Guia A a Z para Thermodinâmicas, Transferência de calor e massa, e Engenharia de Fluidos
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Nature frequently uses cellular porous materials for functional purposes, such as bones, honeycombs, and foams (Banhart, 2001). Drawing inspiration from nature and this asset, the development of artificial cellular materials has greatly increased in the recent past. Such cellular materials are widely used today in many fields of technology. They are known to have many interesting combinations of physical, mechanical, and thermal properties. Their main characteristic is their very low density, inducing significant radiative transfer. There is a wide range of applications for these materials, such as use in shock absorbers, heat exchangers, filters, catalyst carriers, or insulating materials. Several textbooks cover the topic of cellular materials and give a general overview of their physical properties, including the standard book by Gibson and Ashby (1999). The book by Öchsner et al. (2008) covers one of physical characteristics (i.e., thermal properties). An overview on their radiative properties and possible applications can be found in the book by Dombrovsky and Baillis (2010) (see, also, the articles Open cell foam and Closed cell foam). Depending on the application domain, the solid matrix could be made of carbon, metal, ceramic, or polymer. Carbon, metal, and ceramic foams exhibit an open cell structure with porosities ranging from 0.8 to 0.95, whereas polymer cellular materials can either be open cell or closed cell with a porosity that could be even higher. Metal and ceramic open cell foams can be applied to advanced energy and combustion systems, such as low-NOx combustion burners. Solar thermal energy systems for fuel and chemical processing can be cited as other applications where ceramic foams are envisioned to exchange absorbed radiative energy. Note that nanotube-based carbon foams are used for hydrogen sorption. Carbon foam with or without matrices saturated with phase-change material (PCM) can be also used for thermal protection purposes. For applications requiring lightness and high insulating efficiencies at ambient temperatures, some polymer foams--such as polyurethane, extruded polystyrene, or expanded polystyrene--are essentially used. Many references dealing with all of these possible applications can be found in the book by Dombrovsky and Baillis (2010).

In the majority of these applications, due to the high temperature level and/or the very high porosity of the material, the total heat transfer is formed due to both conduction and thermal radiation. Over time, experience has indicated the existence of a correlation between the foam morphology and the foam thermal properties. There is a large body of theoretical publications concerning the effect of foam structure and porosity on the foam thermal properties. However, the models developed cannot exhaust the problem because of the diverse complex structure of different materials (see the article Classification of foam structures). The reader is referred to a specific radiative model applied to the open cell foam structure for carbon foams (Baillis et al., 1999), ceramic foams (Zeghondy et al., 2006; Petrasch et al., 2007), and metallic foams (Loretz et al., 2008a,b). Several studies (Glicksman et al., 1992; Kuhn et al., 1992; Coquard and Baillis, 2006; Coquard et al., 2009; Kaemmerlen et al., 2010) have modeled the radiative properties of closed cell foam, such as polystyrene and polyurethane. Other studies have been concerned with the determination of the foam radiative properties on the basis of the parameter identification method using directional-hemispherical or directional-directional transmittance and reflectance measurements. For instance, one can refer to the papers by Skocypec et al. (1991), Hale and Bohn (1993), and Hendricks and Howell (1996) on reticulated ceramics. Zhao et al. (2004) have reported the results of an experimental study of open cell metal foams characterized by high porosity at various cell sizes. Kuhn et al. (1992) and Baillis et al. (2002) identified the radiative properties of polystyrene and/or polyurethane foams. Both extinction and scattering coefficients were determined by assuming some variants of the scattering phase function: isotropic scattering, the Henyey-Greenstein scattering function, or a combination of different scattering functions.

The works on the coupled radiation and conduction heat transfer and in a large temperature range, from ambient to fire temperature, are a few. Coquard et al. (2010) report progress on the knowledge of heat transfer in open cell foams and give an overview of published works on the experimental or theoretical characterizations of radiative and conductive heat transfers from ambient to high temperatures in such materials. They proposed a prediction model of the conductive and radiative contributions to heat transfer at fire temperatures. This analytical model is based on numerical simulations applied to open cell foams and takes into account the structure of the foam and the optical and thermal properties of the constituents. In addition, they proposed an innovative experimental technique of characterization of heat transfer in foams at high temperatures, which allows independently evaluating the radiative and conductive contributions from a unique and simple measurement.

Note that the predictive models are important in order to optimize the foam structure for better thermal performance. The predictive models require a knowledge and modeling of the foam structure. The foam structure varies significantly depending on whether it is an open cell or closed cell foam (see the article classification of foam structures). The article open cell foams focuses on the radiative properties modeling of open cell carbon, metallic, or ceramic foams and the article closed cell foams focuses on the radiative properties of closed cell polystyrene or polyurethane foams.

REFERENCES

Baillis, D., Raynaud, M., and Sacadura, J.-F., Spectral radiative properties of open-cell foam insulation, J. Thermophys. Heat Transfer, vol. 13, no. 3, pp. 292-298, 1999.

Baillis, D., Arduini-Schuster, M., and Sacadura, J.-F., Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements, J. Quant. Spectrosc. Radiat. Transf., vol. 73, no. 2-5, pp. 297-306, 2002.

Banhart, J., Manufacture, characterisation and application of cellular metals and metal foams, Prog. Mater. Sci., vol. 46, no. 6, pp. 559-632, 2001.

Coquard, R. and Baillis, D., Modeling of heat transfer in low-density EPS foams, ASME J. Heat Transfer, vol. 128, no. 6, pp. 538-549, 2006.

Coquard, R., Baillis, D., and Quenard, D., Radiative properties of expanded polystyrene foams, ASME J. Heat Transfer, vol. 131, no. 1, pp. 012702.1-012702.10, 2009.

Coquard, R., Rochais, D., and Baillis, D., Conductive and radiative heat transfer in ceramic and metal foams at fire temperatures, Fire Technol., DOI: 10.1007/s10694-010-0167-8, 2010.

Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Redding, CT: Begell House, 2010.

Gibson, L. J. and Ashby, M. F., Cellular Solids: Structure and Properties, 2nd ed., Cambridge, UK: Cambridge University Press, 1999.

Glicksman, L. R., Marge, A. L., and Moreno, J. D., Radiation heat transfer in cellular foam insulation, ASME HTD, vol. 203, pp. 45-54, 1992.

Hale, M. J. and Bohn, M. S., Measurements of the radiative transport properties of reticulated alumina foams, Proc. of. ASME/ASES Joint Solar Energy Conference, Washington, DC, April 4-9, pp. 507-515, 1993.

Hendricks, T. J. and Howell, J. R., Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics, ASME J. Heat Transfer, vol. 118, no. 1, pp. 79-87, 1996.

Kaemmerlen, A., Vo, C., Jeandel, G., and Baillis, D., Radiative properties of extruded polystyrene foams: Predictive models and experimental results, J. Quant. Spectrosc. Radiat. Transf., vol. 111, no. 6, pp. 865-877, 2010.

Kuhn, J., Ebert, H. P., Arduini-Schuster, M. C., Büttner, D., and Fricke, J., Thermal transport in polystyrene and polyurethane foam insulations, Int. J. Heat Mass Transfer, vol. 35, no. 7, pp. 1795-1801, 1992.

Loretz, M., Coquard, R., Baillis, D., and Maire E., Metallic foams: Radiative properties/comparison between different models, J. Quant. Spectrosc. Radiat. Transf., vol. 109, no. 1, pp. 16-27, 2008a.

Loretz, M., Maire, E., and Baillis, D., Analytical modelling of the radiative properties of metallic foams: contribution of X-ray tomography, Adv. Eng. Mater., vol. 10, no. 4, pp. 352-360, 2008b.

Öchsner, A., Murch, G. E., and de Lemos, M. J. S., Cellular and Porous Materials: Thermal Properties Simulation and Prediction, Wiley, Weinheim, 2008.

Petrasch, J., Wyss, P., and Steinfeld, A., Tomography-based Monte Carlo determination of radiative properties of reticulate porous ceramics, J. Quant. Spectrosc. Radiat. Transf., vol. 105, no. 2, pp. 180-197, 2007.

Skocypec, R. D., Hogan, R. E., Jr., and Muir, J. F., Solar reforming of methane in a direct absorption catalytic reactor on a parabolic dish: II--Modeling and analysis, Proc. of ASME-ISME 2nd International Solar Energy Conference, New York: ASME Solar Energy Division, pp. 303-310, 1991.

Zeghondy, B., Iacona, E., and Taine, J., Determination of the anisotropic radiative properties of a porous material by radiative distribution function identification (RDFI), Int. J. Heat Mass Transfer, vol. 49, no. 17-18, pp. 2810-2819, 2006.

Zhao, C. Y., Lu, T. J., and Hodson, H. P., Thermal radiation in ultralight metal foams with open cells, Int. J. Heat Mass Transfer, vol. 47, no. 14-16, pp. 2927-2939, 2004.

References

  1. Baillis, D., Raynaud, M., and Sacadura, J.-F., Spectral radiative properties of open-cell foam insulation, J. Thermophys. Heat Transfer, vol. 13, no. 3, pp. 292-298, 1999.
  2. Baillis, D., Arduini-Schuster, M., and Sacadura, J.-F., Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements, J. Quant. Spectrosc. Radiat. Transf., vol. 73, no. 2-5, pp. 297-306, 2002.
  3. Banhart, J., Manufacture, characterisation and application of cellular metals and metal foams, Prog. Mater. Sci., vol. 46, no. 6, pp. 559-632, 2001.
  4. Coquard, R. and Baillis, D., Modeling of heat transfer in low-density EPS foams, ASME J. Heat Transfer, vol. 128, no. 6, pp. 538-549, 2006.
  5. Coquard, R., Baillis, D., and Quenard, D., Radiative properties of expanded polystyrene foams, ASME J. Heat Transfer, vol. 131, no. 1, pp. 012702.1-012702.10, 2009.
  6. Coquard, R., Rochais, D., and Baillis, D., Conductive and radiative heat transfer in ceramic and metal foams at fire temperatures, Fire Technol., DOI: 10.1007/s10694-010-0167-8, 2010.
  7. Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Redding, CT: Begell House, 2010.
  8. Gibson, L. J. and Ashby, M. F., Cellular Solids: Structure and Properties, 2nd ed., Cambridge, UK: Cambridge University Press, 1999.
  9. Glicksman, L. R., Marge, A. L., and Moreno, J. D., Radiation heat transfer in cellular foam insulation, ASME HTD, vol. 203, pp. 45-54, 1992.
  10. Hale, M. J. and Bohn, M. S., Measurements of the radiative transport properties of reticulated alumina foams, Proc. of. ASME/ASES Joint Solar Energy Conference, Washington, DC, April 4-9, pp. 507-515, 1993.
  11. Hendricks, T. J. and Howell, J. R., Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics, ASME J. Heat Transfer, vol. 118, no. 1, pp. 79-87, 1996.
  12. Kaemmerlen, A., Vo, C., Jeandel, G., and Baillis, D., Radiative properties of extruded polystyrene foams: Predictive models and experimental results, J. Quant. Spectrosc. Radiat. Transf., vol. 111, no. 6, pp. 865-877, 2010.
  13. Kuhn, J., Ebert, H. P., Arduini-Schuster, M. C., Büttner, D., and Fricke, J., Thermal transport in polystyrene and polyurethane foam insulations, Int. J. Heat Mass Transfer, vol. 35, no. 7, pp. 1795-1801, 1992.
  14. Loretz, M., Coquard, R., Baillis, D., and Maire E., Metallic foams: Radiative properties/comparison between different models, J. Quant. Spectrosc. Radiat. Transf., vol. 109, no. 1, pp. 16-27, 2008a.
  15. Loretz, M., Maire, E., and Baillis, D., Analytical modelling of the radiative properties of metallic foams: contribution of X-ray tomography, Adv. Eng. Mater., vol. 10, no. 4, pp. 352-360, 2008b.
  16. Öchsner, A., Murch, G. E., and de Lemos, M. J. S., Cellular and Porous Materials: Thermal Properties Simulation and Prediction, Wiley, Weinheim, 2008.
  17. Petrasch, J., Wyss, P., and Steinfeld, A., Tomography-based Monte Carlo determination of radiative properties of reticulate porous ceramics, J. Quant. Spectrosc. Radiat. Transf., vol. 105, no. 2, pp. 180-197, 2007.
  18. Skocypec, R. D., Hogan, R. E., Jr., and Muir, J. F., Solar reforming of methane in a direct absorption catalytic reactor on a parabolic dish: II--Modeling and analysis, Proc. of ASME-ISME 2nd International Solar Energy Conference, New York: ASME Solar Energy Division, pp. 303-310, 1991.
  19. Zeghondy, B., Iacona, E., and Taine, J., Determination of the anisotropic radiative properties of a porous material by radiative distribution function identification (RDFI), Int. J. Heat Mass Transfer, vol. 49, no. 17-18, pp. 2810-2819, 2006.
  20. Zhao, C. Y., Lu, T. J., and Hodson, H. P., Thermal radiation in ultralight metal foams with open cells, Int. J. Heat Mass Transfer, vol. 47, no. 14-16, pp. 2927-2939, 2004.
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