Patent Grant
9951446
In recent years, personal cooling technologies have been developed to provide local environmental control to ensure the user remains thermally comfortable when in extreme environmental conditions such as those faced by athletes, the military, or EMS personnel. However, there remains a distinct lack of such technologies for everyday use by the average end user who spends the majority of the time in a sedentary state. This is especially important for indoor environments where incorporation of such technologies can offset energy consumed by HVAC systems for cooling while maintaining sufficient levels of thermal comfort. For instance, recent studies have shown that in the United States alone, residential and commercial buildings consume nearly 41% of total energy use each year with 37% of that energy devoted solely to heating and cooling, according to the 2011 Buildings Energy Data Book from the U.S. Department of Energy—Energy Efficiency & Renewable Energy Department (2011), and an article by Perez-Lombard, L.; Ortiz, J.; Pout, C.: A Review on Buildings Energy Consumption Information, Energy Build, 2008, 40, 394-398. To reduce energy usage, buildings have incorporated more renewable energy sources such as solar power, implemented advanced HVAC systems, utilized higher performing thermal insulation, and phase change materials for thermal storage all of which requires significant financial investment, as described in articles by Sadineni, S. B.; Madala, S.; Boehm, R. F.: Passive Building Energy Savings: A Review of Building Envelope Components in journal Renewable Sustainable Energy Reviews, 2011, 15, 3617-3631; by Wang, S.; Ma, Z. in Supervisory and Optimal Control of Building HVAC Systems: A Review, HVAC&R Research, 2008, 14, 3-32; by Memon, S. A. in Phase Change Materials Integrated in Building Walls: A State of the Art Review in journal Renewable Sustainable Energy Reviews, 2014, 31, 870-906. Instead, personal thermal comfort technologies offer a potentially low cost solution towards mitigating energy use by HVAC systems. Although these technologies can be used in a variety of indoor and outdoor environments, the focus of this work is to provide personal cooling in temperature regulated indoor environments.
At present, several technologies are commercially available which provide varying degrees of personal cooling. However, these technologies are typically tailored as high performance products, such as sportswear, body armor, and personal protection equipment, thus limiting functionality for everyday use. Arguably the most prevalent personal comfort technology used in industry today is moisture wicking where sensible perspiration is drawn away from the skin to the outer surface of the fabric and evaporated to ambient air thus cooling the wearer passively, as described in Hong, C. J.; Kim, J. B. A Study of Comfort Performance in Cotton and Polyester Blended Fabrics. I. Vertical Wicking Behavior. Fibers Polymer. 2007, 8, 218-224; Kaplan, S.; Okur, A. Thermal Comfort Performance of Sports Garments with Objective and Subjective Measurements, Indian Journal of Fibre & Textile Research, 2012, 37, 46-54; and Das, B.; Das, A.; Kothari, V. K.; Fanguiero, R.; de Araújo, M. Effect of Fibre Diameter and Cross-Sectional Shape on Moisture Transmission through Fabrics, Fibers and Polymer. 2008, 9, 225-231. The drawback of this technology is that it is activated only when the wearer is sufficiently perspiring so that moisture accumulates on the skin; thus, moisture wicking is not suitable to provide cooling for sedentary individuals. Other technologies utilize phase change materials in the form of cold packs which can effectively draw heat from the human body due to the high latent heat of melting associated with water and other refrigerants as described in, for example McCullough, E. A.; Eckels, S. Evaluation of Personal Cooling Systems for Soldiers, 13th International Society of Environmental Ergonomics Conference, Boston, Mass., USA, 2009; pp. 200-204; Gao, C.; Kuklane, K.; Wang, F.; Holmér, I. Personal Cooling with Phase Change Materials to Improve Thermal Comfort from a Heat Wave Perspective. Indoor Ai 2012, 22, 523-530; Muir, I. H.; Bishop, P. A.; Ray, P. Effects of a Novel Ice-Cooling Technique on Work in Protective Clothing at 28C, 23C, and 18C WBGTs, American Industrial Hygiene Association Journal, 1999, 60, 96-104; and Rothmaier, M.; Weder, M.; Meyer-Heim, A.; Kesselring, J. Design and Performance Cooling Garments Based on Three-Layer Laminates, Medical & Biological Engineering & Computing, 2008, 46, 825-832. However this technology tends to be bulky in size and requires frequent replacement of the cold packs over time rendering this technology inconvenient and expensive to the end user. And finally, several technologies provide active cooling through use portable air conditioning units or liquid cooling, for example as described in Elbel, S.; Bowers, C. D.; Zhao, H.; Park, S.; Hrnjak, P. S. Development of Microclimate Cooling Systems for Increased Thermal Comfort of Individuals. International Refrigeration and Air Conditioning Conference; 2012; p. 1183; Kayacan, O.; Kurbak, A. Effect of Garment Design on Liquid Cooling Garments, Textile Research Journal, 2010, 80, 1442-1455; Yang, J.-H.; Kato, S.; Seok, H.-T. Measurement of Airflow around the Human Body with Wide-Cover Type Personal Air-Conditioning with PIV, Indoor and Built Environment, 2009, 18, 301-312; Yang, Y.-F.; Stapleton, J.; Diagne, B. T.; Kenny, G. P.; Lan, C. Q. Man-Portable Personal Cooling Garment Based on Vacuum Desiccant Cooling. Applied Thermal Engineering, 2012, 47, 18-24; and Nag, P. K.; Pradhan, C. K.; Nag, A.; Ashetekar, S. P.; Desai, H. Efficacy of a Water-Cooled Garment for Auxiliary Body Cooling in Heat, Ergonomics 1998, 41, 179-187. These systems not only consume power, but also tend to be prohibitively expensive.
In some embodiments described herein, a radiative cooling fabric comprises woven yarn, wherein the woven yarn substantially comprises fibers having a diameter of approximately 1 μm, and the average separation between fibers in said yarn ranges from about 3 μm to about 10 μm. In another embodiment, the radiative cooling fabric provides an IR transmittance at wavelengths between about 5 μm to about 30 μm ranging from about 30% to about 99%, and a visible reflectance between about 300 nm to about 800 nm ranging from about 40% to about 60%. In another embodiment, the radiative cooling fabric has a porosity of about 0.1 to about 0.2. In another embodiment, the radiative cooling fabric comprises a yarn which has an average diameter ranging from about 30 μm to about 300 μm. In another embodiment, the radiative cooling fabric comprises an average yarn spacing ranging from about 3 μm to about 100 μm. In another embodiment, the fibers in the radiative cooling fabric comprise one or more of polyesters, cellulose, cellulosics, cellulose acetate, polyethylene, polypropylene, or polycaprolactam and other nylons. In another embodiment, the fibers in the radiative cooling fabric consist essentially of one polymer. In another embodiment, the fibers of the radiative cooling fabric comprise 2 or more polymers. In another embodiment, the fibers of the radiative cooling fabric have a core-sheath structure. In another embodiment, the yarn of the radiative cooling fabric comprises fibers of one or more of polyesters, cellulose, cellulosics, cellulose acetate, polyethylene, polypropylene, or polycaprolactam and other nylons. In some other embodiments, the yarn of the radiative cooling fabric comprises fibers having substantially the same composition. In some other embodiments, the yarn of the radiative cooling fabric comprises 2 or more types of fibers. In some other embodiments, the fabric comprises 2 or more types of yarns. In some other embodiments, are provided a garment comprises the radiative cooling fabric.
The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements). Each document referenced herein is incorporated by reference in its entirety for all purposes.
To overcome the limitations of conventional personal cooling technologies, in various embodiments the present disclosure is directed inter alia to radiative cooling fabrics such as infrared-transparent, visible-opaque fabrics (ITVOF), and garments made from such fabrics, which utilize the human body's innate ability to thermally radiate heat as a cooling mechanism during the summer season when environmental temperatures are high. A heat transfer model was developed in order to determine the required IR optical properties of the ITVOF to ensure thermal comfort is maintained for environmental temperatures exceeding the neutral band. From this analysis, it was experimentally observed that existing textiles fail to meet these requirements due to a combination of intrinsic material absorption and structural backscattering in the IR wavelength range. In lieu of these loss mechanisms, a design for an ITVOF has been developed using a combination of optimal material composition and structural photonic engineering. Specifically, synthetic polymers which support few vibrational modes were identified as candidate materials to reduce intrinsic material absorption in the IR wavelength range. To reduce backscattering losses, individual fibers are designed to be comparable in size to visible wavelengths in order to minimize reflection in the IR by virtue of weak Rayleigh scattering while remaining optically opaque in the visible wavelength range due to strong Mie scattering. By additionally reducing the size of the yarn, which is defined as a collection of fibers, less material is used thus decreasing volumetric absorption in the IR wavelength range even further. The ITVOF design is numerically demonstrated to exhibit a high transmittance and a low reflectance in the IR wavelength range while remaining optically opaque in the visible wavelength range. Compared to conventional technologies, an ITVOF can be manufactured into simple form factors while providing a fully passive means to cool the human body regardless of the physical activity level of the user.
Heat Transfer Analysis
In order to quantify the potential cooling power using thermal radiation, the maximum radiative heat transfer achievable between the human body and the surrounding environment can be computed using the Stefan-Boltzmann law. Past studies, such as by Steketee, J. Spectral Emissivity of Skin and Pericardium, in Physics in Medicine and Biology, 1973, 18, 686-694 and by Sanchez-Marin, F. J.; Calixto-Carrera, S.; Villasenor-Mora, C. Novel Approach to Assess the Emissivity of the Human Skin, in Journal of Biomedical Optics, 2009, 14, 024006, have shown that human skin behaves like a blackbody with an emittance near unity in the IR wavelength range. Even if the skin is wet due to perspiration, the emittance is still 0.96 corresponding to water, which suggests human skin is an effective IR emitter for all levels of physical activity, according to the textbook by Incropera, F. P.; Dewitt, D. P.; Bergman, T. L.; Lavine, A. S. Fundamentals of Heat and Mass Transfer; John Wiley & Sons, Inc., 2007. If it is assumed the surface area of an average adult human body is A=1.8 m2, the temperature of human skin is T0=33.9° C. (93° F.), and the ambient temperature is T3=23.9° C. (75° F.), which corresponds to the upper limit of a typical neutral temperature band for human thermal comfort in buildings, the radiative heat transfer coefficient between the skin and the environment is hr=6.25 W/m2K, according to the studies by Hoyt, T.; Lee, K. H.; Zhang, H.; Arens, E.; Webster, T., Energy Savings from Extended Air Temperature Setpoints and Reductions in Room Air Mixing. International Conference on Environmental Ergonomics, 2009; and by Federspiel, C., Predicting the Frequency and Cost of Hot and Cold Complaints in Buildings. Cent. Built Environment, 2000. Under these conditions, the cooling power predicted by the Stefan-Boltzmann law is 112 W, according to Mills, A. F. Heat Transfer; Prentice Hall, 1998. Radiative heat loss from the human body is thus comparable to natural convection and the cooling power actually exceeds the total heat generation rate of qgen=105 W assuming a base metabolic rate at rest of 58.2 W/m2, according to ASHRAE Handbook-Fundamentals; ASHRAE, 2005. From this estimation, it can be observed that thermal radiation clearly has the potential to provide significant cooling power.
To fully harness thermal radiation for cooling, clothing fabrics should be transparent to mid- and far-infrared radiation which is the spectral range where the human body primarily emits. Although a total hemispherical transmittance of unity would be ideal, it would be useful to determine the transmittance required for the ITVOF to provide the necessary cooling power for an individual to feel comfortable at different indoor temperatures. This criterion is determined by assuming the cooling power should equal the total heat generation rate of qgen=105 W at a skin temperature of T0=33.9° C. (93° F.) and a typical room temperature of T3=23.9° C. (75° F.). Under these conditions, the effective heat transfer coefficient is equal to href=5.8 W/m2K which is less than the maximum achievable using thermal radiation. If the ambient temperature increases, the additional cooling power, qcool, needed is equal to the difference between the total heat generation rate, qgen, and the heat loss due to href,
qcool=qgen−href(T0−T3) (1)
For this study, the goal is to provide cooling at an elevated ambient temperature of T3=26.1° C. (79° F.), which past studies have shown can lead to nearly 40% energy savings in indoor environments for certain regions of the United States. Using equation (1) at this temperature, the fabric must provide 23 W of additional cooling.
Based on this criterion, a more detailed one-dimensional steady-state heat transfer model is used to determine the total mid- to far-IR transmittance and reflectance required for the ITVOF. This model, as illustrated in
From this model, the effect of the fabric's optical properties on the total cooling power was evaluated by calculating the maximum ambient temperature that can be sustained without compromising personal thermal comfort.
In both cases, a reflective fabric is more detrimental to cooling performance than an absorptive fabric since a high absorbance implies a high emittance, which would allow clothing to radiate thermal radiation to the environment albeit at a lower temperature. It can also be observed in
To determine quantitatively the optical properties required for the ITVOF to provide 23 W of additional cooling at an ambient temperature of T3=26.1° C. (79° F.), additional cooling power curves were computed as a function of the fabric's total reflectance and transmittance in
For the case where ta=1.05 mm and h=3 W/m2K in
Experimental Characterization of Common Clothing
In order to design the ITVOF, a baseline reference was first established by characterizing the optical properties of common clothing. Specifically, the optical properties of undyed cotton and polyester fabrics, which comprise nearly 78% of all textile fiber production, were measured in both the visible and IR wavelength ranges, as in the article by the Oerlikon Leybold Group, The Fiber Year 2006/07—A World Survey on Textile and Nonwovens Industry, 2007.
The visible wavelength optical properties of both fabric samples were measured using a UV/visible spectrometer. To account for the diffuse scattering of light from the samples, an integrating sphere was used to measure the hemispherical reflectance and transmittance of the fabric in the wavelength range of 400 nm to 800 nm. The results are shown in
Although these fabric samples exhibit a high transmittance, their apparent opaqueness is due to a combination of the contrast sensitivity of the human eye and the diffuse scattering of light. The human eye is a remarkably sensitive optical sensor that can respond to a large range of light intensities, as described in Ferwada, J. Elements of Early Vision for Computer Graphics. IEEE Xplore: Computer Graphics and Applications, 2001, 21, 21-23; and Wandell, B. A. Foundations of Vision; Sinauer Associates, 1995. However, past studies, such as Stevens, S. S. On the Psychophysical Law, Psychological Review, 1957, 64, 153-181; Fechner, G. T. Elemente Der Psychophysik; Breitkopf and Hartel: Leipzig, 1860; Stevens, S. S. To Honor Fechner and the Repeal of His Law. Science 1961, 133, 80-86; and Steinhardt, J. Intensity Discrimination in the Human Eye: I. The Relation of DeltaI/I to Intensity, in the Journal of General Physiology, 1936, 20, 185-209, have shown that the human eye can only perceive variations in light intensity when the change in intensity relative to the background is sufficiently large. This implies that for clothing to appear opaque, the fraction of light reflected by the skin and observed by the human eye must be sufficiently smaller than the fraction of light reflected by the fabric into the same direction. For these fabric samples, light will reflect and transmit diffusively. In addition, skin is also a diffuse surface with a reflectance that is as high as 0.6 at longer wavelengths, as described by Norvang, L. T.; Milner, T. E.; Nelson, J. S.; Berns, M. W.; Svaasand, L. O. Skin Pigmentation Characterized by Visible Reflectance Measurements. Lasers in Medical Science, 1997, 12, 99-112. Since the observation of skin requires light to be reflected from the skin and transmitted through the fabric twice, more light will be scattered into directions beyond what is observable by the human eye compared to light that is only reflected by the fabric thus ensuring the opaque appearance of the fabric. It is for these reasons that common clothing appears opaque to the human eye despite an inherently high transmittance. From these results, the criteria for opaqueness of the ITVOF design are assessed by comparing the hemispherical reflectance and transmittance to measured data shown in
The IR transmittance spectra of the fabric samples, shown in
The reasons for the low transmittances are two-fold. First, cotton and polyester are highly absorbing in the IR wavelength range.
Design and Simulation of an ITVOF
Based on the heat transfer modeling and the experimental results, the design strategy for an ITVOF is to use alternative synthetic polymers which are intrinsically less absorptive in the IR wavelength range and to structure the fibers to minimize the overall reflectance of the fabric in order to maximize radiative cooling. In general, synthetic polymers with simple chemical structures are ideal since fewer vibrational modes are supported thus resulting in less absorption. Additionally, these polymers must also be compatible with extrusion and drawing processes to ensure manufacturability for large scale production. Based on these criteria, polyethylene and polycaprolactam (nylon 6), a type of nylon, were identified as potential candidate materials. Other polyolefins such as polypropylenes, polyethylene/polypropylene copolymers, and other nylons such as nylon 6,6 (i.e., a copolymer of hexamethylene diamine and adipic acid), nylon 6/66 (i.e., a copolymer of caprolactam, hexamethylene diamine, and adipic acid), nylon 66/610 (i.e., a copolymer of caprolactam, hexamethylene diamine, and sebacic acid), nylon 11 (i.e., a polymer of 11-aminoundecanoic acid), nylon 12 (i.e., a polymer of ω-aminolauric acid), nylon 4,6, nylon 4,10, etc. can be used. In addition, polyesters such as PET, cellulose, and cellulose derivatives such as cellulose acetate, reconstituted cellulose, and other cellulosic polymers can also be used. It should be emphasized however that given the full gamut of synthetic polymers available, other synthetic polymers may also be suitable for an ITVOF.
Polyethylene is one of the simplest synthetic polymers available and the most widely used in industry today. The chemical structure of polyethylene consists of a repeating ethylene monomer with a total length that varies depending on the molecular weight. Because the chemical structure consists entirely of carbon-carbon and carbon-hydrogen bonds, few vibrational modes are supported. This is evidenced in
Nylon (McMaster 8539K191) exhibits a similar structure to polyethylene with the key difference being the inclusion of an amide chemical group. As shown in
Compared to cotton and polyester,
In order to further improve the IR transparency of an ITVOF constructed from these materials, structural photonic engineering can be introduced for both the fiber and yarn. Specifically, absorption by weaker vibrational modes can be minimized by reducing the material volume. This can be accomplished by simply decreasing the yarn diameter. To minimize backscattering of IR radiation, the fibers can also be reduced in size such that the diameter is small compared to IR wavelengths. In this manner, incident IR radiation will experience Rayleigh scattering where the scattering cross section of infinitely long cylinders in this regime decreases rapidly as a function of the diameter raised to the 4th power. By reducing the scattering cross section, back scattering of IR radiation will significantly decrease resulting in an overall lower IR reflectance.
Conversely, for the visible wavelength range the ITVOF must instead have a low transmittance to ensure ITVOF-based clothing is opaque to the human eye. Since polyethylene and nylon are not strongly absorptive in the visible wavelength range, reflection must be maximized. This can be achieved by using fibers that are comparable in size to visible wavelengths so that incident light experiences Mie scattering. In exactly the same manner that conventional clothing is opaque to IR radiation, fibers in this regime can support optical resonances that significantly increase the scattering cross section of each fiber thus increasing the overall backscattering of incident light. Since the fabric is composed of an array of these fibers, not only will the total reflectance increase, but light scattering with the fabric will become more diffuse. In conjunction with the contrast sensitivity of the human eye, this design approach can ensure the ITVOF is opaque to the human eye. Thus, the beauty of this structuring approach is that with an optimally chosen fiber diameter, two different regimes of light scattering are utilized in different spectral ranges in order to create a fabric which is simultaneously opaque in the visible wavelength range and transparent in the IR wavelength range.
In regards to the coloration of the ITVOF, polyethylene and nylon exhibit dispersionless optical properties in the visible wavelength range and with sufficient backscattering appear white in color. Despite the chemical inertness of polyethylene, it is possible to provide coloration through the introduction of pigments during fiber formation when polyethylene is in a molten state, according to Charvat, R. A. Coloring of Plastics: Fundamentals; John Wiley & Sons, Ltd., 2005. On the other hand, nylon fibers can be colored easily using conventional dyes, for example as described in Colorants and Auxiliaries: Organic Chemistry and Application Properties; Shore, J., Ed.; Society of Dyers and Colourists, 2002. Depending on the pigment or dye, additional vibrational modes may be introduced in the IR wavelength range reducing the overall transparency.
To theoretically demonstrate the present strategy to create an ITVOF, numerical finite-element electromagnetic simulations were performed on a polyethylene fabric structure illustrated in
Floquet periodic boundary conditions are used on the right and left boundaries to simulate an infinitely wide structure. Perfectly matched layers are used on the top and bottom boundaries to simulate an infinite free space. Simulations were conducted for incident light polarized parallel and perpendicular to the fiber axis at normal incidence. The optical properties for unpolarized light were determined by taking an average of the results for both polarizations. The optical constants of bulk polyethylene were taken from the literature. Although the manufacture of polymer fibers and the subsequent stress imposed when woven into fabrics can introduce anisotropy in the dielectric permittivity, it has been experimentally shown that the optical properties of drawn UHMWPE exhibit minimal change when subjected to a high draw ratio and high stresses, in the past studies by Schael, G. w. Determination of Polyolefin Film Properties from Refractive Index Measurements. II. Birefringence, in the Journal of Applied Polymer Science, 1968, 12, 903-914; and by Wool, R. P.; Bretzlaff, R. S. Infrared and Raman Spectroscopy of Stressed Polyethylene, in the Journal of Polymer Science Part B: Polymer Physics, 1986, 24, 1039-1066. Therefore, anisotropic effects were neglected in this study.
To assess the impact of reducing the size of the fiber (Df) and the yarn (Dy), the IR optical properties were computed by varying the yarn diameter (Dy=30 μm, 50 μm, and 100 μm) assuming a fixed fiber diameter of Df=10 μm and by varying the fiber diameter (Df=1 μm, 5 μm, and 10 μm) assuming a fixed yarn diameter of Dy=30 μm. The results are shown in
However, the spectral optical properties in
When the fiber diameter is reduced to 5 μm, the absorbance exhibits a marginal decrease. On the other hand, the reflectance actually increases compared to the case where Df=10 μm. This indicates that the fiber is still sufficiently large enough to support cavity resonant modes. Although there are fewer modes supported, as shown by the variation in reflectance, these modes become leakier for smaller size fibers thus resulting in a larger scattering cross section and a higher reflectance. As a result, there is little enhancement to the overall IR transmittance. Once the fiber diameter decreases to 1 μm, the reflectance dramatically decreases, which suggests the fiber is sufficiently small such that incident mid- to far-IR radiation will primarily experience Rayleigh scattering. In this Rayleigh regime, the fibers are too small to support cavity mode resonances thus reducing the reflection of IR radiation. Furthermore, the reduction in fiber size further reduces the total material volume again decreasing the absorbance. As a result, the total mid- to far-IR transmittance further increases from 0.76 for Df=10 μm to 0.972 for Df=1 μm, making the structure even more transparent to thermal radiation emitted by the human body. Simultaneously, the total mid- to far-IR reflectance decreases substantially from 0.19 to 0.021. By reducing the fiber diameter, the resulting improvements to the optical properties enable this ITVOF design to clearly surpass the requirements needed to provide 23 W of additional cooling at an ambient temperature of 26.1° C. (79° F.) based on
To assess the visible opaqueness, additional simulations were performed for the polyethylene-based ITVOF design assuming a constant refractive index of n=1.5 and an extinction coefficient of k=5·10−4 based on literature values for the visible wavelength range from 400 nm to 700 nm. These simulations were performed for the optimal design where Df=1 μm, Dy=30 μm, Ds=1 μm, and Dp=5 μm. The results are shown in
It can also be observed in
Based on these results, it may appear that the creation of an ITVOF requires substantial reduction in material volume since the highest IR transmittance of 0.972 was predicted for the smallest yarn diameter (Dy=30 μm) and fiber diameter (Df=1 μm). Although decreasing both of these parameters will certainly improve the overall transmittance in the IR wavelength range, additional simulations for various fiber diameters (Df=1 μm, 5 μm, and 10 μm) assuming a larger yarn diameter of Dy=50 μm show a similar trend in the enhancement of transmittance. For a fiber diameter of Df=1 μm, the total hemispherical IR transmittance and reflectance was 0.969 and 0.019, respectively, which is similar to the case where Dy=30 μm despite a material volume that is three times larger at 445 μm2. This result shows that reducing the fiber diameter is far more effective to improving transmittance compared to reducing the yarn diameter. Therefore, it may be suitable to create an ITVOF that is comparable in size to conventional fabrics so long as the fiber diameter is sufficiently small.
Suitable fiber diameters for an ITVOF should therefore be approximately 1 μm, ranging from about 0.5 μm to about 3.0 μm, including about 0.5 μm, about 0.6 μm, about 0.7 μm, about 0.8 μm, about 0.9 μm, about 1 μm, about 1.1 μm, about 1.2 μm, about 1.3 μm, about 1.4 μm, about 1.5 μm, about 1.6 μm, about 1.7 μm, about 1.8 μm, about 1.9 μm, about 2.0 μm, about 2.1 μm, about 2.2 μm, about 2.3 μm, about 2.4 μm, about 2.5 μm, about 2.6 μm, about 2.7 μm, about 2.8 μm, about 2.9 μm, about 3.0 μm, inclusive of all ranges and subranges therebetween.
In various embodiments, the average spacing or separation between fibers in the ITVOF fabric or yarn should be approximately 5 μm, ranging from about 3 μm to about 10 μm, including about 3 μm, about 4 μm, about 5 μm, about 6 μm, about 7 μm, about 8 μm, about 9 μm, or about 10 μm, inclusive of all ranges and subranges therebetween.
In various embodiments, the yarn of the ITVOF fabric should have an average diameter ranging from about 30 μm to about 300 μm, including about 30 μm, about 35 μm, about 40 μm, about 45 μm, about 50 μm, about 55 μm, about 60 μm, about 65 μm, about 70 μm, about 75 μm, about 80 μm, about 85 μm, about 90 μm, about 95 μm, about 100 μm, about 105 μm, about 110 μm, about 115 μm, about 120 μm, about 125 μm, about 130 μm, about 135 μm, about 140 μm, about 145 μm, about 150 μm, about 155 μm, about 160 μm, about 165 μm, about 170 μm, about 175 μm, about 180 μm, about 185 μm, about 190 μm, about 195 μm, about 200 μm, about 205 μm, about 210 μm, about 215 μm, about 220 μm, about 225 μm, about 230 μm, about 235 μm, about 240 μm, about 245 μm, about 250 μm, about 255 μm, about 260 μm, about 265 μm, about 270 μm, about 275 μm, about 280 μm, about 285 μm, about 290 μm, about 295 μm, or about 300 μm, inclusive of all ranges and subranges therebetween.
In various embodiments, the ITVOF fabric should have an average yarn spacing or separation ranging from about 3 μm to about 100 μm, including about 3 μm, about 4 μm, about 5 μm, about 6 μm, about 7 μm, about 8 μm, about 9 μm, about 10 μm, about 15 μm, about 20 μm, about 25 μm, about 30 μm, about 35 μm, about 40 μm, about 45 μm, about 50 μm, about 55 μm, about 60 μm, about 65 μm, about 70 μm, about 75 μm, about 80 μm, about 85 μm, about 90 μm, about 95 μm, or about 100 μm, inclusive of all ranges and subranges therebetween.
In various embodiments, the IR transmittance of the ITVOF fabric at wavelengths between about 5 μm to about 30 μm should range from about 30% to about 99%, including about 30%, about 35%, about 40%, about 45%, about 50%, about 55%, about 60%, about 65%, about 70%, about 75%, about 80%, about 85%, about 90%, about 95%, or about 99% inclusive of all ranges and subranges therebetween.
In various embodiments, the visible reflectance of the ITVOF fabric at wavelengths between about 300 nm to about 800 nm should range from about 40% to about 60%, including about 40%, about 45%, about 50%, about 55%, or about 60%, inclusive of all ranges and subranges therebetween.
In addition, a polyethylene-based ITVOF may not exhibit sufficient fabric handedness due to the nature of the material used. To ensure the fabric is comfortable to the wearer, it may be necessary for the fabric to be composed of a mixture of different material fibers which will affect the transmittance of the fabric. To assess the potential extent in which the transmittance will be reduced, simulations were also performed for different volumetric concentrations of polyethylene and polyester (PET) again assuming Df=1 μm and Dy=30 μm. The optical constants for PET were also taken from the literature. For the most absorbing case of 25% PE/75% PET, the total hemispherical mid- to far-IR transmittance and reflectance was 0.728 and 0.038, respectively, which indicates that a fabric blend can still achieve a high transmittance and a low reflectance to provide sufficient cooling using thermal radiation.
The design for an infrared-transparent visible-opaque fabric (ITVOF) is demonstrated in order to provide personal cooling via thermal radiation from the human body to the ambient environment. The ITVOF design is developed to be made of polyethylene, which is an intrinsically low absorbing material, and structured the fibers to be sufficiently small in order to maximize the IR transparency and the visible opaqueness. For a 1 μm diameter fiber and a 30 μm diameter yarn, the total mid- and far-IR transmittance and reflectance are predicted to be 0.972 and 0.021, respectively, which exceed the minimum transmittance of 0.644 and maximum reflectance of 0.2 required to provide sufficient cooling at an elevated ambient temperature of 26.1° C. (79° F.). Simultaneously, the total hemispherical reflectance and transmittance in the visible wavelength range are comparable to existing textiles which indicates that the design is optically opaque to the human eye.
In some embodiments, the fibers of the ITVOF can comprise a single type of polymer, for example a polyester, a cellulose or other cellulosic fiber, a rayon (cellulose acetate), polyethylene, polypropylene, or a nylon, such as polycaprolactam. In other embodiments, the fibers can comprise two or more polymers, for example as a blend or in a bi-phasic structure such as a core-sheath structure.
In various embodiments, the ITVOF fabric can comprise a single type of yarn, wherein the yarn can comprise a single type of fiber, or can include different types of fibers in the same yarn. Alternatively, the ITVOF fabric can include two or more types of yarns, wherein the yarns can comprise the same or different types of fibers.
The ITVOF fabric of the present disclosure can be used to fabricate garments. Such garments can comprise only the ITVOF fabric, or can incorporate or combine the ITVOF fabric of the present disclosure with other suitable fabrics, whereby the ITVOF fabric provides personal cooling, while the other fabrics provide other mechanical, decorative, or functional properties.
The fabrication of an ITVOF can be achieved using conventional manufacturing processes including drawing, extrusion, or electrospinning. Thermal and mechanical evaluation can be conducted using standardized testing methods as shown in previous studies including the use of thermal manikins, wash and dry cycling, and subject testing, as described in the standard handbooks: ASTM D3995-14, Standard Performance Specification for Men's and Women's Knitted Career Apparel Fabrics: Dress and Vocational; ASTM Standard F1868, Standard Test Method for Thermal and Evaporative Resistance of Clothing Materials Using a Sweating Hot Plate; and ISO 11092 Textiles—Physiological Effects—Measurement of Thermal and Water-Vapour Resistance under Steady-State Conditions (sweating Guarded-Hotplate Test). Additionally, vapor transport through the fabric, which is another key component for thermal comfort, must also be considered in future ITVOF designs. Although the porosity of the proposed ITVOF design is based on typical clothing, e.g. within a range of about 0.1 to about 0.2, it would nonetheless be useful to quantitatively assess vapor transport to optimally design ITVOF-based clothing, according to the ASTM Standard E96/E96M, 2013, Standard Test Methods for Water Vapor Transmission of Materials, 2013. The inclusion of coloration for aesthetic quality is another important aspect that must be considered without compromising the effectiveness of radiative cooling. Alternative synthetic polymers, such as polypropylene or polymeric blends of UHMWPE and PET, are also suitable for use in an ITVOF design. Ultimately, ITVOF-based clothing offers a simple, low-cost approach to provide cooling locally to the human body in a variety of indoor and outdoor environments without requiring additional energy consumption, compromising breathability, or requiring any lifestyle change. Therefore, ITVOF provides a simple solution to reduce the energy consumption of HVAC systems by enabling higher temperature set points during the summer.
Suitable fabrication methodologies can include, for example the use a three step fabric production process consisting of (1) extrusion of a molten polymer through a spinneret into a bundle of fibers, (2) drawing of the fibers to reduce diameter and increase mechanical strength, and (3) spooling the fibers into a yarn. This fabrication method consists of combining spinneret-based polymer extrusion (widely utilized for polymer fiber production) with a drawing and fiber/yarn structuring system to create the ITVOF.
The design requirements (i.e., form factor, size, processing parameters, spinneret design, and system performance optimization) can be refined in order to fabricate the optimal ITVOF structure. Specifically, the system components (laboratory spinning machine and drawing system) can be designed, implemented and the resulting fiber performance can be tested under a range of temperature conditions. The disclosed designs can be utilized in a full-scale industrial implementation, but are exemplified herein using a prototype fabric (5 cm×5 cm) which represents a section of a full-scale garment. This exemplified equipment can be readily modified by the skilled artisan to meet the specifications required to produce the optimal ITVOF design in bulk.
The manufacturing scheme is illustrated in
Nylon and polyethylene polymers exemplified herein are available from the Sigma Aldrich Company, but suitable commercial sources are well known to the skilled artisan. All samples are vacuum-dried at 110° C. for 24 h prior to being placed into the extruder for processing in order to reduce the moisture content of the polymer. Nylon is typically melt spun from the extruder at 230° C. Likewise, polyethylene is melt spun from the extruder at 140° C.
The exemplified system utilizes a laboratory scale spinneret machine (Hills, Inc. LBS-100,
Once the optimal fabric design is determined, the extrusion spinneret, a multi-pore module through which melted polymer is extruded and machined to specification.
Generally, polymer fibers used in textiles are drawn after being extruded. This results in a number of improvements—first, it decreases the fiber diameter to the targeted value. Second, by drawing the fiber, it improves mechanical and durability properties of the fiber. Production of the ITVOF mates the spinning machine to a post-extrusion drawing system to draw the polymer fibers to the desired size and create the structure required to maintain fiber spacing in the yarn.
Polymer extrusion equipment and a method for the fabrication of polymer nanofibers with diameters between 50 and 500 nm are disclosed. These fibers exhibit ultra-high thermal conductivity (achieved through a drawing process) as shown in
More recently, a novel continuous fabrication process is developed to produce highly aligned polymer sheets, as described in Loomis, J.; Ghasemi, H.; Huang, X.; Thoppey, N.; Wang, J.; Tong, J. K.; Xu, Y.; Li, X.; Lin, C.-T.; Chen, G. Continuous Fabrication Platform for Highly Aligned Polymer Films. TECHNOLOGY 2014, 1-11. Alignment of molecular chains within polymers is a desirable trait for many applications as it results in superior mechanical and thermal properties in the polymeric materials. Therefore, fabrication techniques known in the art are directly applicable to the ITVOF fabrication as provided herein.
Once a spool of yarn is created using the developed approach, the next step is to weave this yarn into a fabric. In order to accomplish this task, a yarn is woven using commercially available looms (Glimakra Emilia rigid heddle loom) to create initial prototypes. In this manner, several weaving patterns can be explored to assess cooling, strength, and comfort. The loom, as shown in
The process to color ITVOF will depend on the material components being dyed (nylon, polyethylene, etc.). Colorants are typically divided into two major classes: dyes and pigments. The demarcation between them is based chiefly on solubility. A pigment relies on insolubility in the medium in which it is dispersed, while a dye requires some degree of solubility that will allow it to diffuse into the polymeric matrix of a textile fiber.
According to the different interaction between the dyes and fiber/yarn/fabric, strategies to color nylon/polyethylene fabric are classified into the following classes: (a) dyes exploiting hydrogen bonding between electron donating nitrogen atoms (—N:) in the dye and polar —OH or —CONH— groups in the fabric, (b) charged, water-soluble organic dyes that bind to ionic and polar sites on fabric molecules, and (c) dyeing with inorganic pigments or the precipitation of metal salts on fibers (mineral dyes).
Nylon fibers are hydrophilic and they absorb water readily. The model for the uptake of dyes by these fibers is thus one of water-filled pores through which soluble dye diffuses. In the internal phase these dyes can interact with the nylon chain via a hydrogen bond. In contrast, polyethylene fibers are hydrophobic and absorb comparatively little water. In order to dye polyethylene fibers, the following coloration methods are being considered. One is adding pigment at the stage of fiber formation, and the other is chemical modification of the fibers. The second method has disadvantages such as the loss of the typical properties of the fibers by chemical modification and low color fastness. It is more realistic to consider a “dyeing transition temperature,” which is defined by a temperature at which there is a rapid increase in the rate of dye/pigment diffusion through a polymer. As these fibers are typically thermoplastic, they undergo a glassy-rubbery transition at a characteristic temperature (Tg). Above this temperature the polymer chain segments are mobile, and at any given time there is a free volume within the polymer matrix. The fiber is thus better regarded as a system of continuously changing regions of “free volume” through which pigments can diffuse.
Azo dyes from blue to red can be considered as colorants for this project. The azo group is an inherently intense chromophore in terms of tinctorial strength, the cost of manufacturing azo dyes is comparatively lower than other expensive dyes. Azo dyes are defined as compounds containing at least one azo group attached to sp2-hybridized carbon atoms, such as benzene, naphthalene, thiazole and thiophene. As a typical donor-acceptor chromogen, the electron-accepting substituents, X, Y and Z and the electron donating substituents R1 and R2 are favorably sited to create visible colors as shown in
The sheer variety of azo dyes requires additional investigation to assess suitability for IR transmissivity. As an example, the FTIR transmittance spectrum is plotted for a common azo dye known as Direct Red 23 in
To assess the suitability of ITVOF for clothing with enhanced cooling power, several key properties can be measured. These properties are generally grouped into four main areas: (1) structural properties of fabricated ITVOF, (2) the opaqueness and transparency of ITVOF in the visible and IR wavelength range, respectively, (3) the improvement in cooling power due to the inclusion of radiative heat transfer and thermal comfort, and (4) the mechanical robustness and comfort of ITVOF. In accordance with the DELTA-FOA program's performance metrics for wearable technologies, the intended performance objectives for technology are summarized in Table 1 as follows.
Structural characterization of the ITVOF can be carried out assess morphology, size, uniformity, and porosity of individual fiber, yarn, and fabrics mainly based SEM imaging. Since fiber pulling can create certain degree of molecular alignment that affect mechanical properties, XRD spectroscopy can be used to assess the crystallinity of the fibers.
The complex interactions between human body, fabric and the ambient environment define the thermal comfort performance. This is critical in influencing product acceptance by the end customer. Often perceptions of discomfort are sensed when clothing impedes the flow of heat and moisture from the body. The principle that governs thermal comfort is the balance of the body heat generation and dissipation as well as the balance of the body water vapor generation and removal. Thus the assessment of thermal comfort performance is primarily heat and moisture transport through the fabric into a controlled environment. With a fixed temperature difference between skin and ambient, the thermal and evaporative resistance should be in a certain range to create heat and moisture balance allowing for optimal comfort.
The thermal resistance can be measured utilizing a well-established guarded hot-plate technique (
In addition, the instantaneous thermal sensation experienced at the initial contact of the material fabric with the skin surface can also be important to an individual's comfort. To assess the warm and cool sensations of a garment fabric, Japan JIS Qmax standard, as described for example by Yoneda, M.; Kawabata, S. Analysis of Transient Heat Conduction and Its Applications. Journal of the Textile Machinery Society of Japan, 1983, 29, 73-83) is followed to setup for the testing system for the samples. To assess this parameter, a commercially available instrument (Model KES-F7 THERMO LABO II, KATO TECH CO., LTD.) as shown in
In clothing, the moisture vapor transmission rate (MVTR) is a measure of breathability and has contributed to greater comfort for wearers of clothing for moderate activity rate. It is measured by the mass rate in which water vapor passes through fabrics, in grams of water vapor per square meter of fabric per 24 hour period (g/m2/day). This property is measured using a commercial system according to the simple dish method, similar to ASTM Standard E96/E96M, 2013, Standard Test Methods for Water Vapor Transmission of Materials, 2013. A typical instrument is shown in
The mechanical characterization of the ITVOF is intended to assess its mechanical strength and lifetime stability under various loading configurations. The evaluation of the mechanical properties of the ITVOF follows ASTM standards for woven textiles. Specifically, the tensile strength is evaluated using Instron testing machines. To assess color fastness and fabric robustness, the ITVOF is washed and dried at least 50 times in accordance to ASTM standards D3995-14, Standard Performance Specification for Men's and Women's Knitted Career Apparel Fabrics: Dress and Vocational. For mechanical comfort performance, an industry CSP adviser is consulted to evaluate the ITVOF handedness. These measurements are conducted in conjunction with characterization, and modeling is carried out in parallel to provide systematic iteration to determine optimal ITVOF design for mechanical robustness and comfort.
UV/Visible Characterization
A custom UV/visible wavelength spectrometer was used to measure the optical properties of the fabric samples in the visible wavelength range. This system consisted of a 500 W mercury xenon lamp source (Newport Oriel Instruments, 66902), a monochromator (Newport Oriel instruments, 74125), an integrating sphere (Newport Oriel Product Line, 70672) and a silicon photodiode (Newport Oriel instruments, 71675). Total hemispherical reflectance measurements were performed by placing the fabric samples onto a diffuse black reference (Avian Technologies LLC, FGS-02-02c) to avoid reflection from the underlying substrate. Total hemispherical transmittance measurements were performed by placing the fabric samples onto the input aperture of the integrating sphere. All measurements were calibrated using a diffuse white reference (Avian Technologies LLC, FWS-99-02c).
Infrared Characterization
A commercially available FTIR spectrometer (Thermo Fisher Scientific, Nicolet 6700) and an IR objective accessory (Thermo Fisher Scientific, Reflachromat 0045-402) was used to measure the optical properties of the fabric samples and the polymer films in the infrared wavelength range. The objective was placed 15 mm behind the samples, corresponding to the working distance of the objective, in order to capture infrared radiation transmitted through the samples. For the fabric samples, the total hemispherical transmittance will be underestimated since not all of the IR radiation that is diffusively transmitted through the fabric sample is captured. However, the objective used in this study was designed to capture IR radiation at a 35.5° acceptance angle. Since it is expected that IR radiation will transmit diffusively, the measured results are likely underestimated by a few percent, which is still in agreement with previous studies.
The following passages include supporting information which provides further details on the heat transfer modeling, the optical constants of polyethylene (PE) and polyethylene terephthalate (PET), Mie theory calculations for a single isolated polyethylene fiber, numerical finite element simulations of a polyethylene-based ITVOF for a larger yarn diameter, and numerical finite element simulations for an ITVOF blend of polyethylene and polyester.
Heat Transfer Model
To evaluate the impact of a fabric's IR optical properties on personal cooling, a 1D steady-state heat transfer model was adopted, as illustrated in
Assumptions
For convenience, all assumptions in the model are summarized as follows,
Table 2 shows a list of the input parameters used in this study. In order to determine the total cooling power through the fabric, the net heat flux in this analysis can be multiplied by the surface area of the human body, A.
Additionally, the fabric is assumed to be partially reflective, transmissive, and absorptive with gray and diffuse optical properties. In conjunction with Kirchoff's law, the fabric's optical properties will adhere to the following relation,
∈c=αc=1−ρc−τc (S1)
where ∈c, αc, ρc, and τc are the fabric's total hemispherical emittance, absorbance, reflectance, and transmittance, respectively.
Model Formalism
In this model, the overall goal is to determine the maximum ambient temperature that can be sustained without compromising a person's thermal comfort as a function of the fabric's optical properties. Although a minimum ambient temperature also exists, this is related to personal heating and is thus beyond the scope of this work. The criterion used to evaluate personal thermal comfort is based on the equivalence of the total cooling power with the total heat generation rate of 105 W from the human body. For a given set of material and environmental conditions, the ambient temperature is increased iteratively until the net cooling power can no longer dissipate the amount of heat generated by the human body. By fixing the skin temperature to be 33.9° C. (93° F.), the primary unknown variables in this model are the inner surface fabric temperature, T1, the outer surface fabric temperature, T2, and the ambient temperature, T3.
Additionally, the air gap thickness, ta, and the convective heat transfer coefficient, h, can also be varied to simulate different environmental conditions (i.e. tight-fitting vs. loose fitting fabric on different areas of the human body, varying levels of air circulation within the ambient environment, etc.) independent of the environment temperature. In order to compare the impact of the fabric's optical properties on personal cooling for various environmental conditions, the air gap thickness and convective heat transfer coefficient are constrained to ensure a consistent baseline neutral temperature band is used regardless of the environmental conditions. To accomplish this, a reference case is adopted to assume an ambient temperature of 23.9° C. (75° F.), corresponding to the upper limit of a typical neutral temperature band. The reflectance and transmittance of the fabric are also assumed to be ρc=0.3 and τc=0.03, respectively, corresponding to measurements of conventional polyester and cotton fabrics as shown in
In various embodiments, the ITVOF fabrics of the present disclosure should have an IR reflectance ranging from about 1% to about 25%, for example about 1%, about 2%, about 3%, about 4%, about 5%, about 6%, about 7%, about 8%, about 9%, about 10%, about 11%, about 12%, about 13%, about 14%, about 15%, about 16%, about 17%, about 18%, about 19%, about 20%, about 21%, about 22%, about 23%, about 24%, or about 25%, inclusive of all ranges and subranges therebetween. In particular embodiments, the IR reflectance is less than about 10%.
In other embodiments, the ITVOF fabrics of the present disclosure should have an IR transmittance between about 5 μm and about 30 μm ranging from about 30% to about 99%, for example, about 30%, about 31%, about 32%, about 30 through 34, 5%, about 36%, about 37%, about 38%, about 39%, about 40%, about 41%, about 42%, about 43%, about 44%, about 45%, about 46%, about 47%, about 48%, about 49%, about 50%, about 51%, about 52%, about 53%, about 54%, about 55%, about 56%, about 57%, about 58%, about 59%, 60%, about 61%, about 62%, about 63%, about 64%, about 65%, about 66%, about 67%, about 68%, about 69%, about 70%, about 71%, about 72%, about 73%, about 74%, about 75%, about 76%, about 77%, about 78%, about 79%, about 80%, about 81%, about 82%, about 83%, about 84%, about 85%, about 86%, about 87%, about 88%, about 89%, about 90%, about 91%, about 92%, about 93%, about 94%, about 95%, about 96%, about 97%, about 98%, or about 99%, inclusive of all ranges and subranges therebetween. In particular embodiments, the IR transmittance is greater than about 30%.
In still other embodiments, the ITVOF fabrics of the present disclosure have both an IR reflectance ranging from about 1% to about 25% and an IR transmittance ranging from about 60% to about 99%, including the ranges and subranges of each disclosed herein. In particular embodiments, the ITVOF fabrics of the present disclosure have an IR reflectance of less than about 10%, and an IR transmittance greater than about 60%.
Control Volume Analysis
The first component of the heat transfer model is to identify relevant control volumes (CV) and to apply an energy balance in order to obtain equations that connect the various heat transfer mechanisms included in this model. As shown in FIG. S1a, there are two control volumes that will be used in this study: CV1 is defined around only the human body and CV2 is defined around the entirety of the surrounding fabric. The expressions obtained when applying an energy balance around CV1 and CV2 are as follows,
CV 1:qgen+qrad,c+τc·qrad,e−(1−ρc)·qrad,s−qcond,a=0 (S2)
CV 2:(1−ρc−τc)·qrad,s+(1−ρc−τc)·qrad,e+qcond,a−2·qrad,c−qconv=0 (S3)
where qgen is the heat generation rate per unit area, qcond,a is the conductive heat flux between the skin and the fabric, qconv is the convective heat flux from the fabric to the ambient environment, qrad,s is the radiative heat flux from the skin, qrad,e is the radiative heat flux from the ambient environment, and qrad,c is the radiative heat flux from the fabric. The conductive, convective, and radiative heat flux terms are expressed using Fourier's law, Newton's law of cooling, and the Stefan-Boltzmann law as follows,
where T0 is the skin temperature, T1 is the inner surface fabric temperature, T2 is the outer surface fabric temperature, T3 is the ambient temperature, ka is the thermal conductivity of air, ta is the air gap thickness, h is the convective heat transfer coefficient, σ is the Stefan-Boltzmann constant equal to 5.67·10−8 Wm−2K−4. In equation (S8), mean temperatures of T1 and T2 are assumed to approximate radiative emission by the fabric. Additionally, in equations (S2), (S3), (S6), and (S7), it was assumed the skin and environment behave like an ideal blackbody with an absorptance and emittance equal to 1.
Based on the control volume analysis, two fundamental equations (S2) and (S3) are obtained to describe the various contributions to heat transfer in this system. Since there are three unknowns that must be solved for, an additional equation is required in order to complete this model. Equations (S2) and (S3) describe heat transfer around the human body and the fabric, respectively. By deduction, the remaining equation must describe the nature of heat transfer within the fabric itself. Specifically, by considering heat conduction, radiative absorption, and radiative emission, a temperature profile can be derived in order to link the unknown temperatures T1 and T2.
Temperature Profile of Fabric
To determine the temperature profile within the fabric, heat conduction and radiative heat transfer must be included in the heat transfer analysis. If a differential volume element is taken within the fabric, as shown in FIG. S1b, the heat equation will take the following form,
where kc is the fabric thermal conductivity and qrad is the net radiative transfer within the fabric. In general, qrad must be determined rigorously using the radiative heat transfer equation in order to account for all absorption, emission, and internal scattering processes. For simplicity, internal scattering effects are assumed to be negligible and only consider IR reflection at the boundaries of the fabric, as will be later shown when determining the expressions for each radiative heat flux. Additionally, self-absorption effects are also neglected. Therefore, the net radiative heat transfer will consist only of incident radiative absorption and outgoing radiative emission as follows,
where qrad,cL′ is the radiative emission from the fabric to the skin, qrad,cR′ is the radiative emission from the fabric to the ambient environment, qrad,s′ is the absorption of radiation emitted from the skin, and qrad,e′ is the absorption of radiation emitted from the ambient environment.
In general, the analytical form for radiative absorption and emission in the limit of negligible internal scattering will consist of an exponential decay in accordance to the Beer-Lambert law.1 However, the analysis is simplified by instead assuming the absorption and emission profile to be linear as follows,
qrad,i(x)=A·x+B (S11)
where A and B are unknown coefficients that will depend on the boundary conditions assumed for each radiative heat flux. In the limit of high absorption, the approximation of a linear absorption and emission profile will be inaccurate. Despite this limitation, it is nonetheless expected that this approximation will provide a reasonable estimation of heat transfer through the fabric since the difference in the inner and outer fabric temperature is not expected to be large, thus inherently making this analysis less sensitive to the absorption and emission profile used. Using equation (S11) and appropriate boundary conditions for each radiative flux, the following is obtained,
1. Emission from fabric to skin:
2. Emission from fabric to ambient environment:
3. Absorption by fabric from skin:
4. Absorption by fabric from ambient environment:
Upon substituting equations (S12)-(S15) into (S10) and using the definition of heat fluxes defined by (S6)-(S8), the heat equation will become,
where a mean temperature of T1 and T2 is again used to approximate radiative emission from the fabric. Although radiative emission from the fabric technically depends on the local temperature T as a function of position x, the use of a mean temperature is a reasonable approximation since T1 and T2 are not expected to be significantly different.
To determine the temperature profile, all that remains is to integrate equation (S16) and apply appropriate boundary conditions,
The boundary conditions applied in this analysis includes temperature and heat flux continuity at surface 1 (x=0) as follows,
Upon applying (S19) and (S20) in equations (S17) and (S18), the final expression is obtained for the temperature profile within the fabric,
By taking x=tc in equation (S21), the following temperature relation is obtained,
Therefore, with equations (S2), (S3), and (S22), there is now a complete set of equations to describe heat transfer from a human body covered by fabric to the ambient environment. These equations are used to first obtain the air gap thickness, ta, for the previously described reference case with an assumed convective heat transfer coefficient. Following this calculation, the same equations are used to solve for T1, T2, and T3 as a function of the fabric's optical properties and the assumed environmental conditions. From this analysis, one can find the maximum ambient temperature, T3, which can be sustained without compromising personal thermal comfort.
Each document cited herein is incorporated in its entirety for all purposes.
This application is a continuation of PCT Application No. PCT/US2015/050720, entitled “Infrared Transparent Visible Opaque Fabrics,” and filed on Sep. 17, 2015, which claims the benefit under 35 U.S.C. § 119(e) of U.S. Application No. 62/051,348, entitled “Infrared Transparent Visible Opaque Fabrics,” and filed on Sep. 17, 2014. Both of these applications are hereby incorporated by reference herein.
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|---|---|---|---|
| 4340091 | Skelton | Jul 1982 | A |
| 20040116025 | Gogins | Jun 2004 | A1 |
| 20080170982 | Zhang | Jul 2008 | A1 |
| 20150147573 | Zhang | May 2015 | A1 |
| 20150308018 | Zhang | Oct 2015 | A1 |
| 20160083872 | Zhang | Mar 2016 | A1 |
| Number | Date | Country |
|---|---|---|
| 2014087161 | Jun 2014 | WO |
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| Number | Date | Country | |
|---|---|---|---|
| 20180030626 A1 | Feb 2018 | US |
| Number | Date | Country | |
|---|---|---|---|
| 62051348 | Sep 2014 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | PCT/US2015/050720 | Sep 2015 | US |
| Child | 15461055 | US |
