2009

Heat transfer is governed by three distinct mechanisms: convection, conduction, and radiation. Unlike convection or conduction, heat transfer through radiation does not occur through a particular medium. To understand this phenomenon one must enter into the atomic or quantum realm. All atoms, at finite temperatures, are continuously in motion. Consequently, it may be understood that the mechanism of radiation is derived from the energetic vibrations and oscillations of these atomic particles, namely electrons.

Figure 1. A portion of the electromagnetic spectrum, from high-energy gamma rays to low-energy microwaves. Thermal radiation encompasses some of the ultraviolet and all of the visible and infrared portions of the spectrum.

At finite temperatures, conditions exist in which electrons are in a thermally excited state. These conditions are sustained by internal energy and thus, are directly associated with temperature. In these thermally excited states electrons emit energy in the form of quanta or photons, resulting in the propagation of electro-magnetic waves. Accordingly, the emission of electromagnetic waves from these thermally excited electrons make up the thermal radiation portion of the electromagnetic spectrum, which occurs between 0.1μm and 100μm. Thermal radiation thus encompasses the near UV, and the entire VIS and IR portion of the electromagnetic spectrum (Figure 1).

Thermal radiation propagates from a radiating surface in all possible directions and is emitted over a range of wavelengths. Thus, the magnitude of emitted radiation must be described such that it is defined both by its wavelength and its direction — its spectral and its directional components — respectively. As a result, radiative terms are used to treat these components. Spectral intensity Iλ,e is defined as the energy flux, at a specific wavelength λ, per unit area, in a direction normal to that area, per unit solid angle about that direction, per unit wavelength (Figure 2). It has units of (W/m2*sr*μm) and is given by the equation:

Alternatively, spectral emissive power Eλ, is defined as energy flux in all direction, at a wavelength λ, per unit area, per unit wavelength; and is in units of (W/m2*μm) and is given by the equation:

Eλ is the energy flux based on the surface area of the actual radiating surface while Iλ,e is the energy flux through a projected area. It is also necessary to account for incident radiation on a surface due to emission and reflection of radiation from other surfaces. The incident radiation from all surfaces is defined as the irradiation (Γλ); Γλ is the energy flux at a wavelength λ that is incident on a surface, per unit area, per unit wavelength. It has units of (W/m2*μm) and is given by the equation:

Finally, the radiosity (Ρ) can be introduced. The radiosity is similar in definition to the emissive power, but also accounts for irradiation. As a result, Ρ is associated with the radiant energy from both direct emission and reflection, and Ρλ is thus defined as the radiant energy, at a wavelength λ, (in all directions), per unit area, per unit wavelength. It has units of (W/m2*μm) and is given by the equation:

(Note, “e+r” refers to the total intensity due to emission and reflection).

In order to connect these terms and their associations with real surfaces, they must relate to something of theoretical measure. This relation, of course, is the concept of a blackbody. A blackbody is a theoretical object that is both the perfect emitter and absorber of radiation; it is an ideal surface. The characteristics of a blackbody are as follows:

  • Absorbs all incident radiation independent of wavelength and direction.
  • For a given wavelength and finite, nonzero temperature, no object can emit more energy at the same temperature.
  • It is a diffuse emitter.

The Planck Distribution approximates a blackbody where the spectral intensity of a blackbody, at a given temperature, is given by the equation:

The spectral emissive power is given by the equation:

Wien’s displacement law prescribes a peak wavelength to a given temperature, and is given by the equation:

Where C3 = 2897.8 μm.K

For example, the sun, which can be approximated as a blackbody at 5800 K, has a max spectral distribution at about .5 μm using Wien’s displacement law (Figure 3) This peak is in the visible spectrum. Alternatively, a blackbody at 1450 K, would have a max spectral distribution at about 2.0 μm; corresponding to SWIR portion of the electromagnetic spectrum.

The total emissive power of a blackbody may be found using the Stefan-Boltzmann law, which expresses the total emissive power of a blackbody, as:

Where C1 = 3.742x108 W.μm4/m2 and C2 = 1.439x104 μm.K

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