Performance of double-circulation water-flow window system as solar collector and indoor heating terminal Chunying LI 1

4 Numerical model development 
The incident solar irradiation provides important heating 
source during winter and brings about cooling load during 
summer. In the present study, the incident solar irradiation 
on water-flow window (G
total
) is divided into 14 parts, 
including the reflected and the transmitted parts, the 
absorbed parts by the glass panes, as well as the absorbed 
and delivered parts by the flowing water stream, as in Eq. (1).
Total
ref
trans
1
2
3
4
5
6
7
8
9
10
11
12
G
G
G
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
=
+
+
+
+
+
+
+
+
+
+
+
+
+
(1) 
where, 
G
Total
, the total incident solar radiation (W); 
G
ref
= 
γ·G
T
, the reflected solar radiation at outside 
surface of glass pane g1 (W); 
G
trans
= 
τ·G
T
, the solar radiation transmitted through the 
window to indoor (W); 
Q
1
= 
h
c,1a
·
A·(T
g1
− 
T
a
), the convective heat flow from 
outside surface of glass pane g1 back to ambient environ-
ment (W); 
Q
2
= 
h
c,6rm
·
A·(T
g6
− 
T
rm
), the convective heat flow from 
indoor surface of glass pane g6 to room space (W); 
Q
3
= 
h
r,1a
·
A·(T
g1
− 
T
a
), the radiation heat flow from 
outdoor surface of glass pane g1 to environment that 
includes the sky and surrounding solid surfaces (W); 
Q
4
= 
h
r,6rm
·
A·(T
g6
− 
T
rm
), the radiation heat flow from 
indoor surface of glass pane g6 to room surfaces (W); 
g 1
g 1
g 1
g 1
T
Q
ρ D C A
t
5
¶
=
¶
, the rate of heat storage within 
glass pane 
g1 (W); 
g 3
g 3
g 3
g 3
T
Q
ρ D C A
t
6
¶
=
¶
, the rate of heat storage within 
glass pane 
g3 (W); 
g 4
g 4
g 4
g 4
T
Q
ρ D C A
t
7
¶
=
¶
, the rate of heat storage within 
glass pane 
g4 (W); 
g 6
g 6
g 6
g 6
T
Q
ρ D C A
t
8
¶
=
¶
, the rate of heat storage within 
the glass pane 
g6 (W); 
f 2
f 2
f 2
f 2
T
Q
ρ D C A
t
9
¶
=
¶
, the rate of heat storage within 
the water volume of external window cavity 
f2 (W); 
f
f
f
f
T
Q
ρ D C A
t
5
10
5
5
5
¶
=
¶
, the rate of heat storage within 
the water volume of internal window cavity 
f5 (W), 
(
)
f 2
f 2
f 2
f 2
Q
m C
T
T
11
,out
,in
=
-
, the rate of heat extraction 
by the flowing water within external window cavity 
f2 (W), 
(
)
f 5
f 5
f 5
f 5
Q
m C
T
T
12
,out
,in
=
-
, the rate of heat extraction 
by the flowing water within internal window cavity 
f5 (W). 
The simulation code was developed with FORTRAN and 
finite difference approach based on simplified unidirectional 
steady-state model. A previously validated program (single- 
circulation water-flow window system) was modified 
accordingly. The simulation results coincide well with the 
results from experiments, with both scale-down cell and 
full-scale air-conditional room (Li 2012). In the present 
simulation model, the double-circulation water-flow window 
system was taken as 2 superimposed single-circulation 
water-flow window systems. In the previous investigations, 
the code of the single-circulation configuration was validated 
with different glazing properties and weather conditions. This 
means that the decomposition of incident solar radiation, 
the calculation of heat transfer through the window 
components, as well as the heat absorption process of the 
flowing liquid within window cavities are modeled correctly. 
Thus, the models and the program in use are accurate 
enough to predict the performance of water-flow window. 
At every time step, the program read in weather data 

---

Li et al. / Building Simulation / Vol. 13, No. 3 
580 
and inlet water temperature of both circulations, and 
processed the heat/mass flow calculation. The temperatures 
of glass panes and flowing water were calculated by solving 
the heat balance equations. Afterwards, the system solar 
thermal collection could be calculated with water flow rate 
and its temperature rise in the window cavity. Whereas
the system thermal efficiency is calculated as solar thermal 
collection divided by the simultaneous incident solar 
radiation. Meanwhile, the comprehensive indoor heat gain 
through the window is composed of two parts: the directly 
transmitted solar thermal energy, and the heat release from 
the inner glass pane (g6 in Fig. 2) through convective and 
radiation heat transfer. The first part, i.e. G
trans
can be 
calculated with total incident solar energy and the com-
prehensive solar transmissivity of the window. The second