relatively high thermal conductivity of water, the thickness of the vest does not substantially impact the results (e.g. even doubling of the thickness to 1 cm has minor effects). Assuming that the SAP-enclosing fabrics are thin and wet, I neglected their thermal resistances. If these values were taken into account, the results would not change significantly because the added resistances would be still significantly smaller than that of the fat layer (e.g. the top and bottom 0.5 mm thick layers of wet cotton enclosing the SAP contribute 10−3/ 0.25 = 0.004 m2 °C W−1 while the fat contributes about 0.03 m2 °C W−1). In addition, I assumed a direct and wet skin-fabric contact and neglected the corresponding thermal contact resistance [49]. While complex air gaps can form in such interfaces and substantially degrade transport processes [50], most personal cooling garments are designed to be close fitting. With this assumption, I also implicitly assume that sweating is suppressed or has negligible effects. Appendix A describes the mathematical formulation of this analysis, while the Introduction Section covers key results that are expanded on in discussion in the Supplemental Material. Since the 1D model cannot capture augmentation of transport processes by the shading elements, I developed a multiphysics finite element method (FEM) model that simulates evaporative cooling in the two-dimensional (2D) domain schematically defined in Fig. 1b. This 2D formulation neglects many three-dimensional body geometry, posture, and flow effects [51], but enables exploration of a wide range of shade geometries that would be otherwise computationally prohibitive. The FEM model couples convection, conduction, and radiation heat transfer as well as water vapor transport between saturated vest and air. Simulating the latter is important because, as shown in Fig. 2a, in the range of conditions of interest (Tair of 30 to 40 °C and ϕair of 0.1 to 1) cooling and humidification of air have comparable and opposing effects on its density ( ρ ). For example, the red dashed line shows that in order to be heavier than the dry and hot air (Tair =40 °C and ϕair = 0.1), the temperature of the water–vapor saturated fluid near the vest surface

2.2. Validation of the FEM model in the natural convection regime In order to validate the individual components of the FEM model, I compared the simulation results for natural convection on a vertical plate with heights varying from 1 to 40 cm and representative conditions (a vest surface temperature, Teva , of 30 °C and a fractional relatively humidity at this location, ϕeva , of 1 along with Tair =40 °C and ϕair =0.1) against models and experimental data available in the literature. The values of the simulated heat and mass transfer coefficients in the natural convection in absence of phase change are within 5% of Churchill and Chu [55] as well as of Gerbhart and Pero [56] correlations (see the Supplemental Material). In addition, I simulated temperature-driven natural convection on vertical surface with triangular texture and obtained good agreement with Oosthuizen’s results [57,58]. With the incorporation of the phase change model, the FEM simulations can match recent experiments by Boulogne and Dollet [59]. These authors studied mass loss due to natural convection driven evaporation from a 5 mm thick water-saturated hydrogel plates with various heights that were vertically suspended in a controlled environment 3

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

Fig. 2. (a) Plot of moist air density as a function of its temperature and relative humidity, (b-d) bench-marking of the coupled heat, mass, laminar flow, and phase change FEM simulations against Boulogne and Dollet [59] transient evaporation experiments: simulated evolution of the (b) velocity field and (c) sample surface mass evaporation flux (ṁ e"va ), water mass loss (Δ mass), and the average surface temperature (T ) for a 15 cm tall and 8 cm wide hydrogel sample, and (d) comparison of the simulated and experimentally measured time-averaged ṁ e"va for hydrogel plates with width of 8 cm and height varied from 2 to 21 cm; (e–f) the results of multiphysics FEM simulations of vertical evaporative vests with height of 2 and 40 cm in contact with skin and fat layers in sun-shaded and sunny (αT = 0.7) conditions: (e) the simulated steady-state average heat transfer coefficients (insets show corresponding steady-state velocity and temperature fields) and (f) the corresponding simulated steady-state average evaporative vest surface temperatures as well as those calculated using the 1D model with corresponding heat transfer coefficient.

as evaporation beings to cool the surface, the density of air near the sample starts to increase, which slows the upward flow and decreases ṁ e"va . Around 400 s after start of evaporation, a stagnation point near the center of the plate emerges and is surrounded by upwards and downwards flows. After 500 s, the temperature-decrease induced downward flow dominates entirely, as indicated by the direction (see red arrows of Fig. 2b) and increase of the near surface air velocity as well as increase of ṁ e"va . The latter parameter continues to increase for another 500 s, then slowly decreases due to lowering of the saturated water concentration at the now cooler plate surface. Despite these intricate changes, integrating ṁ e"va shows that the simulated mass loss from the hydrogel plate increases nearly linearly in time, which matches Boulogne and Dollet’s [59] experiments (see Fig. 2d). Having validated the coupled FEM model against correlations and experiments from literature (without radiation which acts as a surface heat source for the vertical unshaded plate), I next simulate the vertical evaporative cooling vest and compare these results against those obtained from the 1D resistive network analysis.

(Tair =22 °C and ϕair =0.5). Besides the milder environmental conditions, this system closely corresponds to the evaporative vests of interest consisting of highly water-swollen materials. As confirmed by my results, to a first approximation, the thermophysical properties of such material can be assumed to be those of stagnant water (in contrast, evaporation from a fabric such as cotton must take into account moisture-content dependent properties [1,22]). Unfortunately, Boulogne and Dollet [59] did not report variation of the sample temperature during the experiment. Because of this limitation, the plot in Fig. 2d shows that I compared the simulated and the measured water evaporation mass fluxes from hydrogel plates with heights of 2 to 21 cm (ṁ e"va ), which are in excellent agreement. Since the mass evaporation flux oscillates during the evaporation process (e.g. 15 ± 3 × 10−6 kgm−2 s−1 in the cases shown in Fig. 2b & 2c), the simulated values in Fig. 2d represent a time-average ṁ e"va . The detailed multiphysics FEM simulations reveal that the oscillation in the mass evaporation rate are caused by gradual reversal of the flow driven by a switch of the dominating effect on buoyancy. Specifically, the velocity fields in Fig. 2b show that the initially lighter, water-saturated air near the sample causes an upward flow. However,

4

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

Fig. 3. The effect of louver shade geometry on the cooling performance of the vertical evaporative vest with a height of 40 cm: (a) schematic explaining the shade geometry definitions, (b) example steady-state velocity and temperature fields for directly attached louver with 32 elements that are 1.25 cm long and have indicated tilt angles, (c) plot showing impact of the shade size and tilt angle on body and evaporative heat fluxes for directly attached louver; (d) steady-state velocity and temperature fields and (e) plot showing impact of the width of the ventilation gap on performance of a vest shaded by a louver with 1.25 cm long elements with 10°, 20°, and 30° tilt angles.

evaporative vest. With the representative hot and dry stagnant conditions (Tair =40 °C and ϕair =0.1), the body cooling and the evaporative heat fluxes for this simplified vest model without any radiation are 136.9 Wm−2 and 159.2 Wm−2, respectively (η=0.86). These qbody " and −2 qeva and 102.8 Wm−2, " of are substantially decreased to 67.2 Wm respectively, if the vest is radiatively heated by the surroundings (assumed to be at the temperature of air) but is fully shaded from the sun. Again highlighting the need for shading, if the vest is exposed to both direct solar and surrounding radiation in stagnant conditions, the body −2 −2 is heated by qbody " =271 Wm . " = −70.25 Wm despite a very high qeva In the following two sub-sections, I discuss how this situation is improved by addition of louver (Section 3.1) and slitted (Section 3.2) shades in natural convection conditions. These results reveal that in the case of the louver shade with an optimal vest-shade gap, nearly vertical elements provide the best cooling performance. Since such shade geometry is a close match to the slitted architecture that provides basically the same shading efficiency in natural convection conditions, in Section 3.3 I focus on how external flow impacts cooling performance of the simplified evaporative vest with just the slitted shade geometry. These simulations reveal that the introduction of the “ventilation gap” between the vest and the shade, while beneficial under natural convection, results in an excessive, highly wind-speed dependent, rate of water evaporation from the vest surface under forced convection. Based on these results, I conclude the Section by proposing a collapsible slitted shade design that mostly mitigates this issue.

2.3. Comparison of the FEM and resistive model results for vertical vest without shade structure The FEM model enables modeling the impact of the boundary conditions on the flow transport processes that were previously treated with a single input parameter (the heat transfer coefficient) in the 1D resistive network model. Thus, to further validate of the FEM model I simulated evaporative cooling of an individual standing in sun-shaded and sunny areas and compared it against the resistive network analysis. In order to provide a range of hc , I simulated vertical cooling plates with heights between 2 and 40 cm. The plots in Fig. 2e show that the hc in both the sun-covered and sun-exposed scenarios are in the range of 2 to 2.5 Wm−2 °C−1 for the tallest plates and increase to 4 to 4.5 Wm−2 °C−1 for the shortest plates. Highlighting the value of comprehensive multiphysics simulations, the velocity and temperature fields in the insets of Fig. 2e show that these deceptively close heat transfer coefficient values stem from opposing physical processes. Specifically, without solar radiation the surface of the vest cools significantly below the environment, resulting in a downward flow that is caused by temperature-driven increase in the air density. In turn, due to solar radiation the temperature of the vest is near or higher than that of the environment, resulting in an upward flow that is predominantly caused by water vapor concentration-driven decrease in the air density. In either case, plot in Fig. 2f shows that the simulated average steadystate evaporative vest temperatures agree closely with those predicted by the 1D model calculations with hc corresponding to those obtained from FEM simulations. This close match provides another validation of the FEM model, which I use next to explore the impact of the sun and wind shading elements on performance of the evaporative vest.

3.1. The cooling performance of vest covered by louver shade under natural convection Starting with the louver shade, I first simulated tilted, parallel straight shading elements that were directly attached to the vest surface across its entire width (i.e. no gap in schematic in Fig. 3a). The elements were spaced such that they would cover the entire vest surface when aligned vertically. For this arrangement, I considered variations in the

3. Results and discussion In this Section, I use the validated multiphysics model to simulate and quantify how shading impacts the cooling performance of the 5

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

range recommended for effective ventilation of impermeable rain gear [60–63]. Having quantified how vest performance is augmented by geometry of the louver shade, next I briefly explore the impact of radiative properties of the shade surface. If the best performing louver shade, with nearly vertical elements and the 15 mm ventilation gap, has αT = 0.5, the shades do heat up significantly above the air temperature (see Supplemental Material). This heating, however, leads to formation of a very strong convective air flow on the inner side of the shade that −2 −2 provides qbody by increasing qeva (η= " to 244.9 Wm " of 90.5 Wm 0.37) Intriguingly, if the same louver shade has αT = 0.7, the wearer −2 experiences only mildly lower qbody with mildly higher " of 76.8 Wm −2 qeva (η=0.28). These results are in agreement with " of 266.7 Wm Shkolnik et al.[64] and Hes et al.[31] who explained why there is little difference in cooling experienced by Bedouins wearing black or white robes in the desert (see further discussion in Supplemental Material). To summarize, the cooling performance of louver shade is maximized by use of short and nearly vertical elements and introduction of about 15 mm wide ventilation gap for the natural convection flow. With such arrangement and geometry, use of more absorbing shades does not change the cooling rate experienced by the wearer much but does significantly increase the water usage. Next, I evaluate how these characteristics are impacted by switching of the shade type from louver to slitted.

angle and length of the shading element. I simulated elements with the tilt angle varied between 10° (nearly vertical) and 67.5° (nearly horizontal). I also considered variation in shade’s length by simulating louvers consisting of 8 elements that are 5 cm long, of 16 elements that are 2.5 cm long, and of 32 elements that are 1.25 cm long. Rather disappointingly, even in the best case, adding louvers provides a very −2 −2 mild relief from the sun (qbody " ≈60–100 Wm , and " ≈ 20 Wm , qeva η≈0.2 to 0.33 see Fig. 3c). The best case occurs for the shortest shade elements with length of 1.25 cm and tilt below 30°; if the louver consists of longer elements or if the elements have a higher tilt angle, the wearer is either experiencing negligible cooling or is getting heated. The undesirable effect of increasing the element length likely stems from lower heat and mass transfer coefficient in each of the exposed vest surface segments in-between element attachments (as shown in plot in Fig. 2e decreasing plate height from 5 cm to 2 cm leads to over 30% increase in hc ). In turn, the physical reasons underlying the negative impact of increasing shade tilt can be inferred from the representative velocity and temperature field images shown in Fig. 3b. In particular, higher tilt significantly increases solar exposure and thus increases the temperature at the element tips. This temperature increase drives a strong natural convection flow of air that can be 6 °C hotter than the environment, providing stronger convective heating of the vest surface. The highly tilted and heated elements also radiatively heat the vest surface through emission in FIR and, since diffusive reflection was assumed, to some degree through reflection of the impacting solar radiation. In addition, increasing the tilt angle increases exposure of the vest to the FIR radiation from the surrounding. In short, even for the optimal arrangement and geometry of elements, vests with directly attached shades provide under one-third of the body cooling for a hy−2 pothetical fully sun protected vest (qbody as compared to " of 20 Wm 67 Wm−2). The poor performance of the cooling vest with directly attached louvers can be significantly improved by introducing a ventilation gap in-between the evaporation surface and the shading structure. Such gaps consisting fully of air or in some cases of low density spacer fabrics are often introduced under rain or cold-weather gear with low air and moisture permeability to enhance natural or forced convection flow from openings in various parts of the garments [23,60–63]. It is evident from illustrative flow and temperature fields in Fig. 3d that introduction of the space enables formation of a continuous upwards flow in the gap, and as shown in plot in Fig. 3e, improved cooling performance. The magnitude of this improvement, however, is strongly dependent on the gap width. Specifically, a gap with small width below around 4 mm leads to a relatively high temperature of air near the vest surface and a mild body cooling heat flux of about 20 Wm−2. As the gap width increases, the air velocity in the space increases and air temperature near the vest surface decreases. These two effects enhance the body cooling rate. In particular, the value of qbody " peaks with a ventilation gap of about 15 mm, with the highest cooling flux of 89 Wm−2 with a qeva " of 154.5 Wm−2 (η=0.58) achieved for the nearly vertical shade array (tilt angle of 10°). Impressively, this vest with louver shade provides higher degree of cooling in sunny conditions than a vest without any shade that is not exposed to solar radiation (67 Wm−2). This implies that the optimized louver shade not only provides effective shading from direct solar radiation but also provides some reduction in the FIR radiation exposure and enhances the convective flow. As can be inferred from Fig. 3d and 3e, the peaking of qbody " with a gap width of about 15 mm stems from the upper part of the vest surface becoming exposed to the solar radiation as the shades widens. Naturally, the exact amount of such exposure would depend on the solar radiation incident angle and could be mitigated by vertically extending the shade array. In either case, the saturation of qeva " near same point implies such design is rather unnecessary because increasing of the gap width beyond about 15 mm would not provide any further user cooling enhancement. This gap width is comparable to the boundary layer thickness and is also in the

3.2. The cooling performance of vests covered by slitted shades under natural convection Cutting horizontal slits is a simple method of increasing air and moisture permeability of fabrics and has been previously proposed as means of increasing sweat evaporation from exercising individuals [65] and of increasing water evaporation from a liquid-saturated cooling vest [66]. Here, I use the multiphysics model to quantify the cooling performance of an evaporative vest covered by a reflective shade with long horizontal slits under natural convection conditions (see schematic in Fig. 4a). I assumed that the slits are cut in a 1 mm wide, highly reflective shade and, have height equal to the shade width. As in the case of the louver shade, I also study the impact of the ventilation gap width. The representative velocity and temperature fields in Fig. 4b and the corresponding plot in Fig. 4c summarize the body cooling and evaporative heat fluxes attained by the vest with a shade and the number of slits ranging from 25 to 200 (corresponding to 6% to 50% open shade area). As in the case of the louver shade, the value of body cooling heat flux peaks while the evaporative heat flux saturates with a ventilation gap width of about 15 mm. In quantitative terms, the peak values of −2 −2 and qeva (η≈0.5 to 0.6) qbody " of 145 to 160 Wm " of 80 to 85 Wm obtained with use of the slitted shade are nearly the same as those achieved by using the louver shade. These peak values do not change much as the number of slits increases from 25 to 100 but are degraded substantially when the number of slits increases to 200. Since half of the latter the shade is open, the degradation of the cooling performance likely stems from higher exposure to FIR radiation from the environment. For the same reason, increasing the slit height also significantly degrades the cooling performance of the vest (see Supplemental Material). For the small slits, their number has even more dramatic impact on the evaporation rate when the ventilation gap is much smaller or collapsed. In particular, if the gap width is below 5 mm qeva " decreases dramatically from 170 Wm−2 to 50 Wm−2 as the number of slits is decreased from 200 to 25. The dip observed in the evaporation flux from the shades with 100 and 200 openings as the gap is introduced and increased likely stems from first suppression and then slow reemergence of the boundary layer near the vest surface. In either case due to the inhibited convection the body cooling rate for any number of the slit openings is very low (near or below 20 Wm−2). 6

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

three-dimensional flows [51], consequently my simulations only provide an estimate of the impact of forced convection on the performance of the shaded vest. Despite slowing down as it passes through the slits, the air flow parallel to the vest surface significantly increases both qbody " " and qeva before escaping through the top and bottom ventilation openings. For example, the plot in Fig. 5b shows that for a shaded vest with ventilation gap of about 15 mm, qbody increases from 100 Wm−2 to " −2 −2 200 Wm and qeva " increases from around 200 to 350 Wm when air speed increases from 0.25 to 1 ms−1. For a greater air velocity, the body cooling flux saturates around 250 Wm−2 to 300 Wm−2 (also shown in the case of the vests without shading structures in plot in Fig. 1c) while the evaporative flux continues to increase up to around 700 Wm−2 with air speed of 5 ms−1. Interestingly, changing the number of the 1 mm tall slits from 25 to 200 has relatively small impact on these values. In all cases, I conclude the shades are quite effective in blocking solar radiation because the simulated values are comparable to that obtained for a vest without any shading structures that are not exposed to solar radiation (see Fig. 1c and the Supplemental Material). However, the agreement between these two scenarios also shows that slitted shades with 15 mm ventilation gaps are not effective in reducing the excessive water use stemming from forced convection. In addition, increasing of the absorptivity of the shade material has a negligible impact on the results (see Supplemental Material). If the increase in air flow impacting the vest is caused by movement of the wearer, the increase in the body cooling and evaporative fluxes is likely desirable and needed to compensate for the increased metabolic heat generation. However, if the wearer is more or less stationary and exposed to wind, the additional cooling and associated large water use are likely unnecessary. As I will show next, this issue can be mitigated by collapsing the ventilation gap (see schematic in Fig. 5c). With such a geometry change, the shade will predominantly reduce the evaporation flux by simply decreasing the exposed wet surface area. Importantly, adjusting the number of slits between 50 and 100 enables marked decrease of qeva " values while maintaining moderate values of qbody " . In particular, for a shade with 50 slits and wind speeds increasing from 1.5 −2 to 5 ms−1 qbody while qeva " will " will increase from 77.5 to 95 Wm −2 increase from 160 to 230 Wm (ηdecrease from 0.48 to 0.41). In turn, increasing the number of slits to 100 at the same wind speeds results in −2 qbody and qeva " increase from 245 to " increase from 120 to 150 Wm −2 345 Wm (η decrease from 0.49 to 0.43). In contrast to other simulated geometries, the heat fluxes values are strongly affected by the radiative properties of the shades. Specifically, due to the direct vest-shade contact, increasing the absorptivity of the shades to 0.5 and 0.7 results in heating of the wearer, irrelevant of the air speed (see Supplemental Material). Altogether, the simulation results indicate that an evaporative vest covered by a highly reflective shade with 50 slits and a ventilation gap of around 15 mm that collapses when exposed to air flow can provide the wearer with nearly sun and wind independent cooling flux between 80 and 95 Wm−2 with an evaporation flux between 160 and 230 Wm−2. If the wearer desires a moderately higher cooling flux, increasing the number of slits to 100 enables increase in qbody " from 75 to −2 150 Wm−2 but at a cost of a higher qeva " from 175 to 345 Wm (values represent range from natural convection to forced convection with air speed of 5 ms−1). In forced convection conditions, doubling the number of slits results in, albeit more wind-speed dependent, 50% increase in the wearer cooling as well as evaporative flux. In all these scenarios, a moderate η of 0.4 to 0.5 is achieved. This again highlights that both of these shades provide a dramatic performance improvement over an unshaded vest that is exposed to sun. To reinforce this point, in stagnant and sunny condition a wearer of a vest without shading elements experiences a heating flux of about 100 Wm−2 despite an evaporation flux of over 300 Wm−2. The wearer can experience cooling if exposed to air movement but at a cost of a dramatically increased water consumption

Fig. 4. The effect of the slitted shade on cooling performance of the vertical evaporative vests with a height of 40 cm in sunny conditions: (a) schematic explaining the shade geometry definitions; (b) example steady-state velocity and temperature fields for a shade with 50 slits with 1 mm height and varied ventilation gap width; and (c) plot showing impact of the ventilation gap width and number of slits (n ) on the body cooling and evaporative heat fluxes.

In all, under natural convection the cooling performance of the evaporative vest is highly improved by increasing the ventilation gap width to about 15 mm and having a moderate number (50 to 100) of the 1 mm tall slits. Using these geometrical settings, varying the radiative properties of the shade surface has a nearly identical impact as that of the louver shade (i.e.qbody " remains about the same but at a cost of significantly increased qeva " , see Supplemental Material). In addition, once the geometry of the louver or slitted shade is adjusted, the type of shade does not have a major impact on the vest cooling performance and water usage. Consequently, in the next sub-section I focus on modeling cooling performance of vests covered by just the slitted shade geometry exposed to external forced air flow.

3.3. The cooling performance of vests with slitted shades under forced convection I showed in the introduction that sun-shading of the evaporative vests is most important under natural convection conditions, which were studied in previous sub-sections. However, in many scenarios the wearer of the vest will either be exposed to wind or moving. Thus, in this sub-section I will use the multiphysics model to estimate the impact of wind on the performance of the evaporative vest protected from sun by the geometrically optimized slitted shade (please refer to Section 3.2). As the schematics in Fig. 5 show, I restrict the simulations to 2D laminar flow of the dry and hot air that is normal to surface of the vest (even for highest simulated velocity, the Reynolds number for flow over the vest is below turbulence threshold, on the order of 104 to 105). Naturally an individual can be exposed to significantly more complex 7

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

Fig. 5. The effect of slitted shade geometry on the cooling performance of the vertical evaporative vests with height of 40 cm: (a) & (c) schematics explaining the shade geometry definitions and example steady-state velocity and temperature fields for shades with 50 slits with 1 mm height and (a) 15 mm and (c) 0 mm (collapsed) wide gap; (b) & (d) corresponding plots showing impact of the ventilation gap width and number of mesh openings (n ) on the body cooling and evaporative heat fluxes ((b) 15 mm and (d) 0 mm).

rate (e.g. at 1.5 ms−1 and 5 ms−1 q"body is 70 and 200 Wm−2 while q"eva is 650 and 920 Wm−2 (thus η of 0.1 to 0.2). To put this in more palpable terms, to achieve the q"eva of 650 and 920 Wm−2, the unshaded evaporative vest would need to store 1 to 1.4 kgm−2 to provide an hour of cooling in the sun. By introducing the collapsible slitted shades the mass of the stored water required to provide comparable cooling flux for one hour can be reduced to 0.25 to 0.35 kgm−2 for shades with 50 slits and 0.25 to 0.5 kgm−2 for shade with 100 slits. Consequently, the vest with rationally designed, reflective slitted shades can provide cooling with much smaller stored water requirements or for significantly extended period of time, nearly independent of sun and wind exposure.

evaporative vest design concept enable cooling of the wearer in sunny conditions but it also reduces the weight of the water required for cooling by a factor of four. While evaluating these results there are several important points to keep in mind. First, I simulated a highly simplified model of an individual wearing a vest that does not capture many aspects of reality. Thankfully, humans are not two-dimensional, perfectly vertical or simply composed of skin and fat layers of uniform thickness. Threedimensional and heterogenous realities of our bodies as well as their complex vascular systems will induce local variation in the cooling rate (e.g. higher cooling flux in areas with thinner fat layer or more vasculature). Similarly, natural and forced convection flow around our bodies is also three-dimensional and a lot more complex than the twodimensional flows that I have simulated [51]. Furthermore, the heat fluxes that I presented are steady-state values that, especially in the natural convection case, can take a substantial amount of time to reach (this of course time depends on the initial conditions). This fact, however, can be used to wearers advantage—the vest can be soaked with cool water that will provide an additional transient cooling effect. In addition, the cooling flux provided by the recommended vest design (about 90 Wm−2 with a boost to 150 Wm−2) is relatively moderate. The resulting cooling of about 50 to 80 W is sufficient for low exertion activities such a gardening or strolling (assuming that both back and front of the wearer are covered providing a representative surface area of 0.6 m2 [1]). It is intuitive to think that this cooling rate could be increased, especially in natural convection conditions, by texturing of the vest surface. However, exploratory simulations of an evaporative vest with an array of short fins that I conducted revealed that this is not a promising approach (see Supplemental Material). For higher exertion activities such as running or biking, the evaporative cooling rate could be enhanced with an air flow induced by more open shade structure or powered elements such as fans [9,67–71]. Interestingly, the actual cooling rate might also be higher due to transient effects such as body

4. Conclusions Exposure of evaporative cooling garments to sun and/or to air flow dramatically degrades or even negates their cooling capabilities and increases required water use. In this work, I proposed that this issue can be resolved by covering of the vest with perforated reflective sun and wind-shading elements. Using comprehensive multiphysics simulation, I quantified the impact of the geometry and the radiative properties of either louver or slitted shades on cooling of an individual wearing an evaporative vest in hot and arid conditions (40 °C and 10% relative humidity). Under natural convection conditions, wearer cooling and water usage efficiency are optimized by introducing about 1.5 cm ventilation gap between the vest surface and the shading structures. In forced convection conditions, however, such a gap results in excessive, highly wind-speed dependent, water evaporation rate. Based on these results, I proposed a slitted shade design with a collapsible ventilation gap that can provide nearly condition independent moderate cooling flux of around 80 to 95 Wm−2 through closing of the gap. If required due to high wearer exertion rate, the vest could also provide about 50% higher cooling rate by maintaining of the gap. Not only does this shaded 8

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

popularity of both female and male clothing slashing that lasted another two centuries [73,74]. As I have argued before [12], adapting to a heating climate might similarly trigger broad adoption of either sexspecific or historically inspired fashion elements if with incorporation of engineered materials they provide enhanced cooling capabilities.

and clothing (or the shade structure) movement induced pumping of air in the ventilation gap [72]. Consequently, the presented results should be treated as estimates that are useful in judging the relative performance of the various discussed vest and shade arrangements. Nevertheless, the overall conclusions and the proposed cooling garment design with collapsible reflective perforated shade are quite promising, and I hope will encourage further investigations that resolve the caveats that I mentioned. Lastly, in modern times, exterior textured elements such as ruffles and slashes that I modeled are typically associated with female garments and thus might be deemed not acceptable by some. However, for most of their history following their introduction in 16th century Spain, ruffles were unisex [73]. Interestingly, ruffles evolved from slashes. Specifically, pulling of flexible strings sewn into multilayer clothing with slashed exterior intensifies natural wrinkling of the fabrics, leading to formation of the ruffles [73]. In turn, the deliberate cutting of outerwear to reveal underlying layers supposedly stems from Swiss army soldiers who after pillaging burgundy in 1477 cut bits of highly colored tents and banners and threaded them through holes in their own clothing [73]. The modified uniforms caught attention of Swiss aristocracy, whose imitation of this fashion statement commenced

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements I would like to thank Dr. Kenneth Chad Manning and Dr. Akshay Phadnis from ASU for commenting on the manuscript and Pawel Lezanko for discussions about performance of evaporative vests used by bikers. I would also like to thank Agata and Stefan Rykaczewski for providing me the motivation to think about what the future in our desert might look like and how to make it little bit easier for them.

Appendix A. One-dimensional steady-state model formulation The steady-state energy balance on the system illustrated in Fig. 1 dictates that:

qeva " = qbody " + qconv " + qrad " + qsolar "

(A1)

In turn, the body cooling heat flux is equal to:

qbody " =

Tcore − Teva = R

Tcore − Teva Lfat kfat

+

Lskin kskin

+

Lvest kwater

(A2)

where Tcore and Teva are the body core (37 °C) and evaporative vest surface temperatures, respectively. The convective heat flux can be calculated as:

qbody " = hc (Tair − Teva)

(A3)

For forced convection around a human body hc has been correlated to air speed (units of ms−1) as hconv = 8.1v 0.5, where the two empirical parameters are representative values for the front as well as the back of a male [1]. The evaporative heat flux can be computed as [1]:

qeva " = heva (Pw, eva (Teva) − Pw, air (Tair , ϕair )) = CL hc (Pw, eva − Pw, air )

(A4)

where heva is the evaporative heat transfer coefficient that can be calculated using the Lewis relationships as heva ≈ CL hc ≈0.0168hc [1]. In turn, Pw, air and Pw, eva are partial pressures of water in air and at the surface of the evaporative vest, respectively. For given Tair and ϕair the partial pressure of water (in Pa) can be calculated as: ⎛20.386 −

Pw, air (Tair , ϕair ) = 133.3ϕair e⎝

5132 ⎞ 273 + Tair ⎠

(A5)

With assumption of fully saturated air (i.e. ϕair =1), I also used this relationship to calculate the partial water vapor pressure at the surface of the evaporative vest. In the presented calculations, I used Tair =40 °C and ϕair =0.1, which corresponds to typical daytime conditions in Phoenix, Arizona from May through beginning of October. During these months as well as throughout most of year Arizona, as with most arid regions, is sunny. Consequently, the fraction of solar radiation that directly impacts the vest wearer, expressed in terms of the clearness index, skt , is about 0.8 (i.e. the diffuse fraction, skd , is about 0.2). The clear sky solar radiation on a horizontal surface, Ig , for a given solar zenith angle, θz , can be calculated as [1]: −0.057

Ig = 1098cosθz e cosθz

(A6)

From noon until two in the afternoon in Phoenix in middle of June the zenith angle varies between 0° and about 30° and, correspondingly, Ig varies between 1050 Wm−2 and 890 Wm−2. For a vertically standing individual, the direct solar heat flux, Ib , on the back or front of the torso can be calculated as skt sinθz Ig /cosθz . In turn, the diffusive solar heat flux, Id , can be calculated as skd Ig . From these calculations, the representative values for the direct and diffusive solar heat fluxes on an individual’s back are 420 Wm−2 and 180 Wm−2, respectively. Taken together, these result in an −2 estimated qsolar for θz corresponding to two in the afternoon. This estimate neglects any reflected solar radiation and also could be " of 600 Wm substantially higher or lower dependent on cloud cover, infrastructure in the surrounding as well as time of the day and year [1,75]. Naturally, a portion of this heat flux is absorbed by the hydrated vest. Representative values of the total, hemispherical surface absorptivity (αT ) of the vest for a worst-case (highly absorbing wet-cotton fabric with black pigment) and good-case scenarios (mildly absorbing shite wet-cotton fabric) areαT ≈ 0.7 and αT ≈ 0.5, respectively (see Supplemental Material for calculation details) [76,77]. For simplicity, I adapted the linearized formulation of the FIR radiative heat exchange that is often employed in analysis of human temperature control within an enclosure:

qrad " = hrad (Tair − Teva)

(A7) −2

I assumed a radiative heat transfer coefficient (hrad ) of 4.5 Wm

°C

−1

that is typical for most human body parts [1]. As a further simplification, I

9

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

assumed that the surrounding emits at temperature equal to that of the air, which could be questionable if effective emissivity of the sky is much −2 lower than one. Either way, with (Tair − Teva)≈5 °C to 10 °C, qrad " ≈ 25 to 50 Wm , which is minor as compared to the other heat fluxes. Substitution of Eqs. A(2)–A(7) into Eq. A(1) results in an expression for Teva :

Teva =

−0.0168hc (Pw, eva (Teva) − Pw, air (Tair , ϕair )) +

Tcore R

+ Tair (hc + hrad ) + αT qsolar "

hrad + hc + 1/ R

(A8)

To simulate sun-shaded conditions, I assumed that qsolar " = 0 but maintain qrad " as specified by Eq. A(7). This scenario is more relevant than zero radiation case because, even if entirely protected from the sun, the vest is likely to be exposed to FIR radiation from the shades themselves (see inset in Fig. 1d. Due to the highly non-linear nature of the dependence of partial pressure of water vapor on temperature, I solved Eq. A(8) iteratively by guessing an initial value of Teva for pressure calculations. Appendix B. Two-dimensional multiphysics finite element method (FEM) model formulation The FEM model takes into account laminar fluid flow dynamics, transport of water vapor in air as well as conduction, convection, phase-change, and radiation heat transfer. Since by far the most complex situation occurs in absence of a forced flow, I will focus on describing model formulation in natural convection conditions. The effects on air density by both temperature and water vapor concentration are automatically captured by coupling the recently added “Moisture Transport in Air” and “Heat Transfer in Moist Air” physics interfaces in COMSOL Multiphysics 5.4a FEM software. These interfaces are coupled to the “Laminar Flow Interface” that solves the two-dimensional transient continuity and moment conservation (with weakly compressible flow assumption) equations:

δρ + ∇∙ (ρu) = 0 δt

(B1)

δρ 2 + ρ (u∙∇) u = ∇ ⎡−pI + μ (∇u + (∇u)T ) − μ (∇u) I⎤ + F + ρg δt 3 ⎣ ⎦

(B2)

where μ is the dynamic viscosity of the fluid, t is the time variable, u is the velocity field, p is pressure field, g is the gravitational acceleration, I is the identity tensor, and F is the body force. The model domain is a square with height and width that is 10 cm greater than height of the vest, that is represented by a 5 mm thick vertical plate on the left side of the domain. The 2 mm thick skin and 5 mm thick fat layers are represented as contacting vertical plates with height equal to the vest. Since in these layers only heat conduction is taken into account, I placed these two layers outside of the fluid flow domain and assumed that their top and bottom sides are insulated. In regards to the flow problem, I modeled the top, bottom, and right domain boundaries as “open boundaries” with zero normal stress and compensation for the hydrostatic pressure approximation. Since in absolute terms the mass contribution due to the evaporation of water is small, I assumed that the vest surface is a wall on which the no-slip condition applies (as are any shading elements). In turn, I modeled the short vertical boundaries above and below the vest surface as “symmetry” boundaries (i.e. no flow across but enables a parallel velocity component). For natural convection simulations, the fluid initially is stagnant. The fluid temperature, density, and dynamic viscosity are obtained through the “Nonisothermal Flow” multiphysics interface that couples the “Laminar Flow” and “Heat Transfer in Moist Air” interfaces. The latter interface solves the transient energy equation without internal heat generation given by (with temperature of the environment used as reference):

ρcp

δρ + ρcp u∇T = ∇ (k∇T ) δt

(B3)

where cp is the specific heat at constant pressure and k is the thermal conductivity. I modeled the top, bottom, and right domain boundaries as having a constant temperature equal to that of the environment. In turn, I assumed that the left-hand side boundary of the fat layer has a constant temperature of 37 °C that is corresponds to human body core temperature [1]. As in the flow problem, I modeled the short vertical boundaries above and below the vest surface as “symmetry” boundaries with zero heat flux across. I used the in-built COMSOL material library to model the temperature-dependent thermophysical properties of the fat, skin, and vest (water) layers. For simplicity I assumed that the vest consists predominantly of water and does not substantially dry-out during the simulation time and, consequently, is reasonably well approximated by a stagnant water layer. The fluid properties stem from the “Heat and Moisture” multiphysics interface that couples the “Heat Transfer in Moist Air” and “Moisture Transport in Air” interfaces. It is also this multiphysics interface that accounts for the latent heat sink flux on the surface of the vest that is modeled as:

qeva " = Hvap ṁ eva " = Hvap K eva Mv (Cw, sat (Teva) − Cw, air )

(B4) −1

−1

where Hvap is the latent heat of vaporization of water (units of Jkg ), Mv is the molar mass of water (units of kg mol ), ṁ e"va is the evaporation mass flux, and K eva is a simulation parameter referred to as the evaporation rate (units of ms−1). The saturated vapor concentration at the local temperature of the vest surface (Cw, sat (Teva) with units of mol m−3) and water vapor concentration right above surface (Cw, air ) are calculated by COMSOL according to Pw, air / Tair Rg (with ideal gas constant Rg equal to 8.314 Jmol−1K−1) with vapor pressure (units of Pa) calculated not by Eq. A(5) but according to [78]: ⎛

7.5Tair

⎞

Pw, air (Tair , ϕair ) = 610.7ϕair 10⎝ 273.15 − 35.85 + Tair ⎠

(B5)

Following recommendations from COMSOL’s application library, K eva was set to a value high enough so that it did not impact the solution (see Supplemental Material). In this implementation, Eq. B(4) can be thought to enforce equilibrium between the “liquid” surface of the vest and the vapor. Eq. B(4) also specifies how ṁ e"va , which is the boundary mass source term in the “Moisture Transport in Air” interface, is calculated by COMSOL (i.e. the “wet surface boundary condition”). This interface solves the transient water vapor transport problem given by:

d z Mv

δCw, air + d z Mv u∇Cw, air = ∇ (d z Mv Dw, air ∇Cw, air ) δt

(B6)

where d z is the thickness of the domain (1 m) and Dw, air is the water vapor diffusion coefficient in air. In the simulation, I calculated the reference 10

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

water vapor concentration using Eq. B(5) with Tair =40 °C and ϕair =0.1. I modelled the top, bottom, and right domain boundaries as having a constant moisture content corresponding to fractional relative humidity of ϕair =0.1 with reference temperature of 40 °C. As in the flow problem, I modeled the short vertical boundaries above and below the vest surface as “symmetry” boundaries with zero mass flux across. To take into account the flow field, “Moisture Transport in Air” and “Laminar Flow” interfaces are coupled using the “Moisture Flow” multiphysics interface. To incorporate the radiative heat transport, I coupled the “Surface-to-Surface Radiation” interface with the heat transfer interface using the “Heat Transfer with Surface-to-Surface Radiation” multiphysics interface. I assumed that air was a transparent, non-participating medium with refractive index of 1 (all other regions were opaque) and I solved for the surface-to-surface radiation between the vest and the shading elements using the Hemicube method with radiation resolution of 256. For simplicity, I treated the surfaces as diffusive and gray (see Supplemental Material for indepth discussion of the radiative properties) and I set the surrounding temperature equal to Tair = 40 °C. Without radiative shades, the diffuse component of solar radiation can be easily accounted for with the “include diffuse irradiance” option. However, with incorporation of shading elements, I found that this option yielded non-physical results stemming from diffuse radiation source in the shaded space between vest surface and shades. To resolve this issue, for the shaded vest simulations I approximated the solar radiation as a simple source at an infinite distance incident at 30° from the vertical axis with source heat flux of 1000 Wm−2. Regarding the shading elements themselves, I assumed that they are 1 mm thick, and for simplicity impermeable to moisture and air transport. Naturally, most fabrics are permeable to both moisture and air, which significantly impacts the wearers thermoregulation [62,63,79]. Consequently, especially in the highly reflective case, the shades can be thought of metalized mylar reflective blanket covered fabrics (I assumed that thermophysical properties of the bulk of the shades correspond to cotton). In regards to the FEM simulation specifics, I set the mesh using “User-controlled mesh” with calibration for “Fluid dynamics” with predefined element size of “Fine” (largest size allowed through empirical grid independence study). With these options, COMSOL generated a complex mesh that included refined boundary layer-type mesh elements near small features and the evaporation surface and free triangular mesh elements elsewhere. COMSOL dynamically sets the time step based on “physics controlled” tolerance. With the exception of the fat, skin, and water layer initial temperature which I adjusted based on estimates from the one-dimensional model, I set the initial values of other parameters to corresponding boundary values. In all simulations, solution converged using default solver settings. Appendix C. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.applthermaleng.2020.115122.

References [19]

[1] E.H. Wissler, Human Temperature Control: A Quantitative Approach, first ed., Springer, Berlin, Germany, 2018. [2] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons Inc, New York, 2011. [3] C. Mora, B. Dousset, I.R. Caldwell, F.E. Powell, R.C. Geronimo, C.R. Bielecki, C.W.W. Counsell, B.S. Dietrich, E.T. Johnston, L.V. Louis, Global risk of deadly heat, Nat. Clim. Chang. 7 (2017) 501–506. [4] S.C. Sherwood, M. Huber, An adaptability limit to climate change due to heat stress, Proc. Natl. Acad. Sci. 107 (2010) 9552–9555. [5] M. Li, S. Gu, P. Bi, J. Yang, Q. Liu, Heat waves and morbidity: current knowledge and further direction-a comprehensive literature review, Int. J. Environ. Res. Public Health 12 (2015) 5256–5283. [6] C. Mora, C.W.W. Counsell, C.R. Bielecki, L.V. Louis, Twenty-seven ways a heat wave can kill you: deadly heat in the era of climate change, Circ. Cardiovasc. Qual. Outcomes. 10 (2017) e004233. [7] J.F. Reynolds, A. Grainger, D.M. Stafford Smith, G. Bastin, L. Garcia-Barrios, R.J. Fernández, M.A. Janssen, N. Jürgens, R.J. Scholes, A. Veldkamp, Scientific concepts for an integrated analysis of desertification, L. Degrad. Dev. 22 (2011) 166–183. [8] J. Huang, H. Yu, X. Guan, G. Wang, R. Guo, Accelerated dryland expansion under climate change, Nat. Clim. Chang. 6 (2016) 166. [9] F. Wang, W. Song, An investigation of thermophysiological responses of human while using four personal cooling strategies during heatwaves, J. Therm. Biol. 70 (2017) 37–44. [10] W. Song, F. Wang, C. Zhang, Intermittent wetting clothing as a cooling strategy for body heat strain alleviation of vulnerable populations during a severe heatwave incident, J. Therm. Biol. 79 (2019) 33–41. [11] L. Yang, H. Yan, J.C. Lam, Thermal comfort and building energy consumption implications–a review, Appl. Energy 115 (2014) 164–173. [12] K. Rykaczewski, Cool future fashion: Personal cooling as part of social adaptation to hotter climates, Temperature. 6 (2019) 97–100. https://doi.org/DOI: 10.1080/ 23328940.2019.1574201. [13] B. Givoni, H.S. Belding, The cooling efficiency of sweat evaporation, in: Biometeorology, Elsevier, 1962: pp. 304–314. [14] N. Kondo, T. Nishiyasu, H. Ikegami, The influence of exercise intensity on sweating efficiency of the whole body in a mild thermal condition, Ergonomics 39 (1996) 225–231. [15] M. Guan, S. Annaheim, J. Li, M. Camenzind, A. Psikuta, R.M. Rossi, Apparent evaporative cooling efficiency in clothing with continuous perspiration: a sweating manikin study, Int. J. Therm. Sci. 137 (2019) 446–455. [16] F.N. Craig, J.T. Moffitt, Efficiency of evaporative cooling from wet clothing, J. Appl. Physiol. 36 (1974) 313–316. [17] M. Guan, S. Annaheim, M. Camenzind, J. Li, S. Mandal, A. Psikuta, R.M. Rossi, Moisture transfer of the clothing–human body system during continuous sweating under radiant heat, Text. Res. J. 0040517519835767 (2019). [18] G. Havenith, M.G. Richards, X. Wang, P. Brode, V. Candas, E. den Hartog, I. Holmér,

[20]

[21]

[22]

[23]

[24] [25] [26]

[27]

[28]

[29]

[30] [31]

[32]

[33]

[34] [35]

11

K. Kuklane, H. Meinander, W. Nocker, Apparent latent heat of evaporation from clothing: attenuation and “heat pipe” effects, J. Appl. Physiol. 104 (2008) 142–149. G. Havenith, P. Bröde, E. den Hartog, K. Kuklane, I. Holmer, R.M. Rossi, M. Richards, B. Farnworth, X. Wang, Evaporative cooling: effective latent heat of evaporation in relation to evaporation distance from the skin, J. Appl. Physiol. 114 (2013) 778–785. B. Alber-Wallerström, I. Holmer, Efficiency of sweat evaporation in unacclimatized man working in a hot humid environment, Eur. J. Appl. Physiol. Occup. Physiol. 54 (1985) 480–487. V. Candas, J.P. Libert, J.J. Vogt, Influence of air velocity and heat acclimation on human skin wettedness and sweating efficiency, J. Appl. Physiol. 47 (1979) 1194–1200. S.F. Neves, J. Campos, T.S. Mayor, Effects of clothing and fibres properties on the heat and mass transport, for different body heat/sweat releases, Appl. Therm. Eng. 117 (2017) 109–121. F. Wang, S. Del Ferraro, L.-Y. Lin, T. Sotto Mayor, V. Molinaro, M. Ribeiro, C. Gao, K. Kuklane, I. Holmér, Localised boundary air layer and clothing evaporative resistances for individual body segments, Ergonomics 55 (2012) 799–812. R.M. Rossi, High-performance sportswear, in: High-Performance Appar., first ed., Woodhead Publishing, 2018: pp. 341–356. L. Peng, B. Su, A. Yu, X. Jiang, Review of clothing for thermal management with advanced materials, Cellulose 1–34 (2019). E. Pakdel, M. Naebe, L. Sun, X. Wang, Advanced functional fibrous materials for enhanced thermoregulating performance, ACS Appl. Mater. Interfaces 11 (2019) 13039–13057. K. Fu, Z. Yang, Y. Pei, Y. Wang, B. Xu, Y. Wang, B. Yang, L. Hu, Designing textile architectures for high energy-efficiency human body sweat- and cooling-management, Adv. Fiber Mater. 1 (2019) 61–70, https://doi.org/10.1007/s42765-0190003-y. Y. Zhong, F. Zhang, M. Wang, C.J. Gardner, G. Kim, Y. Liu, J. Leng, S. Jin, R. Chen, Reversible humidity sensitive clothing for personal thermoregulation, Sci. Rep. 7 (2017) 44208. J. Mu, G. Wang, H. Yan, H. Li, X. Wang, E. Gao, C. Hou, A.T.C. Pham, L. Wu, Q. Zhang, Molecular-channel driven actuator with considerations for multiple configurations and color switching, Nat. Commun. 9 (2018) 590. K. Bal, L. Hes, V. Bajzik, Analytical model to study a new design concept for providing comfort in hot arid climate, Indian J. Fibre Text. Res. 42 (2017) 379–385. L. Hes, K. Bal, M. Boguslawska-Baczek, Why black clothes can provide better thermal comfort in hot climate than white clothes, in: Fiber Soc. Spring Conf. (Liberec, Czech Republic, 21-23 May, 2014. F.G. Beltrami, T. Hew-Butler, T.D. Noakes, Drinking policies and exercise-associated hyponatraemia: is anyone still promoting overdrinking? Br. J. Sports Med. 42 (2008) 796–801. F.M. Bright, G.K. Chaseling, O. Jay, N.B. Morris, Self-paced exercise performance in the heat with neck cooling, menthol application, and abdominal cooling, J. Sci. Med. Sport. 22 (2019) 371–377. C. Sunderland, R. Stevens, B. Everson, C.J. Tyler, Neck-cooling improves repeated sprint performance in the heat, Front. Physiol. 6 (2015) 314. C.J. Tyler, C. Sunderland, Cooling the neck region during exercise in the heat, J.

Applied Thermal Engineering 171 (2020) 115122

K. Rykaczewski

Athl. Train. 46 (2011) 61–68. [36] M. Rother, J. Barmettler, A. Reichmuth, J.V. Araujo, C. Rytka, O. Glaied, U. Pieles, N. Bruns, Self-sealing and puncture resistant breathable membranes for waterevaporation applications, Adv. Mater. 27 (2015) 6620–6624. [37] M. Rothmaier, M. Weder, A. Meyer-Heim, J. Kesselring, Design and performance of personal cooling garments based on three-layer laminates, Med. Biol. Eng. Comput. 46 (2008) 825–832. [38] R. Nayak, S. Kanesalingam, S. Houshyar, L. Wang, R. Padhye, A. Vijayan, Evaluation of thermal, moisture management and sensorial comfort properties of superabsorbent polyacrylate fabrics for the next-to-skin layer in firefighters’ protective clothing, Text. Res. J. 88 (2018) 1077–1088. [39] M.A.R. Bhuiyan, L. Wang, R.A. Shanks, J. Ding, Polyurethane–superabsorbent polymer-coated cotton fabric for thermophysiological wear comfort, J. Mater. Sci. 54 (2019) 9267–9281. [40] P. Glampedaki, V. Dutschk, R. Paul, Superabsorbent finishes for textiles, Funct. Finish. Text. Improv. Comf. Perform. Prot. (2014) 283. [41] Y. Yang, J. Stapleton, B.T. Diagne, G.P. Kenny, C.Q. Lan, Man-portable personal cooling garment based on vacuum desiccant cooling, Appl. Therm. Eng. 47 (2012) 18–24, https://doi.org/10.1016/j.applthermaleng.2012.04.012. [42] Y. Yang, D. Rana, C.Q. Lan, T. Matsuura, Development of Membrane-based Desiccant Fiber for Vacuum Desiccant Cooling, ACS Appl. Mater. Interfaces. 8 (2016) 155778–15787. [43] S.A. Bumbarger, T.H. Bumbarger, Protective multi-layered liquid retaining composite, 2002. [44] J. Taylor, Body cooling device, (2007) U.S. Patent Application No. 11/228, 931. [45] F. Gordon, Flexible cooling garment, (2008) U.S. Patent Application No. 11/766, 103. [46] S.H. Gallaher, Cooling article of clothing and method of use for same, (2016) U.S. Patent 9,265,654. [47] M.J. Courtney, W.J. Gorak, G.D. Culler, C.S. Weyl, Cooled protective garment, (2010) US Patent 7,730,557, 2010. [48] D. Smolko, G. Kevorkian, Cooling garment, (2006) U.S. Patent Application No. 11/ 434,998. [49] K. Rykaczewski, Modeling thermal contact resistance at the finger-object interface, Temperature 6 (1) (2019) 85–95, https://doi.org/10.1080/23328940.2018. 1551706. [50] A. Psikuta, J. Frackiewicz-Kaczmarek, I. Frydrych, R. Rossi, Quantitative evaluation of air gap thickness and contact area between body and garment, Text. Res. J. (2012), https://doi.org/10.1177/0040517512436823. [51] J. Xu, A. Psikuta, J. Li, S. Annaheim, R.M. Rossi, Influence of human body geometry, posture and the surrounding environment on body heat loss based on a validated numerical model, Build. Environ. 166 (2019) 106340. [52] M.F. Modest, Radiative Heat Transfer, Academic press, San Diego, 2013. [53] L. Cai, A.Y. Song, P. Wu, P.-C. Hsu, Y. Peng, J. Chen, C. Liu, P.B. Catrysse, Y. Liu, A. Yang, Warming up human body by nanoporous metallized polyethylene textile, Nat. Commun. 8 (2017) 496. [54] L. Cai, A.Y. Song, W. Li, P. Hsu, D. Lin, P.B. Catrysse, Y. Liu, Y. Peng, J. Chen, H. Wang, Spectrally selective nanocomposite textile for outdoor personal cooling, Adv. Mater. 30 (2018) 1802152. [55] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a vertical plate, Int. J. Heat Mass Transf. 18 (1975) 1323–1329. [56] B. Gebhart, L. Pera, The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat Mass Transf. 14 (1971) 2025–2050. [57] P.H. Oosthuizen, External natural convective heat transfer from bodies having a

[58]

[59] [60] [61]

[62]

[63]

[64] [65] [66] [67]

[68]

[69]

[70]

[71] [72]

[73] [74] [75]

[76] [77] [78] [79]

12

wavy surface for conditions under which laminar, transitional, and turbulent flow can exist, Adv. Heat Transf. 48 (2016) 261–317. P.H. Oosthuizen, A numerical study of laminar and turbulent natural convective heat transfer from an isothermal vertical plate with a wavy surface, in: ASME 2010 Int. Mech. Eng. Congr. Expo., American Society of Mechanical Engineers, 2010: pp. 1481–1486. F. Boulogne, B. Dollet, Convective evaporation of vertical films, Soft Matter. 14 (2018) 1665–1671. A.D. Spink, Waterproof/breatheable garment construction, (2001). W.A. Lotens, G. Havenith, Ventilation of rain-wear determined by a trace gas method, in: I.B. Mekjavic, E.W. Banister, J.B. Morrison (Eds.), Sustain. Hum. Perform. Harsh Environ., © Taylor and Francis, New York, 1988. M.P. Morrissey, R.M. Rossi, The effect of metallisation, porosity and thickness on the thermal resistance of two-layer fabric assemblies, J. Ind. Text. 44 (2015) 912–923. M.P. Morrissey, R.M. Rossi, The effect of wind, body movement and garment adjustments on the effective thermal resistance of clothing with low and high air permeability insulation, Text. Res. J. 84 (2014) 583–592. A. Shkolnik, C.R. Taylor, V. Finch, A. Borut, Why do Bedouins wear black robes in hot deserts? Nature. 283 (1980) 373. S.-M. Yeon, H.-E. Kim, Effect of slit ventilation system in sportswear on physiological responses, Fash. Text. Res. J. 7 (2005) 75–80. C.C. Creagan, I.I.C.E. Bolian, I.J. Singer, Cooling garment, (2002). M. Zhao, C. Gao, F. Wang, K. Kuklane, I. Holmér, J. Li, A study on local cooling of garments with ventilation fans and openings placed at different torso sites, Int. J. Ind. Ergon. 43 (2013) 232–237. X. Wan, F. Wang, Numerical analysis of cooling effect of hybrid cooling clothing incorporated with phase change material (PCM) packs and air ventilation fans, Int. J. Heat Mass Transf. 126 (2018) 636–648. Y. Sun, W.J. Jasper, E.A. DenHartog, Effects of air velocity, air gap thickness and configuration on heat transfer of a wearable convective cooling system, J. Text. Sci. Eng. 5 (2015) 1. Y. Sun, W.J. Jasper, Numerical modeling of heat and moisture transfer in a wearable convective cooling system for human comfort, Build. Environ. 93 (2015) 50–62. A.-S. Yang, Y.-C. Shih, C.-L. Lee, M.-C. Lee, Investigation of flow and heat transfer around internal channels of an air ventilation vest, Text. Res. J. 84 (2014) 399–410. N. Ghaddar, K. Ghali, J. Harathani, E. Jaroudi, Ventilation rates of micro-climate air annulus of the clothing-skin system under periodic motion, Int. J. Heat Mass Transf. 48 (2005) 3151–3166. J. Laver, The Concise History of Costume and Fashion, Scribner, New York, NY, 1969. S. Brown, Fashion: The Definitive History of Costume and Style, first ed., NY, DK, New York, 2012. A. Middel, E.S. Krayenhoff, Micrometeorological determinants of pedestrian thermal exposure during record-breaking heat in Tempe, Arizona: introducing the MaRTy observational platform, Sci. Total Environ. 687 (2019) 137–151. W.W. Carr, D.S. Sarma, M.R. Johnson, B.T. Do, V.A. Williamson, W.A. Perkins, Infrared absorption studies of fabrics, Text. Res. J. 67 (1997) 725–738. T. Haran, Short-wave infrared diffuse reflectance of textile materials, (2008). J.L. Monteith, M.H. Unsworth, Principles of Environmental Physics, second ed., Butterworth-Heinemann, London, UK, 1990. M. Patrick Morrissey, R. Michel Rossi, The influence of fabric air permeability on the efficacy of ventilation features, Int. J. Cloth. Sci. Technol. 25 (2013) 440–450.