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Microsystems in Spacecraft Thermal Control 187

2
The thermal energy per unit area (W m ) released by a body at a given
temperature by radiation is termed as the surface emissive power (E). The heat
flux of a radiation process is described by the Stefan–Boltzmann law as shown in
the following equation:

E ¼ «s T 4 (9:5)
2
where E: emissive power (W m )
«: surface emissivity (0 « 1)
4
s: Stefan–Boltzmann constant (5.67 10 8 Wm 2 K )
T: surface temperature (K)

In practice, radiative heat exchange occurs between real or effective surfaces;
for example, between a spacecraft radiator and deep space (very cold) or between a
radiator and Earth (cold, but warmer than deep space). Radiative heat transfer is
calculated as a function of the difference of the surface emissivities and their
respective temperature to the forth power. View factors must also be included,
making the computation somewhat involved.
The surface emissivity («) is the ratio of the body’s actual emissive power to
that of an ideal black body. The emissivity depends on the surface material and
finish, on the temperature (especially at cryogenic temperatures where emissivity
drops off rapidly), and the wavelength. Tabulated values are available for emissiv-
ity; however, measured values are required as the actual properties of a surface can
vary as ‘‘workmanship’’ issues impact the value. Additionally, the build-up of
contamination or the effect of radiation on a surface can impact emissivity.
Hence, ‘‘beginning-of-life’’ and ‘‘end-of-life’’ properties are often quoted. At cryo-
genic temperatures, emissivity tends to fall off rapidly. According to Kirchoff’s law
a surface at thermal equilibrium has the property that a given temperature and
wavelength, the absorptivity equals the emissivity. By applying the conservation of
energy law, get the following equation for a opaque surface:
1 « ¼ r (9:6)

where « is the emissivity and r is the reflectivity of the surface. This equation
measures emissivity via reflectivity which is normally simpler to measure.
Since the radiation emitted by a spacecraft falls into the infrared and far
infrared regime of the electromagnetic spectrum, emissivity is normally given as
an average over these wavelengths. The solar absorptivity (a) describes how
much solar energy is absorbed by the material and is averaged over the solar
spectrum. Surface emissivity and solar absorptivity are important parameters for
spacecraft materials. Typically, a spacecraft radiator, which is used to cool the
spacecraft via radiation, is built from surfaces with a high emissivity but a low solar
absorptivity.

© 2006 by Taylor & Francis Group, LLC