Research Papers: Heat and Mass Transfer

Modeling the Effect of Infrared Opacifiers on Coupled Conduction-Radiation Heat Transfer in Expanded Polystyrene

[+] Author and Article Information
A. Akolkar

illwerke vkw Professorship for Energy Efficiency,
Vorarlberg University of Applied Sciences,
Hochschulstrasse 1,
Dornbirn 6850, Austria;
Unit for Material Technology,
University of Innsbruck,
Technikerstraße 13,
Innsbruck 6020, Austria
e-mail: anupam.akolkar@fhv.at

N. Rahmatian, J. Petrasch

illwerke vkw Professorship for Energy Efficiency,
Vorarlberg University of Applied Sciences,
Hochschulstrasse 1,
Dornbirn 6850, Austria

S. Unterberger

Unit for Material Technology,
University of Innsbruck,
Christian Doppler Laboratory for Cement
and Concrete Technology,
Technikerstraße 13,
Innsbruck 6020, Austria

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 13, 2018; final manuscript received June 27, 2018; published online August 20, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(11), 112005 (Aug 20, 2018) (10 pages) Paper No: HT-18-1222; doi: 10.1115/1.4040784 History: Received April 13, 2018; Revised June 27, 2018

Heat transfer properties of two expanded polystyrene (EPS) samples of similar density, one without (white) and one with graphite opacifier particles (gray), are compared. Tomographic scans are used to obtain cell sizes of the foams. Using established models for closed-cell polymer foams, the extinction coefficient and the effective thermal conductivity are obtained. The effect of opacifiers is modeled using (1) an effective refractive index for the polystyrene walls within a cell model for the EPS and (2) a superposition of extinction due to a particle cloud upon extinction predicted by the cell model, where particles are modeled as oblate spheroids, or equivalent volume, surface, or hydraulic diameter spheres. Modeled effective conductivities are compared with measurements done on a guarded hot-plate apparatus at sample mean temperatures in the range from 0 °C to 40 °C. Typically, cells of the gray EPS are about 40% larger than those of the white EPS and the cell walls in the gray EPS are thicker. The refractive index mixing model and the model with graphite opacifier particles as oblate spheroids overpredict extinction, however, the mean error in the effective conductivity predicted by the oblate spheroids model is only 2.7%. Equivalent volume/surface sphere models underpredict extinction, but still yield a low mean error in effective conductivity of around 4%. While the oblate spheroids model has a lower mean error, the computationally less expensive equivalent volume or equivalent surface models can also be recommended to model the inclusions.

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Fig. 1

Oblate spheroidal geometry used to model graphite opacifier particles

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Fig. 2

Sample raster images from tomographic scans for specimens of the (a) white EPS and (b) gray EPS

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Fig. 3

Chord length distribution results for (a) white EPS sample and (b) gray EPS sample. Notice how the mean as well as median chord lengths for the gray EPS sample is larger than those for the white EPS sample.

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Fig. 4

Comparative thermogravimetry to determine the percentage by mass of graphite in the gray EPS sample

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Fig. 5

(a) Sample micrograph of a cell wall in gray EPS at 1000× magnification, (b) segmented image showing particles, and (c) particle radius distribution and fitted log-normal distribution wr

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Fig. 6

Real (n′) and imaginary (n″) parts of the refractive index of polystyrene (PS) and graphite (c) in the wavelength range 2–50 μm

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Fig. 7

Cell diameter distributions chosen for the models of white and gray EPS samples

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Fig. 8

(a) Transport extinction coefficients modeled for white and gray EPS samples using the mixed refractive index method and (b) change in transport extinction coefficients for increasing opacifier content in foam

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Fig. 9

(a) Transport extinction coefficients modeled for the gray EPS sample by superposing extinction by cells with extinction by oblate spheroidal graphite particles and (b) change in transport extinction coefficients for increasing proportion of graphite particles in polymer matrix of foam cells

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Fig. 10

Comparison of transport extinction coefficients obtained by equivalent sphere models for graphite particles with the oblate spheroidal model values for the gray EPS with 5% by mass carbon in the polystyrene matrix

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Fig. 11

Total conductivity model value prediction for white and gray samples compared with measurement data in the 0–40 °C temperature range



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