Page 121 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 93

Figure 3.10 Heat transfer by radiation at the ground surface.

The rate equation governing radiation is the Stefan Boltzmann law. According to
,as
this law the heat flux density emission radiated by a surface (i.e. a heat source), _q
rad;e
a consequence of the thermal energy of the matter bounded by the surface reads
4
ð3:8Þ
_ q 5 Eσ SB T
rad;e s
where E is the surface emissivity and σ SB is the Stefan Boltzmann constant
28 2 4
(5.67 3 10 W/(m K )). The surface emissivity is a measure of the emissive radiation
efficiency of the surface. It is equal to 1 for a so-called ‘black body’, that is a body that
(1) emits radiation independent of direction, (2) absorbs all incoming radiation and (3)
is the source of highest emission at any given wavelength and temperature. Surface
emissivity is typically of 0.9 for most construction materials, depending on surface
material and finish (ASHRAE, 2012).
Radiation may also be absorbed by a surface as a consequence of the presence of
other heat sources in the surroundings. In this case a portion or the entire rate of ther-
mal energy that would incident the surface unit area by irradiation may be absorbed,
that is
4
_ q 5 α irr σ SB T N ð3:9Þ
rad;a