A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering
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Porous media such as cellular or fibrous materials present performance in combination with physical, mechanical, and thermal properties. They are very interesting materials for use in aerospace, automotive, marine, and building applications. There is a wide range of applications for these materials, such as in shock absorbers, heat exchangers, filters, catalyst carriers, or insulating materials. Only building thermal insulation is a main scope of the application. Indeed, in Europe the building sector is the most important primary energy consumer since it represents 40% of the total energy, ahead of the energy used in transport and industry, and it represents about 20% of greenhouse gas emissions. The use of heat insulation material is, therefore, very important in order to lower the heating and air-conditioning requirements in buildings.

Porous media are usually semi-transparent materials that absorb, emit, and scatter radiation. The most common assumption made to solve the radiative transfer problem in such complex materials involves treating the disperse medium as continuous and homogeneous media and using the so-called “effective radiative properties” in the radiative transfer equation. Thus, characterization of the radiative properties of porous materials is crucial.

A review of thermal radiation phenomena in spherical particulate media has been given by Tien and Drolen (1987). Concerning the radiative properties for particulate media, the majority of the textbooks, such as those of Brewster (1992), Siegel and Howell (2002), and Modest (2003) usually focused on simple-shape particles: spherical particles and long circular cylinders. A review of the thermal radiation properties of real dispersed media were reported by Baillis-Doermann and Sacadura (2000). The recent book by Dombrovsky and Baillis (2010) presents both theoretical prediction and experimental determination of the spectral radiative properties of real disperse media; these authors focused on the determination of the radiative properties of some important materials such as foams, fibrous materials, various ceramics, polymer coatings containing microspheres, and aerogel superinsulations (see, also, the articles Highly porous cellular foams, Low porosity foams, Highly porous isotropic and anisotropic fibrous materials, Low-porosity ceramics for thermal barrier coatings, Paint coatings containing hollow glass microspheres, Silica-based nanoporous composite materials).

Radiative properties determinations of such complex media are based on theoretical and experimental approaches (see the article Experimental study and theoretical modeling of spectral radiative properties of dispersed materials).

Concerning theoretical approaches, the radiative characteristics can be predicted from the porosity and decomposition of the morphology of elementary particles constituting the materials. For example, from particle size distribution by considering a random arrangement of particles, the Mie theory or the geometric optics laws can be used assuming independent scattering [see the article Radiative properties of particles and fibers (theoretical analysis)]. Other theoretical methods consist of determining the radiative characteristics from a Monte Carlo approach with optic geometric laws at the microscopic scale, taking into account the complex morphology of the porous medium and the effect of dependent scattering due to the proximity of particles.

Other approaches are based on the experimental measurement of both the reflectance and transmittance of the medium on a macroscopic scale combined with an inverse method used to identify the radiative properties of material (see the article A basis of experimental characterization and identification procedure). For applications requiring only the knowledge of hemispherical data, the simplest transport radiative properties can be used. However, if the details concerning the scattering pattern are required (depending on the application), the well-known Henyey-Greenstein or isotropic phase function model is not suitable and a more elaborate scattering phase function model and bi-directional measurement are required to obtain more information about a real phase function.

Obviously, each type of material has its own complexity and requires specific investigations. Due to the potential complexity of the different porous media and the number of radiative properties to be determined, there is no single response to the problem of their determination (details and recommendations can be found in the following specific articles: Highly porous cellular foams, Low porosity foams, Highly porous isotropic and anisotropic fibrous materials, Low-porosity ceramics for thermal barrier coatings, Paint coatings containing hollow glass microspheres, Silica-based nanoporous composite materials).

REFERENCES

Baillis-Doermann, D. and Sacadura, J.-F., Thermal radiation properties of dispersed media: Theoretical prediction and experimental characterization, J. Quant. Spectrosc. Radiat. Transf., vol. 67, no. 5, pp. 327-363, 2000.

Brewster, M. Q., Thermal Radiative Transfer and Properties, New York: Wiley, 1992.

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

Modest, M. F., Radiative Heat Transfer, 2nd ed., New York: Academic, 2003.

Siegel, R. and Howell, J. R., Thermal Radiation Heat Transfer, 4th ed., New York: Taylor & Francis, 2002.

Tien, C. L. and Drolen, B. L., Thermal radiation in particulate media with dependent and independent scattering, Annu. Rev. Numer. Fluid Mech. Heat Transfer, vol. 1, pp. 1-32, 1987.

References

  1. Baillis-Doermann, D. and Sacadura, J.-F., Thermal radiation properties of dispersed media: Theoretical prediction and experimental characterization, J. Quant. Spectrosc. Radiat. Transf., vol. 67, no. 5, pp. 327-363, 2000.
  2. Brewster, M. Q., Thermal Radiative Transfer and Properties, New York: Wiley, 1992.
  3. Dombrovsky, L. A. and Baillis, D., Thermal Radiation in Disperse Systems: An Engineering Approach, Redding, CT: Begell House, 2010.
  4. Modest, M. F., Radiative Heat Transfer, 2nd ed., New York: Academic, 2003.
  5. Siegel, R. and Howell, J. R., Thermal Radiation Heat Transfer, 4th ed., New York: Taylor & Francis, 2002.
  6. Tien, C. L. and Drolen, B. L., Thermal radiation in particulate media with dependent and independent scattering, Annu. Rev. Numer. Fluid Mech. Heat Transfer, vol. 1, pp. 1-32, 1987.
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