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Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles
Journal Pre-proofs Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles Hiroki Gonome, Kohei Wakabayashi PII: DOI: Reference:
S1359-4311(19)35424-9 https://doi.org/10.1016/j.applthermaleng.2020.115083 ATE 115083
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
4 August 2019 12 February 2020 13 February 2020
Please cite this article as: H. Gonome, K. Wakabayashi, Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles, Applied Thermal Engineering (2020), doi: https:// doi.org/10.1016/j.applthermaleng.2020.115083
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier Ltd.
Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles
Hiroki Gonome*, Kohei Wakabayashi
Graduate School of Science and Engineering, Yamagata University, Yamagata, 992–8510, Japan
*Corresponding author. Tel.: +81–23–826–3103 E-mail address: [email protected]
1
Abstract Many areas on earth have hot climates because of the high temperatures during summer and strong solar radiation. Water mist cooling is useful as an environmentally friendly urban system that can provide relief in these high-temperature conditions. To improve the utilization of the water mist cooling system, radiative transfer analysis was conducted to develop a mist cooling device that can block the uncomfortable solar radiation without causing discomfort because of the use of nano- and microsized droplets and bubbles. Herein, the radiative properties of single-water droplets and bubbles are calculated from a broad range of particle sizes and wavelengths. The extinction and scattering efficiencies of microscale droplets and bubbles are high in the solar spectral region, and they have the potential to reflect near infrared light. To model the radiative transfer in a water mist layer, a radiation analysis was conducted in a parallel plane model in one-dimension. The effects of particle size on spectral reflectance and total solar reflectance were discussed. The total solar reflectance is shown to increase with increasing particle sizes until it reaches its maximum value. It is demonstrated that undesirable thermal radiation can be reflected with the use of optimized water particles.
Keywords: Radiative transfer; Particulate media; Mist cooling; Nanoparticle; Environmentally friendly urban system
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1.
Introduction There are many areas on earth with hot climates where the summer air temperature and intense solar
irradiation make the physical presence in the outdoors unpleasant and even harmful. In particular, we refer to the existence of an urban heat island in urban or metropolitan areas if it is significantly warmer than its surrounding rural areas. To provide relief from the high-temperature environment, there exist a variety of devices that spray water droplets [1-5]. These devices reduce the air temperature based on the evaporation of water droplets, but they do not consider or account for the effects of uncomfortable solar radiation. The solar energy that reaches the surface of the earth in the range of 0.3 to 2.5 μm is divided into three parts (air mass = 1.5): a) the ultraviolet (UV) region (5%), b) visible (VIS) region (43%), and c) near infrared (NIR) region (52%). Additionally, these devices sometimes lead to uncomfortable wet states because water droplets deform facial make-up or wellcoiffed hair. Thus, if these uncomfortable wet states can be minimized or eliminated, the utility of the mist cooling device can be improved. This study conducts an analytical investigation to describe how nanoscale water droplets generated by misting systems can serve as an effective filter for solar radiation. Additionally, this study analyzes the radiative transfer in the mist layer formed by the nanoscale water bubbles. Nanoscale water droplets can reduce the volume of water and wetness unpleasantness, while bubbles can reduce the mass of water by a greater extent compared to droplet mass. It is noted that the uses of stable nanoscale water droplets and bubbles are impractical given the present technologies [6, 7]. However, our analysis presents the usefulness of nanoscale water droplets and bubbles, which can attenuate solar radiation and minimize possible uncomfortable wet states in the future. The humidification and reduction of air temperature that result from mist cooling systems are significant for human comfort. However, as confirmed by the analysis presented herein, they can also provide considerable protection from radiation transfer to humans. The protective properties of water droplet curtains against intense irradiation caused by fires have been studied extensively to devise effective water mist usage schemes [8-14]. High-density water misting systems with relatively large droplets with diameters in the range of 20–200 μm have been considered. The principal effect was the attenuation (absorption and scattering) of the diffuse infrared irradiation caused by the water droplets. These studies simulated radiation from fires for which the irradiation source consisted mostly of radiation in the infrared spectral range. To investigate the effects of water droplets in meteorological phenomena, Maruyama et al. [15] investigated the propagation of collimated and diffuse solar irradiation, and incoming infrared irradiation from the sky and from the earth in a fog layer. Heavy fog systems with thicknesses equal to
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several hundred meters were the focus of their study with monodisperse water droplets with sizes in the range of 1–50 m. Dombrovsky et al. [16] studied the potential of water misting systems for spraying micrometer water droplets for protection from solar irradiation with particular emphasis on harmful ultraviolet (UV) radiation given its effects on human tissue and induced damage. In this study, a radiative transfer analysis was conducted to develop a mist cooling device that can block uncomfortable solar radiation without causing uncomfortable wetness states. The radiative properties of singlewater droplets and bubbles are calculated for a broad range of particle sizes and wavelengths. To model the radiative transfer in a water mist layer, a radiation analysis was conducted in a parallel plane model in one dimension. The effects of particle sizes on spectral reflectance and total solar reflectance are also discussed.
2. 2.1.
Materials and Methods Radiative properties of single-water particles The scattering and absorption of radiation by a single homogeneous spherical particle in a nonabsorbing
medium can be obtained by solving Maxwell’s equations. The radiative properties of a single spherical particle of diameter dp that interacts with an electromagnetic wave of wavelength are governed by two independent nondimensional parameters: complex refractive index of the particle m = n – ik and the size parameter x = πdp/λ, as described by the Mie scattering theory [17]. The spectral distribution of the real and imaginary parts of the complex index of the refraction of water (H2O) in the range of 0.3–2.5 μm is quoted from the literature [18] (Fig. 1). Using the spectral complex refractive index, the radiative properties of a single particle were calculated. According to the Mie theory, the radiative properties of the particle, such as the extinction efficiency factor Qext and scattering efficiency factor Qsca, can be calculated using the following equations [19].
Qsca
2 x2
(2k 1)( a
Qext
2 x2
(2k 1) Re a
k 1
n
2
bn ) , 2
k 1
n
bn ,
(1)
(2)
where an and bn are the Mie scattering coefficients. The medium is assumed to be air, which is nonabsorbing with a refractive index equal to 1.0; the particle size varies from 0.01 to 10 μm. The spectral radiative properties of a single water droplet are calculated as shown in Fig. 2. The properties of the water droplet are plotted as a function of wavelength and particle diameter. The absorption efficiency is high only at 2.0 and 2.5 μm in the NIR region, whereby the same peak of the imaginary part of the complex refractive index is evoked when the particle diameter is approximately 10 μm. In other wavelength and particle
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diameter regions, the absorption efficiency was almost zero. This means that a water droplet may not evaporate from the absorption of radiative heat and can serve as a cooling source when the heat of evaporation is the same as that of the mist cooling. The extinction and scattering efficiencies are high in the solar spectral region when the particle diameter is > 1.0 μm. This means that a particle greater than 1.0 μm has the potential to reflect NIR light. The radiative properties of stratified spheres (e.g., water bubbles) can be calculated as explained by Kerker [20] and Bohren et al. [21] based on the inclusion of the relative refractive indices of the core and coating to that of the external medium; in this study, the core was air and the coating was water. The ratio between the internal and external diameters was expressed as q = dp, in/dp, out, and the particle size varied from 0.01 to 10 μm. The spectral radiative properties of a single water bubble were calculated as shown in Fig. 3. The spectral tendencies of a water bubble are almost the same as those of a water droplet. This means that a water bubble can reflect solar irradiance in the same manner as the water droplet regardless of its smaller mass of water.
2.2.
Radiative properties of a particle cloud A large collection of particles must be considered in the radiative heat transfer process through the mist
layer. If the scattering is independent, then the effects of a large number of particles are simply expressed as their summation. For simplicity, it is often assumed that a particle cloud consists of spheres that are equally large. The fraction of energy scattered by all particles per unit length along the direction of the incoming beam is equal to the scattering cross-section summed over all particles. If np is the number of particles per unit volume, and if all particles have a uniform diameter dp, then the radiative properties of the particle cloud is expressed by [19] 2
2
dp dp Qsca n p , , mono Qext n p , 2 2
s , , mono
(3)
where σs and β are the scattering and extinction coefficients, respectively. Because the phase function in a cloud of uniform particles is the same for each particle, it is also the same for the particle cloud. In this case, the number of particles per unit volume np can be calculated from the total volume of particles per unit volume or from the volume fraction fv using the equation
np
2.3.
6 fv . d 3p
(4)
Radiative transfer analysis To calculate the radiative transfer in the mist layer, the mist layer is handled as a participating medium in a
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plane parallel system in one dimension, as shown in Fig. 4. The radiative transfer in this system can be expressed using the one-dimensional radiative transfer equation (RTE)
1 dI (r, s) I (r, s) dS 4
I (r, s) (s s)d , 4
(5)
where I (W m−2 sr−1) is the radiative intensity, r is a positional vector, s is a directional vector, S (m) denotes a path, and Ω (sr) represents a solid angle. In addition, ω is the single scattering albedo, and it is defined as ω = σs/β; it denotes the relative importance of scattering. To solve the RTE, the radiation element method by ray emission method (REM2) [22] is used. REM2 can be applied to anisotropic media with specular and/or diffuse surface boundaries at arbitrary thermal conditions. The mist layer is divided into N = 102 elements. In this calculation, the dispersed state is assumed to be monodispersed. In fact, the particles can form an agglomeration state, and the particle size distribution can change. This affects the spectral radiative properties of the particle cloud [23, 24]. However, the effect of agglomeration was neglected to simplify the calculation. Elements 1 and N are taken as boundary elements. The S12 approximation of Fiveland was used for the directional division [25]. A refractive index of unity was assumed for air for all elements, and the spectral solar irradiation was evaluated using the Bird’s model [26]. Collimated solar irradiation enters from element N+1 with an incident angle of 21.54°, which means that the air mass is equal to 1.075. Diffuse solar irradiation and the ambient emission enters from element 1. The temperature of each element is assumed to be ambient temperature and presupposed to be fixed at 303.15 K. The basement was considered to be an air layer without any water particles. The details of the calculation by REM2 are provided in the literature [22, 24, 27].
2.4.
Evaluation parameter The performance parameter of the mist layer for solar reflectance in the solar spectral region is
TSR
2.50
0.30
( ) I ( ) d
2.50
0.30
I ( ) d
,
(6)
where I(λ) is the solar irradiation and ρ(λ) is the spectral reflectance of the mist layer.
3. 3.1.
Results and Discussion Spectral reflectance The calculated spectral reflectance of mist layer is shown in Fig. 5 when the volume fraction is 0.20 and
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the thickness of mist layer is 3 m. The spectral reflectance values of the water droplet and bubble in the NIR region were low when the particle diameter was smaller than ~30 nm. The high-spectral reflectance region broadens as the particle diameter increases. When the particle diameter is 1.0 μm, the spectral reflectance is high in the solar spectral region. However, the NIR reflectance is lower in the case of a particle size of 10 μm compared to a particle size of 1.0 μm.
3.2.
Total solar reflectance To quantitatively evaluate the thermal barrier performance, the total solar reflectance was calculated. The
effect of the particle diameter on the total solar reflectance of the mist layer is shown in Fig. 6. The total solar reflectance increases throughout the entire mist layer as a function of increasing particle sizes until it reaches its maximum value. However, the optimum particle sizes are different for water droplets and bubbles. In the case of the water droplet, the optimum particle size is 0.97 µm. In the case of the water bubble, the optimum particle sizes are 1.02, 1.67, 1.77, and 3.13 µm, for q = 0.2, 0.4, 0.6, and 0.8, respectively. Regardless of the particle type, the total solar reflectance of the mist layer can be > 95% for dp values in the range of 0.4–10 µm. This means that undesirable thermal radiation can be reflected using optimized water particles. The effects of volume fraction and layer thickness on the total solar reflectance of the water bubble mist are shown in Fig. 7. The total solar reflectance increases as a function of increasing volume fractions and layer thicknesses dp in the range of 1–400 nm. Irrespective of how large or small volume fractions and layer thicknesses are, the total solar reflectance values of the mist layer were almost same for dp values in the range of 0.4–10 µm. In practice, the volume fraction and layer thickness of the mist layer change owing to the spray behavior and environmental convection effects. This means that a stable thermal barrier performance can be maintained when optimized water particles in the range of 0.4–10 µm are used.
4.
Conclusions In this study, a radiative transfer analysis was conducted to develop a mist cooling device that can block
uncomfortable solar radiation without causing uncomfortable wet states. The effects of the particle size on the spectral reflectance and total solar reflectance of the mist layer were discussed. The spectral radiative properties of a water droplet and a bubble were calculated. Their absorption efficiencies were almost zero in the solar spectrum. Therefore, a water droplet may not evaporate from the radiative heat and can serve as a cooling source when the heat of evaporation is the same as that for mist cooling.
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The extinction and scattering efficiencies of the microscale droplet and bubble are high in the solar spectral region, and they have the potential to reflect NIR light. The spectral reflectance of the mist layer was also calculated. In the cases of both the water droplet and the bubble, increased spectral reflectance regions broadened from the shorter wavelength region as the particle diameter increased. To quantitatively evaluate the thermal barrier performance, the total solar reflectance was also calculated from the calculated spectral reflectance. The total solar reflectance increased when the particle size increased until it reached its maximum value. It is shown that undesirable thermal radiation can be reflected with the use of optimized water particles. In the future, thermal analyses including heat conduction and convection must be conducted. In practical applications, the sizes of water droplets and bubbles may change from the injection to the attachment because of the water evaporation owing to the influx of heat from the surroundings. This may affect the optimum sizes of the water droplets and bubbles. However, we hope that our analyses will contribute to the development of more useful mist cooling devices.
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Role of the Funding Source This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI [grant numbers JP17844848], the Nohmura Foundation for Membrane Structure Technology, Futaba Foundation, and by the Fire and Disaster Management Agency.
Figure legends Fig. 1 Complex refractive index of water [18].
Fig. 2 Spectral radiative properties of a water droplet as a function of the particle diameter. (a) Absorption, (b) extinction, and (c) scattering efficiencies.
Fig. 3 Spectral radiative properties of a water bubble as a function of the particle diameter when q = 0.6. (a) Absorption, (b) extinction, and (c) scattering efficiencies.
Fig. 4 Analytical model of a cooling mist layer.
Fig. 5 Calculated spectral reflectance of the mist layer when fv = 0.2 and t = 3 m. (a) Water droplet, (b) water bubble with q = 0.6, (c) color map of calculated spectral reflectance for water droplet, and (d) color map of calculated spectral reflectance for the water bubble with q = 0.6.
Fig. 6 Effect of particle diameter on total solar reflectance of mist layer when fv = 0.2 and t = 3 m. (a) Overall and (b) magnified views.
Fig. 7 Effects of volume fraction and layer thickness on total solar reflectance of the water bubble mist layer with q = 0.6. (a) Overall and (b) magnified views.
References
[1] K. Zheng, M. Ichinose, N.H. Wong, Parametric study on the cooling effects from dry mists in a controlled environment, Building and Environment 141 (2018) 61-70. [2] N.H. Wong, A.Z.M. Chong, Performance evaluation of misting fans in hot and humid climate, Building and Environment 45(12) (2010) 2666-2678. [3] Y. Hou, Y. Tao, X. Huai, Z. Guo, Numerical characterization of multi-nozzle spray cooling, Applied Thermal Engineering 39 (2012) 163-170. [4] C. Huang, D. Ye, H. Zhao, T. Liang, Z. Lin, H. Yin, Y. Yang, The research and application of spray cooling technology in Shanghai Expo, Applied Thermal Engineering 31(17) (2011) 3726-3735. [5] C. Huang, J. Cai, Z. Lin, Q. Zhang, Y. Cui, Solving model of temperature and humidity profiles in spray cooling zone, Building and Environment 123 (2017) 189-199. [6] T. Makuta, R. Suzuki, T. Nakao, Generation of microbubbles from hollow cylindrical ultrasonic horn, Ultrasonics 53(1) (2013) 196-202. [7] T. Makuta, Y. Aizawa, R. Suzuki, Sonochemical reaction with microbubbles generated by hollow ultrasonic horn, Ultrasonics Sonochemistry 20(4) (2013) 997-1001. [8] S. Dembele, A. Delmas, J.F. Sacadura, A Method for Modeling the Mitigation of Hazardous Fire Thermal Radiation by Water Spray Curtains, Journal of Heat Transfer 119(4) (1997) 746-753.
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[9] S. Dembele, J.X. Wen, J.F. Sacadura, Experimental Study of Water Sprays for the Attenuation of Fire Thermal Radiation, Journal of Heat Transfer 123(3) (2000) 534-543. [10] A. Coppalle, D. Nedelka, B. Bauer, Fire protection: Water curtains, Fire Safety Journal 20(3) (1993) 241-255. [11] A. Dvorjetski, J.B. Greenberg, Theoretical analysis of polydisperse water spray extinction of opposed flow diffusion flames, Fire Safety Journal 39(4) (2004) 309-326. [12] N. Berour, D. Lacroix, P. Boulet, G. Jeandel, Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains, Journal of Quantitative Spectroscopy and Radiative Transfer 86(1) (2004) 9-30. [13] J.-M. Buchlin, Thermal shielding by water spray curtain, Journal of Loss Prevention in the Process Industries 18(4) (2005) 423-432. [14] C.C. Tseng, R. Viskanta, Absorptance and transmittance of water spray/mist curtains, Fire Safety Journal 42(2) (2007) 106-114. [15] S. Maruyama, Y. Mori, S. Sakai, Nongray radiative heat transfer analysis in the anisotropic scattering fog layer subjected to solar irradiation, Journal of Quantitative Spectroscopy and Radiative Transfer 83(3) (2004) 361-375. [16] L.A. Dombrovsky, V.P. Solovjov, B.W. Webb, Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range, Journal of Quantitative Spectroscopy and Radiative Transfer 112(7) (2011) 1182-1190. [17] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330(3) (1908) 377-445. [18] G.M. Hale, M.R. Querry, Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt. 12(3) (1973) 555-563. [19] M.F. Modest, Radiative heat transfer, Academic press2003. [20] M. Kerker, The Scattering of Light and Other Electromagnetic Radiation, Academic press, NewYork, 1969. [21] C.F. Bohren, D.R. Huffman, Absorption and scattering of light by small particles, A WileyInterscience Publication, U.S.A, 1983. [22] S. Maruyama, T. Aihara, Radiation Heat Transfer of Arbitrary Three--Dimensional Absorbing, Emitting and Scattering Media and Specular and Diffuse Surfaces, Journal of Heat Transfer 119(1) (1997) 129-136. [23] J.J. Reinosa, C.M.Á. Docio, V.Z. Ramírez, J.F.F. Lozano, Hierarchical nano ZnO-micro TiO2 composites: High UV protection yield lowering photodegradation in sunscreens, Ceramics International 44(3) (2018) 2827-2834. [24] M. Baneshi, H. Gonome, A. Komiya, S. Maruyama, The effect of particles size distribution on aesthetic and thermal performances of polydisperse TiO2 pigmented coatings: Comparison between numerical and experimental results, Journal of Quantitative Spectroscopy and Radiative Transfer 113(8) (2012) 594-606. [25] W. Fiveland, J. Jessee, Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries, Journal of Thermophysics and Heat transfer 9(1) (1995) 47-54. [26] R.E. Bird, C. Riordan, Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface for Cloudless Atmospheres, Journal of Climate and Applied Meteorology 25(1) (1986) 87-97. [1] K. Zheng, M. Ichinose, N.H. Wong, Parametric study on the cooling effects from dry mists in a controlled environment, Build. Environ. 141 (2018) 61–70. [2] N.H. Wong, A.Z.M. Chong, Performance evaluation of misting fans in hot and humid climate, Build. Environ. 45(12) (2010) 2666–2678. [3] Y. Hou, Y. Tao, X. Huai, Z. Guo, Numerical characterization of multi-nozzle spray cooling, Appl. Therm. Eng. 39 (2012) 163–170. [4] C. Huang, D. Ye, H. Zhao, T. Liang, Z. Lin, H. Yin, Y. Yang, The research and application of spray cooling technology in Shanghai Expo, Appl. Therm. Eng. 31(17) (2011) 3726–3735. [5] C. Huang, J. Cai, Z. Lin, Q. Zhang, Y. Cui, Solving model of temperature and humidity profiles in spray cooling zone, Build. Environ. 123 (2017) 189–199. [6] T. Makuta, R. Suzuki, T. Nakao, Generation of microbubbles from hollow cylindrical ultrasonic horn, Ultrason. 53(1) (2013) 196–202.
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[7] T. Makuta, Y. Aizawa, R. Suzuki, Sonochemical reaction with microbubbles generated by hollow ultrasonic horn, Ultrason. Sonochem. 20(4) (2013) 997–1001. [8] S. Dembele, A. Delmas, J.F. Sacadura, A Method for modeling the mitigation of hazardous fire thermal radiation by water spray curtains, J. Heat Transf. 119(4) (1997) 746–753. [9] S. Dembele, J.X. Wen, J.F. Sacadura, Experimental study of water sprays for the attenuation of fire thermal radiation, J. Heat Transf. 123(3) (2000) 534–543. [10] A. Coppalle, D. Nedelka, B. Bauer, Fire protection: Water curtains, Fire Safety J. 20(3) (1993) 241–255. [11] A. Dvorjetski, J.B. Greenberg, Theoretical analysis of polydisperse water spray extinction of opposed flow diffusion flames, Fire Saf. J. 39(4) (2004) 309–326. [12] N. Berour, D. Lacroix, P. Boulet, G. Jeandel, Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains, J. Quant. Spectroscopy Radiat. Transf. 86(1) (2004) 9–30. [13] J.-M. Buchlin, Thermal shielding by water spray curtain, J. Loss Prevention Process Ind. 18(4) (2005) 423– 432. [14] C.C. Tseng, R. Viskanta, Absorptance and transmittance of water spray/mist curtains, Fire Saf. J. 42(2) (2007) 106–114. [15] S. Maruyama, Y. Mori, S. Sakai, Nongray radiative heat transfer analysis in the anisotropic scattering fog layer subjected to solar irradiation, Journal of Quant. Spectroscopy Radiat. Transf. 83(3) (2004) 361–375. [16] L.A. Dombrovsky, V.P. Solovjov, B.W. Webb, Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range, J. Quant. Spectroscopy Radiat. Transf. 112(7) (2011) 1182–1190. [17] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330(3) (1908) 377–445. [18] G.M. Hale, M.R. Querry, Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt. 12(3) (1973) 555–563. [19] M.F. Modest, Radiative Heat Transfer, 3rd ed., Academic Press, New York, 2003. [20] M. Kerker, The Scattering of Light and Other Electromagnetic Radiation, Academic Press, NewYork, 1969. [21] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-Interscience, U.S.A, 1983. [22] S. Maruyama, T. Aihara, Radiation heat transfer of arbitrary three--dimensional absorbing, emitting and scattering media and specular and diffuse surfaces, J. Heat Transf. 119(1) (1997) 129–136. [23] J.J. Reinosa, C.M.Á. Docio, V.Z. Ramírez, J.F.F. Lozano, Hierarchical nano ZnO-micro TiO2 composites: High UV protection yield lowering photodegradation in sunscreens, Ceram. Int. 44(3) (2018) 2827–2834. [24] M. Baneshi, H. Gonome, A. Komiya, S. Maruyama, The effect of particles size distribution on aesthetic and thermal performances of polydisperse TiO2 pigmented coatings: Comparison between numerical and experimental results, J. Quant. Spectroscopy Radiat. Transf. 113(8) (2012) 594–606. [25] W. Fiveland, J. Jessee, Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries, J. Thermophys. Heat Transf. 9(1) (1995) 47–54. [26] R.E. Bird, C. Riordan, Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth's surface for cloudless atmospheres, J. Climate Appl. Meteorol. 25(1) (1986) 87–97. [27] M. Baneshi, S. Maruyama, H. Nakai, A. Komiya, A new approach to optimizing pigmented coatings considering both thermal and aesthetic effects, J. Quant. Spectroscopy Radiat. Transf. 110(3) (2009) 192–204.
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Highlights
A mist cooling device is developed to block uncomfortable solar radiation
Mist cooling without uncomfortable effects
Radiative transfer analyses were conducted in a mist layer with a plate model
The radiative properties of single-water droplets and bubbles are quantified
It is shown that unwanted thermal radiation can be reflected with water particles
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S1359-4311(19)35424-9 https://doi.org/10.1016/j.applthermaleng.2020.115083 ATE 115083
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
4 August 2019 12 February 2020 13 February 2020
Please cite this article as: H. Gonome, K. Wakabayashi, Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles, Applied Thermal Engineering (2020), doi: https:// doi.org/10.1016/j.applthermaleng.2020.115083
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier Ltd.
Solar barrier performance of water mist cooling: Applications using nano- and microsized droplets and bubbles
Hiroki Gonome*, Kohei Wakabayashi
Graduate School of Science and Engineering, Yamagata University, Yamagata, 992–8510, Japan
*Corresponding author. Tel.: +81–23–826–3103 E-mail address: [email protected]
1
Abstract Many areas on earth have hot climates because of the high temperatures during summer and strong solar radiation. Water mist cooling is useful as an environmentally friendly urban system that can provide relief in these high-temperature conditions. To improve the utilization of the water mist cooling system, radiative transfer analysis was conducted to develop a mist cooling device that can block the uncomfortable solar radiation without causing discomfort because of the use of nano- and microsized droplets and bubbles. Herein, the radiative properties of single-water droplets and bubbles are calculated from a broad range of particle sizes and wavelengths. The extinction and scattering efficiencies of microscale droplets and bubbles are high in the solar spectral region, and they have the potential to reflect near infrared light. To model the radiative transfer in a water mist layer, a radiation analysis was conducted in a parallel plane model in one-dimension. The effects of particle size on spectral reflectance and total solar reflectance were discussed. The total solar reflectance is shown to increase with increasing particle sizes until it reaches its maximum value. It is demonstrated that undesirable thermal radiation can be reflected with the use of optimized water particles.
Keywords: Radiative transfer; Particulate media; Mist cooling; Nanoparticle; Environmentally friendly urban system
2
1.
Introduction There are many areas on earth with hot climates where the summer air temperature and intense solar
irradiation make the physical presence in the outdoors unpleasant and even harmful. In particular, we refer to the existence of an urban heat island in urban or metropolitan areas if it is significantly warmer than its surrounding rural areas. To provide relief from the high-temperature environment, there exist a variety of devices that spray water droplets [1-5]. These devices reduce the air temperature based on the evaporation of water droplets, but they do not consider or account for the effects of uncomfortable solar radiation. The solar energy that reaches the surface of the earth in the range of 0.3 to 2.5 μm is divided into three parts (air mass = 1.5): a) the ultraviolet (UV) region (5%), b) visible (VIS) region (43%), and c) near infrared (NIR) region (52%). Additionally, these devices sometimes lead to uncomfortable wet states because water droplets deform facial make-up or wellcoiffed hair. Thus, if these uncomfortable wet states can be minimized or eliminated, the utility of the mist cooling device can be improved. This study conducts an analytical investigation to describe how nanoscale water droplets generated by misting systems can serve as an effective filter for solar radiation. Additionally, this study analyzes the radiative transfer in the mist layer formed by the nanoscale water bubbles. Nanoscale water droplets can reduce the volume of water and wetness unpleasantness, while bubbles can reduce the mass of water by a greater extent compared to droplet mass. It is noted that the uses of stable nanoscale water droplets and bubbles are impractical given the present technologies [6, 7]. However, our analysis presents the usefulness of nanoscale water droplets and bubbles, which can attenuate solar radiation and minimize possible uncomfortable wet states in the future. The humidification and reduction of air temperature that result from mist cooling systems are significant for human comfort. However, as confirmed by the analysis presented herein, they can also provide considerable protection from radiation transfer to humans. The protective properties of water droplet curtains against intense irradiation caused by fires have been studied extensively to devise effective water mist usage schemes [8-14]. High-density water misting systems with relatively large droplets with diameters in the range of 20–200 μm have been considered. The principal effect was the attenuation (absorption and scattering) of the diffuse infrared irradiation caused by the water droplets. These studies simulated radiation from fires for which the irradiation source consisted mostly of radiation in the infrared spectral range. To investigate the effects of water droplets in meteorological phenomena, Maruyama et al. [15] investigated the propagation of collimated and diffuse solar irradiation, and incoming infrared irradiation from the sky and from the earth in a fog layer. Heavy fog systems with thicknesses equal to
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several hundred meters were the focus of their study with monodisperse water droplets with sizes in the range of 1–50 m. Dombrovsky et al. [16] studied the potential of water misting systems for spraying micrometer water droplets for protection from solar irradiation with particular emphasis on harmful ultraviolet (UV) radiation given its effects on human tissue and induced damage. In this study, a radiative transfer analysis was conducted to develop a mist cooling device that can block uncomfortable solar radiation without causing uncomfortable wetness states. The radiative properties of singlewater droplets and bubbles are calculated for a broad range of particle sizes and wavelengths. To model the radiative transfer in a water mist layer, a radiation analysis was conducted in a parallel plane model in one dimension. The effects of particle sizes on spectral reflectance and total solar reflectance are also discussed.
2. 2.1.
Materials and Methods Radiative properties of single-water particles The scattering and absorption of radiation by a single homogeneous spherical particle in a nonabsorbing
medium can be obtained by solving Maxwell’s equations. The radiative properties of a single spherical particle of diameter dp that interacts with an electromagnetic wave of wavelength are governed by two independent nondimensional parameters: complex refractive index of the particle m = n – ik and the size parameter x = πdp/λ, as described by the Mie scattering theory [17]. The spectral distribution of the real and imaginary parts of the complex index of the refraction of water (H2O) in the range of 0.3–2.5 μm is quoted from the literature [18] (Fig. 1). Using the spectral complex refractive index, the radiative properties of a single particle were calculated. According to the Mie theory, the radiative properties of the particle, such as the extinction efficiency factor Qext and scattering efficiency factor Qsca, can be calculated using the following equations [19].
Qsca
2 x2
(2k 1)( a
Qext
2 x2
(2k 1) Re a
k 1
n
2
bn ) , 2
k 1
n
bn ,
(1)
(2)
where an and bn are the Mie scattering coefficients. The medium is assumed to be air, which is nonabsorbing with a refractive index equal to 1.0; the particle size varies from 0.01 to 10 μm. The spectral radiative properties of a single water droplet are calculated as shown in Fig. 2. The properties of the water droplet are plotted as a function of wavelength and particle diameter. The absorption efficiency is high only at 2.0 and 2.5 μm in the NIR region, whereby the same peak of the imaginary part of the complex refractive index is evoked when the particle diameter is approximately 10 μm. In other wavelength and particle
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diameter regions, the absorption efficiency was almost zero. This means that a water droplet may not evaporate from the absorption of radiative heat and can serve as a cooling source when the heat of evaporation is the same as that of the mist cooling. The extinction and scattering efficiencies are high in the solar spectral region when the particle diameter is > 1.0 μm. This means that a particle greater than 1.0 μm has the potential to reflect NIR light. The radiative properties of stratified spheres (e.g., water bubbles) can be calculated as explained by Kerker [20] and Bohren et al. [21] based on the inclusion of the relative refractive indices of the core and coating to that of the external medium; in this study, the core was air and the coating was water. The ratio between the internal and external diameters was expressed as q = dp, in/dp, out, and the particle size varied from 0.01 to 10 μm. The spectral radiative properties of a single water bubble were calculated as shown in Fig. 3. The spectral tendencies of a water bubble are almost the same as those of a water droplet. This means that a water bubble can reflect solar irradiance in the same manner as the water droplet regardless of its smaller mass of water.
2.2.
Radiative properties of a particle cloud A large collection of particles must be considered in the radiative heat transfer process through the mist
layer. If the scattering is independent, then the effects of a large number of particles are simply expressed as their summation. For simplicity, it is often assumed that a particle cloud consists of spheres that are equally large. The fraction of energy scattered by all particles per unit length along the direction of the incoming beam is equal to the scattering cross-section summed over all particles. If np is the number of particles per unit volume, and if all particles have a uniform diameter dp, then the radiative properties of the particle cloud is expressed by [19] 2
2
dp dp Qsca n p , , mono Qext n p , 2 2
s , , mono
(3)
where σs and β are the scattering and extinction coefficients, respectively. Because the phase function in a cloud of uniform particles is the same for each particle, it is also the same for the particle cloud. In this case, the number of particles per unit volume np can be calculated from the total volume of particles per unit volume or from the volume fraction fv using the equation
np
2.3.
6 fv . d 3p
(4)
Radiative transfer analysis To calculate the radiative transfer in the mist layer, the mist layer is handled as a participating medium in a
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plane parallel system in one dimension, as shown in Fig. 4. The radiative transfer in this system can be expressed using the one-dimensional radiative transfer equation (RTE)
1 dI (r, s) I (r, s) dS 4
I (r, s) (s s)d , 4
(5)
where I (W m−2 sr−1) is the radiative intensity, r is a positional vector, s is a directional vector, S (m) denotes a path, and Ω (sr) represents a solid angle. In addition, ω is the single scattering albedo, and it is defined as ω = σs/β; it denotes the relative importance of scattering. To solve the RTE, the radiation element method by ray emission method (REM2) [22] is used. REM2 can be applied to anisotropic media with specular and/or diffuse surface boundaries at arbitrary thermal conditions. The mist layer is divided into N = 102 elements. In this calculation, the dispersed state is assumed to be monodispersed. In fact, the particles can form an agglomeration state, and the particle size distribution can change. This affects the spectral radiative properties of the particle cloud [23, 24]. However, the effect of agglomeration was neglected to simplify the calculation. Elements 1 and N are taken as boundary elements. The S12 approximation of Fiveland was used for the directional division [25]. A refractive index of unity was assumed for air for all elements, and the spectral solar irradiation was evaluated using the Bird’s model [26]. Collimated solar irradiation enters from element N+1 with an incident angle of 21.54°, which means that the air mass is equal to 1.075. Diffuse solar irradiation and the ambient emission enters from element 1. The temperature of each element is assumed to be ambient temperature and presupposed to be fixed at 303.15 K. The basement was considered to be an air layer without any water particles. The details of the calculation by REM2 are provided in the literature [22, 24, 27].
2.4.
Evaluation parameter The performance parameter of the mist layer for solar reflectance in the solar spectral region is
TSR
2.50
0.30
( ) I ( ) d
2.50
0.30
I ( ) d
,
(6)
where I(λ) is the solar irradiation and ρ(λ) is the spectral reflectance of the mist layer.
3. 3.1.
Results and Discussion Spectral reflectance The calculated spectral reflectance of mist layer is shown in Fig. 5 when the volume fraction is 0.20 and
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the thickness of mist layer is 3 m. The spectral reflectance values of the water droplet and bubble in the NIR region were low when the particle diameter was smaller than ~30 nm. The high-spectral reflectance region broadens as the particle diameter increases. When the particle diameter is 1.0 μm, the spectral reflectance is high in the solar spectral region. However, the NIR reflectance is lower in the case of a particle size of 10 μm compared to a particle size of 1.0 μm.
3.2.
Total solar reflectance To quantitatively evaluate the thermal barrier performance, the total solar reflectance was calculated. The
effect of the particle diameter on the total solar reflectance of the mist layer is shown in Fig. 6. The total solar reflectance increases throughout the entire mist layer as a function of increasing particle sizes until it reaches its maximum value. However, the optimum particle sizes are different for water droplets and bubbles. In the case of the water droplet, the optimum particle size is 0.97 µm. In the case of the water bubble, the optimum particle sizes are 1.02, 1.67, 1.77, and 3.13 µm, for q = 0.2, 0.4, 0.6, and 0.8, respectively. Regardless of the particle type, the total solar reflectance of the mist layer can be > 95% for dp values in the range of 0.4–10 µm. This means that undesirable thermal radiation can be reflected using optimized water particles. The effects of volume fraction and layer thickness on the total solar reflectance of the water bubble mist are shown in Fig. 7. The total solar reflectance increases as a function of increasing volume fractions and layer thicknesses dp in the range of 1–400 nm. Irrespective of how large or small volume fractions and layer thicknesses are, the total solar reflectance values of the mist layer were almost same for dp values in the range of 0.4–10 µm. In practice, the volume fraction and layer thickness of the mist layer change owing to the spray behavior and environmental convection effects. This means that a stable thermal barrier performance can be maintained when optimized water particles in the range of 0.4–10 µm are used.
4.
Conclusions In this study, a radiative transfer analysis was conducted to develop a mist cooling device that can block
uncomfortable solar radiation without causing uncomfortable wet states. The effects of the particle size on the spectral reflectance and total solar reflectance of the mist layer were discussed. The spectral radiative properties of a water droplet and a bubble were calculated. Their absorption efficiencies were almost zero in the solar spectrum. Therefore, a water droplet may not evaporate from the radiative heat and can serve as a cooling source when the heat of evaporation is the same as that for mist cooling.
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The extinction and scattering efficiencies of the microscale droplet and bubble are high in the solar spectral region, and they have the potential to reflect NIR light. The spectral reflectance of the mist layer was also calculated. In the cases of both the water droplet and the bubble, increased spectral reflectance regions broadened from the shorter wavelength region as the particle diameter increased. To quantitatively evaluate the thermal barrier performance, the total solar reflectance was also calculated from the calculated spectral reflectance. The total solar reflectance increased when the particle size increased until it reached its maximum value. It is shown that undesirable thermal radiation can be reflected with the use of optimized water particles. In the future, thermal analyses including heat conduction and convection must be conducted. In practical applications, the sizes of water droplets and bubbles may change from the injection to the attachment because of the water evaporation owing to the influx of heat from the surroundings. This may affect the optimum sizes of the water droplets and bubbles. However, we hope that our analyses will contribute to the development of more useful mist cooling devices.
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Role of the Funding Source This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI [grant numbers JP17844848], the Nohmura Foundation for Membrane Structure Technology, Futaba Foundation, and by the Fire and Disaster Management Agency.
Figure legends Fig. 1 Complex refractive index of water [18].
Fig. 2 Spectral radiative properties of a water droplet as a function of the particle diameter. (a) Absorption, (b) extinction, and (c) scattering efficiencies.
Fig. 3 Spectral radiative properties of a water bubble as a function of the particle diameter when q = 0.6. (a) Absorption, (b) extinction, and (c) scattering efficiencies.
Fig. 4 Analytical model of a cooling mist layer.
Fig. 5 Calculated spectral reflectance of the mist layer when fv = 0.2 and t = 3 m. (a) Water droplet, (b) water bubble with q = 0.6, (c) color map of calculated spectral reflectance for water droplet, and (d) color map of calculated spectral reflectance for the water bubble with q = 0.6.
Fig. 6 Effect of particle diameter on total solar reflectance of mist layer when fv = 0.2 and t = 3 m. (a) Overall and (b) magnified views.
Fig. 7 Effects of volume fraction and layer thickness on total solar reflectance of the water bubble mist layer with q = 0.6. (a) Overall and (b) magnified views.
References
[1] K. Zheng, M. Ichinose, N.H. Wong, Parametric study on the cooling effects from dry mists in a controlled environment, Building and Environment 141 (2018) 61-70. [2] N.H. Wong, A.Z.M. Chong, Performance evaluation of misting fans in hot and humid climate, Building and Environment 45(12) (2010) 2666-2678. [3] Y. Hou, Y. Tao, X. Huai, Z. Guo, Numerical characterization of multi-nozzle spray cooling, Applied Thermal Engineering 39 (2012) 163-170. [4] C. Huang, D. Ye, H. Zhao, T. Liang, Z. Lin, H. Yin, Y. Yang, The research and application of spray cooling technology in Shanghai Expo, Applied Thermal Engineering 31(17) (2011) 3726-3735. [5] C. Huang, J. Cai, Z. Lin, Q. Zhang, Y. Cui, Solving model of temperature and humidity profiles in spray cooling zone, Building and Environment 123 (2017) 189-199. [6] T. Makuta, R. Suzuki, T. Nakao, Generation of microbubbles from hollow cylindrical ultrasonic horn, Ultrasonics 53(1) (2013) 196-202. [7] T. Makuta, Y. Aizawa, R. Suzuki, Sonochemical reaction with microbubbles generated by hollow ultrasonic horn, Ultrasonics Sonochemistry 20(4) (2013) 997-1001. [8] S. Dembele, A. Delmas, J.F. Sacadura, A Method for Modeling the Mitigation of Hazardous Fire Thermal Radiation by Water Spray Curtains, Journal of Heat Transfer 119(4) (1997) 746-753.
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[9] S. Dembele, J.X. Wen, J.F. Sacadura, Experimental Study of Water Sprays for the Attenuation of Fire Thermal Radiation, Journal of Heat Transfer 123(3) (2000) 534-543. [10] A. Coppalle, D. Nedelka, B. Bauer, Fire protection: Water curtains, Fire Safety Journal 20(3) (1993) 241-255. [11] A. Dvorjetski, J.B. Greenberg, Theoretical analysis of polydisperse water spray extinction of opposed flow diffusion flames, Fire Safety Journal 39(4) (2004) 309-326. [12] N. Berour, D. Lacroix, P. Boulet, G. Jeandel, Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains, Journal of Quantitative Spectroscopy and Radiative Transfer 86(1) (2004) 9-30. [13] J.-M. Buchlin, Thermal shielding by water spray curtain, Journal of Loss Prevention in the Process Industries 18(4) (2005) 423-432. [14] C.C. Tseng, R. Viskanta, Absorptance and transmittance of water spray/mist curtains, Fire Safety Journal 42(2) (2007) 106-114. [15] S. Maruyama, Y. Mori, S. Sakai, Nongray radiative heat transfer analysis in the anisotropic scattering fog layer subjected to solar irradiation, Journal of Quantitative Spectroscopy and Radiative Transfer 83(3) (2004) 361-375. [16] L.A. Dombrovsky, V.P. Solovjov, B.W. Webb, Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range, Journal of Quantitative Spectroscopy and Radiative Transfer 112(7) (2011) 1182-1190. [17] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330(3) (1908) 377-445. [18] G.M. Hale, M.R. Querry, Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt. 12(3) (1973) 555-563. [19] M.F. Modest, Radiative heat transfer, Academic press2003. [20] M. Kerker, The Scattering of Light and Other Electromagnetic Radiation, Academic press, NewYork, 1969. [21] C.F. Bohren, D.R. Huffman, Absorption and scattering of light by small particles, A WileyInterscience Publication, U.S.A, 1983. [22] S. Maruyama, T. Aihara, Radiation Heat Transfer of Arbitrary Three--Dimensional Absorbing, Emitting and Scattering Media and Specular and Diffuse Surfaces, Journal of Heat Transfer 119(1) (1997) 129-136. [23] J.J. Reinosa, C.M.Á. Docio, V.Z. Ramírez, J.F.F. Lozano, Hierarchical nano ZnO-micro TiO2 composites: High UV protection yield lowering photodegradation in sunscreens, Ceramics International 44(3) (2018) 2827-2834. [24] M. Baneshi, H. Gonome, A. Komiya, S. Maruyama, The effect of particles size distribution on aesthetic and thermal performances of polydisperse TiO2 pigmented coatings: Comparison between numerical and experimental results, Journal of Quantitative Spectroscopy and Radiative Transfer 113(8) (2012) 594-606. [25] W. Fiveland, J. Jessee, Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries, Journal of Thermophysics and Heat transfer 9(1) (1995) 47-54. [26] R.E. Bird, C. Riordan, Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface for Cloudless Atmospheres, Journal of Climate and Applied Meteorology 25(1) (1986) 87-97. [1] K. Zheng, M. Ichinose, N.H. Wong, Parametric study on the cooling effects from dry mists in a controlled environment, Build. Environ. 141 (2018) 61–70. [2] N.H. Wong, A.Z.M. Chong, Performance evaluation of misting fans in hot and humid climate, Build. Environ. 45(12) (2010) 2666–2678. [3] Y. Hou, Y. Tao, X. Huai, Z. Guo, Numerical characterization of multi-nozzle spray cooling, Appl. Therm. Eng. 39 (2012) 163–170. [4] C. Huang, D. Ye, H. Zhao, T. Liang, Z. Lin, H. Yin, Y. Yang, The research and application of spray cooling technology in Shanghai Expo, Appl. Therm. Eng. 31(17) (2011) 3726–3735. [5] C. Huang, J. Cai, Z. Lin, Q. Zhang, Y. Cui, Solving model of temperature and humidity profiles in spray cooling zone, Build. Environ. 123 (2017) 189–199. [6] T. Makuta, R. Suzuki, T. Nakao, Generation of microbubbles from hollow cylindrical ultrasonic horn, Ultrason. 53(1) (2013) 196–202.
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[7] T. Makuta, Y. Aizawa, R. Suzuki, Sonochemical reaction with microbubbles generated by hollow ultrasonic horn, Ultrason. Sonochem. 20(4) (2013) 997–1001. [8] S. Dembele, A. Delmas, J.F. Sacadura, A Method for modeling the mitigation of hazardous fire thermal radiation by water spray curtains, J. Heat Transf. 119(4) (1997) 746–753. [9] S. Dembele, J.X. Wen, J.F. Sacadura, Experimental study of water sprays for the attenuation of fire thermal radiation, J. Heat Transf. 123(3) (2000) 534–543. [10] A. Coppalle, D. Nedelka, B. Bauer, Fire protection: Water curtains, Fire Safety J. 20(3) (1993) 241–255. [11] A. Dvorjetski, J.B. Greenberg, Theoretical analysis of polydisperse water spray extinction of opposed flow diffusion flames, Fire Saf. J. 39(4) (2004) 309–326. [12] N. Berour, D. Lacroix, P. Boulet, G. Jeandel, Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains, J. Quant. Spectroscopy Radiat. Transf. 86(1) (2004) 9–30. [13] J.-M. Buchlin, Thermal shielding by water spray curtain, J. Loss Prevention Process Ind. 18(4) (2005) 423– 432. [14] C.C. Tseng, R. Viskanta, Absorptance and transmittance of water spray/mist curtains, Fire Saf. J. 42(2) (2007) 106–114. [15] S. Maruyama, Y. Mori, S. Sakai, Nongray radiative heat transfer analysis in the anisotropic scattering fog layer subjected to solar irradiation, Journal of Quant. Spectroscopy Radiat. Transf. 83(3) (2004) 361–375. [16] L.A. Dombrovsky, V.P. Solovjov, B.W. Webb, Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range, J. Quant. Spectroscopy Radiat. Transf. 112(7) (2011) 1182–1190. [17] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330(3) (1908) 377–445. [18] G.M. Hale, M.R. Querry, Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt. 12(3) (1973) 555–563. [19] M.F. Modest, Radiative Heat Transfer, 3rd ed., Academic Press, New York, 2003. [20] M. Kerker, The Scattering of Light and Other Electromagnetic Radiation, Academic Press, NewYork, 1969. [21] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-Interscience, U.S.A, 1983. [22] S. Maruyama, T. Aihara, Radiation heat transfer of arbitrary three--dimensional absorbing, emitting and scattering media and specular and diffuse surfaces, J. Heat Transf. 119(1) (1997) 129–136. [23] J.J. Reinosa, C.M.Á. Docio, V.Z. Ramírez, J.F.F. Lozano, Hierarchical nano ZnO-micro TiO2 composites: High UV protection yield lowering photodegradation in sunscreens, Ceram. Int. 44(3) (2018) 2827–2834. [24] M. Baneshi, H. Gonome, A. Komiya, S. Maruyama, The effect of particles size distribution on aesthetic and thermal performances of polydisperse TiO2 pigmented coatings: Comparison between numerical and experimental results, J. Quant. Spectroscopy Radiat. Transf. 113(8) (2012) 594–606. [25] W. Fiveland, J. Jessee, Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries, J. Thermophys. Heat Transf. 9(1) (1995) 47–54. [26] R.E. Bird, C. Riordan, Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth's surface for cloudless atmospheres, J. Climate Appl. Meteorol. 25(1) (1986) 87–97. [27] M. Baneshi, S. Maruyama, H. Nakai, A. Komiya, A new approach to optimizing pigmented coatings considering both thermal and aesthetic effects, J. Quant. Spectroscopy Radiat. Transf. 110(3) (2009) 192–204.
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Highlights
A mist cooling device is developed to block uncomfortable solar radiation
Mist cooling without uncomfortable effects
Radiative transfer analyses were conducted in a mist layer with a plate model
The radiative properties of single-water droplets and bubbles are quantified
It is shown that unwanted thermal radiation can be reflected with water particles
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