Civil Engineering Reference
In-Depth Information
complexity of, for example, the geometry of the fibrous material, theoretical
models become sophisticated and are not very suitable. Therefore, on the exper-
imental front, an alternative way has been proposed to determine the radiative
properties of a medium of which radiative behaviour would not be easily modelled
with theoretical method (Baillis and Sacadura
2000
).
Radiative heat flux in a partially opaque is often expressed in the form of
Klemens and Kim (
1985
)
Q
radiation
¼
4rn
2
T
3
l
r
T
ð
16
:
5
Þ
where
r
Stefan-Boltzmann constant
n
average index of refraction
l
free path of photons
The mean free path of photons are calculated by absorption and scattering
inside the medium, as well as by the finite dimensions of the medium. Very often,
the scattering and absorption coefficients are functions of frequency f. Mathemat-
ically, the mean free path is expressed as
1
l
ðÞ¼
ð
16
:
6
Þ
l
a
ð
f
Þ
þ
1
1
l
s
ð
f
Þ
þ
l
b
where l
a
is the absorption coefficient, l
s
scattering coefficient and l
b
the boundary
mean free path (Klemens and Kim
1985
).
The transport process of radiation in the fibrous insulation is complicated with
increasing temperature. Very often, to simplify the calculation, surface film
coefficients are used to transpose the radiation into equivalent conduction through
a fictitious surface layer. For example, the equivalent conductivity for radiation in
fibre can be calculated as
k
radiation
¼
16r
3b
T
3
ð
16
:
7
Þ
where b is the extinction coefficient depending on the materials' density and the
specific extinction coefficient (Karamanos et al.
2008
).
5.2.5 Moisture Transport
Moisture transport in fibrous materials can be due to several different modes.
Primary three models are molecular diffusion for gases, capillary for liquids, and
pressure-induced convection or Darcy flow.
