From Blackbodies to Real Surfaces
where is the portion of irradiation absorbed by the surface. Hence, depends on the directional distribution of the incident radiation, as well as on the wavelength of the radiation and the nature of the absorbing surface. The total, hemispherical absorptivity, represents an integrated average over both directional and wavelength. It is defined as the fraction of the total irradiation absorbed by a surface, or:
The value of depends on the spectral distribution of the incident radiation, as well as on its directional distribution and the nature of the absorbing surface. Although is independent on the temperature of the surface, the same may not be said for the total, hemispherical emissivity. Emissivity is strongly temperature dependent.
The reflectivity of a surface defines the fraction of incident radiation reflected by a surface. Its specific definition may take several different forms. We will assume a reflectivity that represents an integrated average over the hemisphere associated with the reflected radiation to avoid the problems from the directional distribution of this radiation. The spectral, hemispherical reflectivity then, is defined as the spectral irradiation that is reflected by the surface. Therefore:
where is the portion of irradiation reflected by the surface. The total, hemispherical reflectivity r is then defined as:
If the intensity of the reflected radiation is independent of the direction of the incident radiation and the direction of the reflected radiation, the surface is said to be diffuse emitter. In contrast, if the incident angle is equivalent to the reflected angle, the surface is a specular reflector. Although no surface is perfectly diffuse or specular, specular behavior can be approximated by polished or mirror-like surfaces. Diffuse behavior is closely approximated by rough surfaces and is likely to be encountered in industrial applications.
where is the portion of irradiation reflected by the surface. The total hemispherical transmissivity is:
The sum of the total fractions of energy absorbed reflected and transmitted must equal the total amount of radiation incident on the surface. Therefore, for any wavelength:
This equation applies to a semitransparent medium. For properties that are averaged over the entire spectrum, it follows that:
For a medium that is opaque, the value of transmission is equal to zero. Absorption and reflection are surface properties for which:
and
For a blackbody, the transmitted and reflected fractions are zero and the emissivity is unity.
An example of a material whose emissivity characteristics change radically with wavelength is glass. Soda-lime glass is an example of a material which drastically changes its emissivity characteristics with wavelength (Figure 2-5). At wavelengths below about 2.6 microns, the glass is highly transparent and the emissivity is nearly zero. Beyond 2.6 microns, the glass becomes increasingly more opaque. Beyond 4 microns, the glass is completely opaque and the emissivity is above 0.97.
|
||||||||||||||||||||||||
Top of Page |
Next Chapter: IR Thermometers & Pyrometers
|