Modeling the Heat Gain of a Window With an Interior Shade ... - inive

Proceedings of Clima 2007 WellBeing Indoors
The incident radiation on the inside of the glass is diffuse radiation reflected from the shade.
Optical properties for diffuse radiation for the glass can be determined for isotropic radiation by
integration over all angles of incidence. This was done using glass properties from a
manufacturer and shown in the next section of this report.
Similarly, the short wave beam radiation fraction absorbed by the glass, Abs bg , is:
Abs bg
∞
n 1 n
τ gb α gd ρss
= α gb + τ gb α gd ∑ [ ρ
+
ss ρ gd ] = α gb +
Eq[5]
n = 0
1 − ρ ss ρ gd
where variables are as defined before and α gb = beam absorptance of the glass (a function of
incidence angle, θ), α gd = diffuse absorptance of glass. Equations 4 and 5 also apply for diffuse
radiation Abs dss and Abs dg , but τ gb is replaced with τ gd and α gb is replaced with α gd (see footnote
7).
Glass
Shade
P τ gb ρ ss 2 ρ gd
2
Abs=ρ ss 2 τ gs ρ gd 2 α ss
τ gb ρ ss
2
ρ gd τ gd ρ ss
2
τ gb ρ gd
2
Abs= ρ ss 2 τ gb ρ g60 α g60
ρ ss
2
τ gb ρ gd
P τ sb ρ ss ρ gd
Abs=ρ ss τ gb ρ gδ α ss
τ gb ρ ss τ gd
ρ ss τ gb ρ gd
Abs= ρ ss τ gb α gd
ρ ss τ gb
P τ gb
Abs=τ gb α ss
ρ gb
τ gb
Abs=α gb
Figure 1. Short wave energy flows.
We can now do a short wave energy balance:
[ cos θAbs
G cd Abs ]
& 3
Q gs = G cnb bg +
dg
Eq[6]
& = [ cos θ Abs
Abs ] Eq[7]
Q ss G cnb
bss + G cd
3 We assume a uniform diffuse short wave field. This is accurate except for the lower floors where the diffuse
radiation is a mix of diffuse sky radiation and ground reflected radiation. We have ignored ground reflected
radiation in this analysis but its inclusion would be straight forward.
dss