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. The thermal motion of charged particles in matter results in charge-acceleration and dipole oscillation. This behavior 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). These volumetric effects are modeled with the Radiative Transport Equation (RTE) for Participating Media Eqn. (1721). 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. If these surfaces form the boundaries of a participating medium, the effects are considered as boundary conditions for solution of the RTE. In the case where these surfaces surround a medium with relatively little volumetric emission, absorption, and scattering, the exchange of energy can be solved for using the surface-to-surface solver (see S2S (Surface-to-Surface) Radiation).

For most heat transfer applications, thermal radiation can be treated as unpolarized due to multiple reflections and scattering 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. Radiation can then be described in terms of rays carrying energy in specific directions.

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

Figure 1. EQUATION_DISPLAY

{\dot{q}}_{b b} ″ = σ {T_{s}}^{4}

(1685)

In this expression, ${\dot{q}}_{b b} ″$ 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 black body.

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}

(1686)

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} ″

(1687)

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).