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# Infrared Radiative Properties of Thin Polyethylene Coating Pigmented With Titanium Dioxide Particles

[+] Author and Article Information
Mehdi Baneshi1

School of Engineering, Tohoku University, 6-6, Aoba, Aramaki-aza, Aoba-ku, Sendai 980-8579, Japanmehdi.baneshi@pixy.ifs.tohoku.ac.jp

Shigenao Maruyama, Atsuki Komiya

Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan

1

Corresponding author.

J. Heat Transfer 132(2), 023306 (Dec 04, 2009) (12 pages) doi:10.1115/1.4000235 History: Received November 21, 2008; Revised April 09, 2009; Published December 04, 2009; Online December 04, 2009

## Abstract

The infrared (IR) radiative properties of $TiO2$ pigment particles must be known to perform thermal analysis of a $TiO2$ pigmented coating. Resins generally used in making pigmented coatings are absorbing at IR wavelengths, which means that the conventional Mie solution (MS) may not be adequate in this domain. There are two approaches to evaluating radiative properties in an absorbing medium: far field approximation (FFA) and near field approximation (NFA). In this study, after reviewing these two approaches, we evaluated the radiative properties of $TiO2$ particles in polyethylene resin as an absorbing matrix in the wavelength range of $1.7–15 μm$ based on the MS, FFA, and NFA. We then calculated the effective scattering and absorption coefficients for different models. To investigate the effect of the particle size and volume concentration on the transmittance of IR wavelengths, we made a nongray radiative heat transfer in an anisotropic scattering monodisperse pigmented layer, with independent scattering using the radiation element method by the ray emission model. The results showed that all three approaches predicted similar results in the particle size domain and volume fraction range utilized in pigmented coatings.

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## Figures

Figure 1

Single scattering properties for a spherical bubble embedded in an absorbing medium with m=1.34−ik where k=0.0, 0.001, 0.01, and 0.05

Figure 2

Single scattering properties for a spherical particle (m′=1.4−0.05i) embedded in an absorbing medium with m=1.2−ik where k=0.0, 0.001, 0.01, and 0.05

Figure 3

Real (solid lines) and imaginary (dashed lines) parts of the complex index of refraction for TiO2 and polyethylene

Figure 4

Scattering, absorption, and extinction efficiencies, and asymmetry parameter as a function of the particle size for nonabsorbing TiO2 particles in polyethylene resin at different wavelengths

Figure 5

Scattering, absorption, and extinction efficiencies, and asymmetry parameter as a function of the particle size for absorbing TiO2 particles in polyethylene resin at different wavelengths

Figure 6

Analysis model of a pigmented coating using the REM2 with related boundary conditions

Figure 7

Effective scattering coefficient of TiO2 monodisperse particles in polyethylene predicted by FFA (solid lines) and the MS (symbols) when (a) dp=0.2 μm and fv=0.5%, 1.0%, 3%, and 5%, and (b) fv=5.0% and dp=0.02, 0.2, 2, and 5 μm

Figure 8

Effective absorption coefficient of TiO2 monodisperse particles in polyethylene predicted by the MS (symbols), NFA (dashed lines), and FFA (solid lines) when (a) dp=0.2 μm and fv=0.5%,1%, 3%, and 5%, and (b) fv=5.0% and dp=0.2, 2, 1, and 5 μm

Figure 9

Spectral hemispherical transmittance of TiO2 monodisperse particles in polyethylene predicted by model 1 (solid lines), model 2 (dashed lines), and model 3 (symbols) when (a) dp=0.2 μm and fv=0.5%, 1%, 3%, and 5%, and (b) fv=5.0% and dp=0.2, 1, 2, and 5 μm

Figure 10

Spectral hemispherical reflectance of TiO2 monodisperse particles in polyethylene predicted by model 1 (solid lines), model 2 (dashed lines), and model 3 (symbols) when (a) dp=1 μm and fv=0.5%, 1%, 3%, and 5%, and (b) fv=5.0% and dp=0.2, 1, 2, and 5 μm

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