S o l a r – o p t i c a l P r o p e r t i e s o f V e n e t i a n B l i n d s
323
b,i i
f,i
f,i
4
f,i
f,i
f,i
G G T
J
τ
ρ
σ
ε
+
+
=
(3)
f,i i
b,i b,i
4
b,i
b,i
b,i
G G T
J
τ
ρ
σ
ε
+
+
=
(4)
where
τ
i
,
ε
i
and
ρ
i
are respectively the transmittance, emittance and reflectance of
surface
i
(subscripts
f
and
b
respecting to front and back sides) and
σ
is the Stefan-
Boltzmann constant (
σ
= 5.67
×
10
-8
W/m
2
K
4
).
The venetian blind’s direct-to-diffuse (
Dd
) transmittance and reflectance are calculated
using equations 3 and 4. However, the first term in the right-hand side of equations 3
and 4 – the radiant flux emitted by surface i
)T (
4
i
i
σ
ε
– was set to zero and replaced by a
source term (
S
i
), which takes into account the external radiation flux. Actually, it is only
necessary to follow the externally imposed radiation to determine the venetian blind
optical properties.
For the direct-to-diffuse case, direct radiation illuminates one part (or even all length) of
the slat. On this illuminated length (
m
, see Fig. 4a) the source fluxes (
S
i,f
) and (
S
i,b
) are
functions of the diffuse reflectance and diffuse transmittance of the slat, as follows:
−
If direct radiation hits front of slats (
φ
≥
-
ψ
):
φ
τ
ρ
cos I
m
D
)
1(
S
Db
DD
f,
blind
Dd
f, slat
f,i
−
=
φ
τ
τ
cos I
m
D
)
1(
S
Db
DD
f,
blind
Dd
slat
b,i
−
=
(5)
−
If direct radiation hits back of slats (
φ
< -
ψ
):
φ
τ
τ
cos I
m
D
)
1(
S
Db
DD
f,
blind
Dd
slat
f,i
−
=
φ
τ
ρ
cos I
m
D
)
1(
S
Db
DD
f,
blind
Dd
b, slat
b,i
−
=
(6)
On the remaining parts of the slats, which receive only diffuse radiation, and on the
openings to the blind fictive cavity, the source fluxes are set to zero.
The front direct-to-diffuse transmittance and reflectance of the venetian blind are:
φ
τ
cos I
G
D
2
Dd
f,
blind
=
φ
ρ
cos I
G
D
1
Dd
f,
blind
=
(7)
Usually, a unitary incident direct flux (
I
D
cos
φ
=
1) is adopted for these calculations. The
amount of radiation that is neither directly or indirectly transmitted nor reflected is the
one that is absorbed by the slat surfaces:
Dd
f,
blind
Dd
f,
blind
DD
f,
blind
Dd
f,
blind
1
ρ
τ
τ
α
−
−
−=
(8)
Back direct-to-diffuse properties are calculated in the same way, but using the
symmetrical slat angle value (
ψ
b
=
-
ψ
f
).
The same methodology is applied to calculate the diffuse-to-diffuse blind properties,
however, the source flux terms are different. For front-side diffuse-to-diffuse properties
the source flux for the opening 1 of the fictive cavity (Fig. 4b) is
S
1
=
I
d
cos
φ
, and for the
remaining elements (all slat elements and back opening 2 – Fig.4b) is equal to zero. The
horizontal incident diffuse flux can also be set to unity (
I
d
cos
φ
=1, hence
S
1
=1). The
following diffuse-to-diffuse (
dd
) blind properties can be obtained as follows:
2
dd
f,
blind
G
=
τ
1
dd
f,
blind
G
=
ρ
(9)
dd
f,
blind
dd
f,
blind
dd
f,
blind
1
ρ
τ
α
−
−=
(10)
