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Research Papers: Radiative Heat Transfer

A Parametric Numerical Study of Optical Behavior of Thermotropic Materials for Solar Thermal Collectors

[+] Author and Article Information
Adam C. Gladen

Mem. ASME
Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: glad0092@umn.edu

Susan C. Mantell

Mem. ASME
Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: smantell@me.umn.edu

Jane H. Davidson

Fellow ASME
Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: jhd@me.umn.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 31, 2013; final manuscript received March 5, 2014; published online April 8, 2014. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 136(7), 072703 (Apr 08, 2014) (12 pages) Paper No: HT-13-1390; doi: 10.1115/1.4027153 History: Received July 31, 2013; Revised March 05, 2014

A Monte Carlo model is applied to determinate the steady state, solar-weighted optical properties of potential thermotropic composite materials for overheat protection of polymer solar absorbers. The key results are dimensionless plots of normal-hemispherical transmittance, reflectance and absorptance as a function of particle size parameter, scattering albedo, and overall optical thickness. The optical behavior of thermotropic materials at different temperatures is represented by a change in the relative refractive index which affects the scattering albedo and optical thickness. At low temperatures where overheat protection is not required, referred to as the clear state, the overall optical thickness should be less than 0.3 to ensure high transmittance for the preferred particle size parameter of 2. At higher temperatures where overheat protection is required, referred to as the translucent state, the overall optical thickness should be greater than 10 and the scattering albedo should be greater than 0.995 to achieve 50% reflectance. A case study of low molecular weighted polyethylene in poly(methyl methacrylate) is presented to illustrate use of the results to guide the design of thermotropic materials.

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Figures

Grahic Jump Location
Fig. 1

Schematic of radiation scattering by phase change thermotropic materials in the (a) clear state and (b) translucent state. Reflection is shown at an angle for clarity

Grahic Jump Location
Fig. 2

The modeling domain

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Fig. 3

Comparison of model predictions to benchmark solution for (a) transmittance and (b) reflectance. (1) Φ = F; ρ = 0.0; τL = 2; (2) Φ = F; ρ = 0.0; τL = 5; (3) Φ = F; ρ = 0.5; τL = 2; (4) Φ = F; ρ=0.5; τL = 5; (5) Φ = B; ρ = 0.0; τL = 2; (6) Φ = B; ρ = 0.0; τL = 5; (7) Φ = B; ρ = 0.5; τL = 2; (8) Φ = B; ρ = 0.5; τL = 5. ‘F’ denotes forward scattering phase function. ‘B’ denotes backward scattering phase function. ‘ρ’ is the reflectivity of the interface at an optical thickness of τL.

Grahic Jump Location
Fig. 4

Transmittance for m = 0.98, x = 2.5, λ = 550 nm, L = 3.5 mm, k = 10−6, and fv = 10% versus: (a) number of rays for a truncation value of 0.0001; (b) truncation value for 5x × 105 rays

Grahic Jump Location
Fig. 5

Normal-hemispherical (a) transmittance and (b) reflectance for x = 2 (g = 0.608 ± 0.01)

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Fig. 6

Normal-hemispherical (a) transmittance and (b) reflectance for x = 7 (g = 0.946 ± 0.003)

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Fig. 7

The calculated absorptive index for PMMA and the measured normal-hemispherical transmittance for a 5.9 mm thick sample

Grahic Jump Location
Fig. 8

Spectral, normal-hemispherical (a) transmittance and (b) reflectance in the clear and translucent states for low molecular weight PE in PMMA fv = 5%; L = 1 mm

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Fig. 9

Effects of thickness in the (a) clear and (b) translucent states for low molecular weight PE in PMMA for fv = 5%

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Fig. 10

Effects of volume fraction in the (a) clear and (b) translucent states for L = 1 mm

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Fig. 11

Normal-hemispherical (a) transmittance and (b) reflectance for x = 0.5 (g = 0.041 ± 0.001)

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Fig. 12

Normal-hemispherical (a) transmittance and (b) reflectance for x = 1.0 (g = 0.168 ± 0.003)

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Fig. 13

Normal-hemispherical (a) transmittance and (b) reflectance for x = 1.5 (g = 0.385 ± 0.008)

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Fig. 14

Normal-hemispherical (a) transmittance and (b) reflectance for x = 2.5 (g = 0.739 ± 0.01)

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Fig. 15

Normal-hemispherical (a) transmittance and (b) reflectance for x = 3.0 (g = 0.794 ± 0.005)

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Fig. 16

Normal-hemispherical (a) transmittance and (b) reflectance for x = 3.5 (g = 0.836 ± 0.005)

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Fig. 17

Normal-hemispherical (a) transmittance and (b) reflectance for x = 5.0 (g = 0.907 ± 0.001)

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Fig. 18

Normal-hemispherical (a) transmittance and (b) reflectance for x = 10.0 (g = 0.967 ± 0.003)

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Fig. 19

Normal-hemispherical (a) transmittance and (b) reflectance for x = 12.5 (g = 0.976 ± 0.004)

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Fig. 20

Normal-hemispherical (a) transmittance and (b) reflectance for x = 15.0 (g = 0.981 ± 0.005)

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