Thermal radiation from opaque materials

Precise assessment of heat transfer, and in particular radiative heat transfer, is necessary in many cases, for example, to control the temperature of parts placed in a furnace for heat treatment, or to assess heat loss in a home with a view to improving insulation and thus saving energy. For a long time, it was considered that radiative exchanges were predominant at high temperatures, since the flux emitted by a surface is proportional to its temperature at the fourth power. However, even at room temperature, radiative exchanges are not to be neglected. For this temperature range, convective and radiative exchanges can be of the same order of magnitude: for example, for a convective exchange coefficient of 5 W · m ^{– 2} · K ^–1 , the surface flux lost through convection by a black wall at a temperature of 25°C in a room at 20°C is 25 W · m ^{– 2} , while the surface flux exchanged by radiation with the walls surrounding the surface, if they are at 20°C, is 29 W · m ^{– 2} .

All bodies, whatever their temperature, emit electromagnetic radiation. In the case of so-called thermal radiation, only the transformation of internal energy into radiative energy (emission) or vice versa (absorption) is taken into account. One of the intrinsic characteristics of this radiation is its frequency, which remains invariant throughout the wave's propagation; the wavelength, on the other hand, depends on the propagation medium. It would therefore be preferable to use frequency to identify the "spectral nature" of the radiation. Unfortunately, in practice, wavelength is used. So as not to go against the usual terms, in this article we consider only the wavelength of electromagnetic radiation in a vacuum or in a medium with a refractive index practically equal to 1 (the case of gases such as N ₂ , O ₂ , air, etc.). With common temperatures ranging from around 80 K to 6,000 K, the usual range of thermal radiation extends from the visible to the mid-infrared, i.e. from 0.3 µm to 50 µm.

This article deals only with radiation from opaque materials, i.e. materials whose thickness is such that no fraction of the incident radiation is transmitted. This thickness depends not only on the wavelength considered and the nature of the material, but also on its surface condition. Surfaces are almost always rough, or covered with impurities or oxides. Consequently, for a large number of materials and for the wavelength range corresponding to thermal radiation, the penetration depth of incident radiation (from nanometers to millimeters)...