Page 122 - Analysis and Design of Energy Geostructures

94 Analysis and Design of Energy Geostructures

where α irr is the surface absorptivity. The surface absorptivity is a measure of the
absorbed radiation efficiency of the surface. It is equal to 1 for a black body while typ-
ically lower than 1 for most construction materials, depending on the nature of the
irradiation, surface material and finish.
Assuming that the surface of interest is part of a ‘grey body’, that is a body that
emits radiation in constant proportion to the corresponding black body radiation, it
results that E 5 α irr . In this case, the net heat flux density exchanged from the surface,
expressing the difference between the thermal energy released due to radiation and
absorbed due to irradiation, reads

4 4
5 Eσ SB ðT 2 T Þ ð3:10Þ
_ q N
rad
s
In many cases it is convenient to express Eq. (3.10) in a linear form as follows
(Bergman et al., 2011)
5 h r ðT s 2 T N Þ ð3:11Þ
_ q
rad
where h r is the radiation heat transfer coefficient that can be calculated as
2 2
h r 5 Eσ SB ðT s 1 T N ÞðT 1 T Þ ð3:12Þ
s N
From Eq. (3.12) it can be noted that the radiation heat transfer coefficient, h r ,
strongly depends on temperature, in contrast to the weak dependence of the convec-
tion heat transfer coefficient, h c .

3.6.2 Radiation heat transfer coefficient values
The radiation heat transfer coefficient can be calculated as (EN ISO 6946, 2007)

3
ð3:13Þ
h r 5 E 4σ SB T
where T is the mean between the surface and air temperatures.

3.6.3 Remarks about radiation
Radiation can markedly characterise heat transfer through fluids in the presence of sig-
nificant temperature variations. Based on this consideration:
• Radiation can significantly characterise heat transfer between built environments
and adjacent energy geostructures when significant sources of thermal energy are
present. Otherwise the contribution of radiation in the global heat transfer may
generally be considered lower than that of convection and neglected.
• Radiation can contribute up to 10% 20% of the global heat transfer in dry coarse-
grained soils (Hermansson et al., 2009). However, the contribution of radiation is
generally less than 1% in coarse-grained soils and becomes even smaller in moist