0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Raps, D. , Hossieny, N. , Park, C. B. , and Altstädt, V. , 2015, “Past and Present Developments in Polymer Bead Foams and Bead Foaming Technology,” Polymer, 56, pp. 5–19. [CrossRef]
Vo, C. V. , and Paquet, A. N. , 2004, “An Evaluation of the Thermal Conductivity of Extruded Polystyrene Foam Blown With HFC-134a or HCFC-142b,” J. Cellular Plast., 40(3), pp. 205–228. [CrossRef]
Papadopoulos, A. , 2005, “State of the Art in Thermal Insulation Materials and Aims for Future Developments,” Energy Build., 37(1), pp. 77–86. [CrossRef]
Kono, J. , Goto, Y. , Ostermeyer, Y. , Frischknecht, R. , and Wallbaum, H. , 2016, “Factors for Eco-Efficiency Improvement of Thermal Insulation Materials,” Key Eng. Mater., 678, pp. 1–13. [CrossRef]
Council, E. , 2010, “Directive 2010/31/EU of the European Parliament and of the Council of 19 May, 2010 on the Energy Performance of Buildings,” Official J. Eur. Union, 53(L153), pp. 13–35.
Global Market Insights, Inc., 2017, “Polystyrene (PS) & Expanded Polystyrene (EPS) Market Size By Product (Polystyrene, Expanded Polystyrene), By Application (Building & Construction, Electrical & Electronics, Packaging), Industry Analysis Report, Regional Outlook (U.S., Canada, Germany, UK, France, Spain, Italy, China, India, Japan, Australia, Indonesia, Malaysia, Brazil, Mexico, South Africa, GCC), Growth Potential, Price Trends, Competitive Market Share & Forecast, 2017–2024,” Technical Report No. GMI2063. https://www.gminsights.com/industry-analysis/polystyrene-ps-and-expanded-polystyrene-eps-market
Jelle, B. P. , 2011, “Traditional, State-of-the-Art and Future Thermal Building Insulation Materials and Solutions—Properties, Requirements and Possibilities,” Energy Build., 43(10), pp. 2549–2563. [CrossRef]
Schuetz, M. , and Glicksman, L. , 1984, “A Basic Study of Heat Transfer Through Foam Insulation,” J. Cellular Plast., 20(2), pp. 114–121. [CrossRef]
Kuhn, J. , Ebert, H.-P. , Arduini-Schuster, M. , Büttner, D. , and Fricke, J. , 1992, “Thermal Transport in Polystyrene and Polyurethane Foam Insulations,” Int. J. Heat Mass Transfer, 35(7), pp. 1795–1801. [CrossRef]
Almanza, O. A. , Rodriguez-Perez, M. A. , and De Saja, J. A. , 2000, “Prediction of the Radiation Term in the Thermal Conductivity of Crosslinked Closed Cell Polyolefin Foams,” J. Polym. Sci., Part B, 38(7), pp. 993–1004. [CrossRef]
Coquard, R. , and Baillis, D. , 2006, “Modeling of Heat Transfer in Low-Density EPS Foams,” ASME J. Heat Transfer, 128(6), p. 538. [CrossRef]
Glicksman, L. , Schuetz, M. , and Sinofsky, M. , 1987, “Radiation Heat Transfer in Foam Insulation,” Int. J. Heat Mass Transfer, 30(1), pp. 187–197. [CrossRef]
Placido, E. , Arduini-Schuster, M. , and Kuhn, J. , 2005, “Thermal Properties Predictive Model for Insulating Foams,” Infrared Phys. Technol., 46(3), pp. 219–231. [CrossRef]
Coquard, R. , Baillis, D. , and Quenard, D. , 2009, “Radiative Properties of Expanded Polystyrene Foams,” ASME J. Heat Transfer, 131(1), p. 012702. [CrossRef]
Coquard, R. , Baillis, D. , and Maire, E. , 2010, “Numerical Investigation of the Radiative Properties of Polymeric Foams From Tomographic Images,” J. Thermophys. Heat Transfer, 24(3), pp. 647–658. [CrossRef]
Kaemmerlen, A. , Vo, C. , Asllanaj, F. , Jeandel, G. , and Baillis, D. , 2010, “Radiative Properties of Extruded Polystyrene Foams: Predictive Model and Experimental Results,” J. Quant. Spectrosc. Radiat. Transfer, 111(6), pp. 865–877. [CrossRef]
Schellenberg, J. , and Wallis, M. , 2010, “Dependence of Thermal Properties of Expandable Polystyrene Particle Foam on Cell Size and Density,” J. Cellular Plast., 46(3), pp. 209–222. [CrossRef]
Coquard, R. , Baillis, D. , and Randrianalisoa, J. , 2011, “Homogeneous Phase and Multi-Phase Approaches for Modeling Radiative Transfer in Foams,” Int. J. Therm. Sci., 50(9), pp. 1648–1663. [CrossRef]
Glicksman, L. R. , and Torpey, M. , 1989, “Factors Governing Heat Transfer Through Closed Cell Foam Insulation,” J. Build. Phys., 12(4), pp. 257–269.
Stovall, T. K. , 2012, “Closed Cell Foam Insulation: A Review of Long Term Thermal Performance Research,” Oak Ridge National Laboratory (ORNL), and Building Technologies Research and Integration Center, Oak Ridge, TN, Report No. ORNL/TM-2012/583. https://www.osti.gov/biblio/1093061
McIntire, O. , and Kennedy, R. , 1948, “Styrofoam for Low-Temperature Insulation,” Chem. Eng. Prog., 44(9), pp. 727–730.
Pisipati, J. S. , Ball, E. E. , Galligan, P. L. , and Gluck, D. G. , 1996, “Carbon Black in Appliance Foam Insulation,” J. Cell. Plast., 32(1), pp. 62–81. [CrossRef]
Vo, C. V. , Bunge, F. , Duffy, J. , and Hood, L. , 2011, “Advances in Thermal Insulation of Extruded Polystyrene Foams,” Cell. Polym., 30(3), p. 137. http://www.polymerjournals.com/pdfdownload/1081744.pdf
Arduini-Schuster, M. , Manara, J. , and Vo, C. , 2015, “Experimental Characterization and Theoretical Modeling of the Infrared-Optical Properties and the Thermal Conductivity of Foams,” Int. J. Therm. Sci., 98, pp. 156–164. [CrossRef]
Baillis, D. D. , Coquard, R. , Randrianalisoa, J. , Dombrovsky, L. A. , and Viskanta, R. , 2013, “Thermal Radiation Properties of Highly Porous Cellular Foams,” Spec. Top. Rev. Porous Media, 4(2), pp. 111–136. [CrossRef]
Ahern, A. , Verbist, G. , Weaire, D. , Phelan, R. , and Fleurent, H. , 2005, “The Conductivity of Foams: A Generalisation of the Electrical to the Thermal Case,” Colloids Surf. A, 263(1–3), pp. 275–279. [CrossRef]
Progelhof, R. C. , Throne, J. L. , and Ruetsch, R. R. , 1976, “Methods for Predicting the Thermal Conductivity of Composite Systems: A Review,” Polym. Eng. Sci., 16(9), pp. 615–625. [CrossRef]
Modest, M. F. , 2001, Radiative Heat Transfer, 2nd ed., Academic Press, New York.
Macleod, H. A. , 2001, Thin-Film Optical Filters, 3rd ed., Institute of Physics Publishing, Bristol, UK.
Heller, W. , 1965, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem., 69(4), pp. 1123–1129. [CrossRef]
Chýlek, P. , Ramaswamy, V. , and Srivastava, V. , 1983, “Albedo of Soot-Contaminated Snow,” J. Geophys. Res., 88(C15), p. 10837. [CrossRef]
Fuller, K. A. , Malm, W. C. , and Kreidenweis, S. M. , 1999, “Effects of Mixing on Extinction by Carbonaceous Particles,” J. Geophys. Res., 104(D13), pp. 15941–15954. [CrossRef]
Kolokolova, L. , and Gustafsonm, B. Å. , 2001, “Scattering by Inhomogeneous Particles: Microwave Analog Experiments and Comparison to Effective Medium Theories,” J. Quant. Spectrosc. Radiat. Transfer, 70(4–6), pp. 611–625. [CrossRef]
Sihvola, A. , 2000, “Mixing Rules With Complex Dielectric Coefficients,” Subsurf. Sens. Technol. Appl., 1(4), pp. 393–415. [CrossRef]
Mishchenko, M. I. , Travis, L. D. , and Mackowski, D. W. , 1996, “T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review,” J. Quant. Spectrosc. Radiat. Transfer, 55(5), pp. 535–575. [CrossRef]
Somerville, W. , Auguié, B. , and Le Ru, E. , 2016, “SMARTIES: User-Friendly Codes for Fast and Accurate Calculations of Light Scattering by Spheroids,” J. Quant. Spectrosc. Radiat. Transfer, 174, pp. 39–55. [CrossRef]
Brunke, O. , Neuser, E. , and Suppes, A. , 2011, “High Resolution Industrial CT Systems: Advances and Comparison With Synchrotron-Based CT,” International Symposium on Digital Industrial Radiology and Computed Tomography - Tu.3.2, Berlin, Germany, June 20--21, pp. 1–9.
GE Sensing and Inspection Technologies GmbH, 2013, “Operating Manual: X-ray Inspection System nanotom m,” GE Sensing and Inspection Technologies GmBH, Wunstorf, Germany.
Measurement and Control GE, 2015, “Phoenix Datos|x CT Software,” GE Measurement and Control, Wunstorf, Germany.
Stock, S. R. , 2009, Microcomputed Tomography: Methodology and Applications, CRC Press, Boca Raton, FL.
Petrasch, J. , Wyss, P. , Stämpfli, R. , and Steinfeld, A. , 2008, “Tomography-Based Multiscale Analyses of the 3D Geometrical Morphology of Reticulated Porous Ceramics,” J. Am. Ceram. Soc., 91(8), pp. 2659–2665. [CrossRef]
Gonzalez, R. C. , and Woods, R. E. , 2002, Digital Image Processing, 2nd ed., Prentice Hall, Upper Saddle River, NJ.
Torquato, S. , 2002, “Random Heterogeneous Materials: Microstructure and Macroscopic Properties,” Interdisciplinary Applied Mathematics, Vol. 16, Springer, New York.
Petrasch, J. , 2009, Tomography-Based Methods for Reactive Flows in Porous Media, VDM Verlag, Saarbruecken, Germany.
Querry, M. R. , Eversman, W. , and Koval, L. R. , 1985, “Optical Constants,” U.S. Army Armament, Munitions and Chemical Command, Aberdeen Proving Ground, MD, Report No. CRDC-CR-85034.
Keyence Deutschland, GmBH , 2017, “Digitalmikroskop Modellreihe VHX-6000,” Neu-Isenburg, Germany.
Haeri, M. , and Haeri, M. , 2015, “ImageJ Plugin for Analysis of Porous Scaffolds Used in Tissue Engineering,” J. Open Res. Software, 3(1), pp. 1–4. [CrossRef]
Taurus Instruments GmBH, 2010, “Thermal Conductivity Measuring Instrument TCA 300 DT,” Weimar/Thüringen, Germany.

Figures

Grahic Jump Location
Fig. 1

Oblate spheroidal geometry used to model graphite opacifier particles

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 11

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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In