Page 195 - Mechanical Engineers' Handbook (Volume 4)

184 Heat-Transfer Fundamentals

i.e., 0, and all of the incident energy will be either reflected or absorbed. For such a

surface,
1

and
1
Light rays reflected from a surface can be reflected in such a manner that the incident
and reflected rays are symmetric with respect to the surface normal at the point of incidence.
This type of radiation is referred to as specular. The radiation is referred to as diffuse if the
intensity of the reflected radiation is uniform over all angles of reflection and is independent
of the incident direction, and the surface is called a diffuse surface if the radiation properties
are independent of the direction. If they are independent of the wavelength, the surface is
called a gray surface, and a diffuse-gray surface absorbs a fixed fraction of incident radiation
from any direction and at any wavelength, and .

Kirchhoff’s Law of Radiation
The directional characteristics can be specified by the addition of a prime to the value; for
example, the spectral emissivity for radiation in a particular direction would be denoted by
. For radiation in a particular direction, the spectral emissivity is equal to the directional
spectral absorptivity for the surface irradiated by a blackbody at the same temperature. The
most general form of this expression states that . If the incident radiation is inde-

pendent of angle or if the surface is diffuse, then for the hemispherical properties.

This relationship can have various conditions imposed on it, depending on whether spectral,
total, directional, or hemispherical quantities are being considered. 19
Emissivity of Metallic Surfaces
The properties of pure smooth metallic surfaces are often characterized by low emissivity
and absorptivity values and high values of reflectivity. The spectral emissivity of metals
tends to increase with decreasing wavelength, and exhibits a peak near the visible region.
At wavelengths 5 m the spectral emissivity increases with increasing temperature,
but this trend reverses at shorter wavelengths ( 1.27 m). Surface roughness has a
pronounced effect on both the hemispherical emissivity and absorptivity, and large optical
roughnesses, defined as the mean square roughness of the surface divided by the wavelength,
will increase the hemispherical emissivity. For cases where the optical roughness is small,
the directional properties will approach the values obtained for smooth surfaces. The presence
of impurities, such as oxides or other nonmetallic contaminants, will change the properties
significantly and increase the emissivity of an otherwise pure metallic body. A summary of
the normal total emissivities for metals are given in Table 17. It should be noted that the
hemispherical emissivity for metals is typically l0–30% higher than the values normally
encountered for normal emissivity.

Emissivity of Nonmetallic Materials
Large values of total hemispherical emissivity and absorptivity are typical for nonmetallic
surfaces at moderate temperatures and, as shown in Table 18, which lists the normal total
emissivity of some nonmetals, the temperature dependence is small.

Absorptivity for Solar Incident Radiation
The spectral distribution of solar radiation can be approximated by blackbody radiation at a
temperature of approximately 5800 K (10,000 R) and yields an average solar irradiation at