Thermal Radiation

Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero, and represents a conversion of thermal energy into electromagnetic energy. It is generated by the thermal motion of charged particles in matter, which results in charge-acceleration and dipole oscillation. This drives the electrodynamic generation of coupled electric and magnetic fields, which cause the emission of thermal radiation.

Electromagnetic radiation, or light, does not require the presence of matter to propagate, and travels the fastest in a vacuum. All forms of matter emit radiation. For gases and some semi-transparent solids (for example, glass and salt crystals at elevated temperatures) emission is a volumetric phenomenon (that is, emission is an integrated effect of local emission throughout the volume). For most solids and liquids, radiation that is emitted from the interior molecules is strongly absorbed by adjoining molecules. Therefore, because all of the emitted radiation originates from molecules near the surface, it can be considered as a surface phenomenon.

Electromagnetic energy propagation can be described at various levels of complexity, depending on the features of the radiation field to be described. For example, if polarization is important, the Tokes parameters are used to describe the intensity field. If wave effects are important, the vector wave quantities from electromagnetic theory such as electric vector, magnetic vector, and the Poynting vector are used. Wave effects become significant when the characteristic length scale for transport, such as spacing between the surfaces, is similar to the wavelength.

For more information, see Modeling Radiation.

For calculating heat transfer in most situations, however, this level of description is overly complicated. For most heat transfer applications, thermal radiation can be treated as unpolarized (multiple reflections and scattering usually nullify polarization effects) and incoherent (waves or photons are usually out of phase). The length scale for transport is usually much larger than the wavelength of radiation, so the limiting description of geometric optics (that is, the wavelength approaches zero) can be applied: the waves are described as bundles of rays carrying energy in a small volume that is associated with the solid angle in the direction of the rays.

The maximum flux at which radiation can be emitted from a surface is given by the Stefan-Boltzmann law:

Figure 1. EQUATION_DISPLAY

q_{b b} ″ = σ {T_{s}}^{4}

(197)

In this expression, $q_{b b} ″$ $[W / m^{2}]$ is the local surface heat flux, $T_{s}$ is the temperature of the surface, and $σ$ is the Stefan-Boltzmann constant $σ = 5.67 \times 10^{- 8}$ $[W / m^{2} K^{4}]$ . Such a surface is called an ideal radiator or blackbody.

The heat flux that is emitted by a real surface is less than the heat flux of an ideal radiator, and is given by:

Figure 2. EQUATION_DISPLAY

q_{e} ″ = {ε q}_{b b} ″ = ε σ {T_{s}}^{4}

(198)

where $0 \leq ε \leq 1$ is the surface emissivity (that is, the relative ability of a surface to emit energy by radiation).

If radiation is incident upon a surface, a portion is absorbed, a portion is reflected, and a portion is transmitted through the material:

Figure 3. EQUATION_DISPLAY

q_{i n c} ″ = q_{a b s} ″ + q_{r e f} ″ + q_{t r a n s} ″ = {α q}_{i n c} ″ + {ρ q}_{i n c} ″ + τ q_{i n c} ″

(199)

The constants in this expression are:


$0 \leq α \leq 1$	The surface absorptivity: the fraction of incident radiation that gets absorbed.
$0 \leq ρ \leq 1$	The reflectivity: the fraction of incident radiation that gets reflected away from the surface.
$0 \leq τ \leq 1$	The transmissivity: the fraction of incident radiation that gets transmitted through the material.

Absorptivity, reflectivity, and emissivity depend on the surface temperature, surface roughness, emission angle, and wavelength of the radiation (the radiation is not monochromatic, but comprises a continuous dispersion of photon energies).