Environmental Engineering Reference
In-Depth Information
The cover temperature is obtained via
T
f
h
gf
T
f
T
g
ρ
g
δ
g
C
g
∂T
g
∂t
σ
T
g
=
−
+
×
−
ε
−
1
ε
−
1
f
+
−
1
g
σε
g
(
T
sky
−
T
g
)
.
+
h
wind
(
T
a
−
T
g
)
+
(4.4.8)
To simulate accurately the transient response time of the collector, it is essential
to take into account the thermal capacity of the water in the collector's header pipes.
The transient response of the fluid in this component has been shown to account for
the experimentally-observed the time lapse between a change in the temperature of the
fluid leaving the end of the riser pipes and when a corresponding perturbation appears
at the outlet of the header pipe. Assuming a uniform flow distribution between the
collector risers, a heat balance on the nth section of the header pipe gives
πD
h
4
∂T
n
∂t
Wρ
w
.
m
=
n
(
T
n
−
1
−
T
n
)
+
(
T
0
−
T
n
−
1
)
.
(4.4.9)
for the connecting pipes, a heat balance for an element of fluid within the pipes gives
πD
h
4
∂T
w
∂t
C
w
.
m
c
∂T
w
∂y
ρ
w
C
w
+
=
U
s
,
a
πD
ρ
(
T
a
−
T
w
)
.
(4.4.10)
for the hot water store, an energy balance on an incremental section of fluid which is
remote from the end sections of the tank gives
k
w
A
s
∂
2
T
w
∂y
2
ρ
w
C
w
A
s
∂T
w
∂
t
C
w
.
m
s
∂T
w
∂y
+
=
+
−
U
s
,
a
P
s
(
T
a
T
w
)
(4.4.11)
.
m
L
.
The boundary conditions for the hot-water store are determined by considering
incremental sections of fluid in contact with either the top or the base of the tank as
δy
.
m
s
=
.
m
c
−
where
−
0, i.e., (
i
) for the top of the tank,
k
w
∂T
w
∂y
U
s
,
a
,
T
(
T
a
−
T
w
)
+
=
0
(4.4.12)
(ii)
for the base of the tank
k
w
∂T
w
U
s
,
a
,
B
(
T
a
−
T
w
)
−
∂y
=
0
(4.4.13)
In a simple mixing model, when warm fluid is introduced below cooler water,
it is assumed that complete mixing ensues and the two adjacent nodes attained a
single temperature. This process is repeated down the tank until a stable themocline is
restored.
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