Environmental Engineering Reference
In-Depth Information
(3.28)
The
heat transition coefficient
(3.29)
can be calculated using the thermal conductivity
λ
of the insulation of a pipe
of outer diameter
d
P
with the outer diameter of the insulation
d
I
. Heat
conductivities
of various materials are given in Table 3.3. For the
surface
coefficient of heat transfer
λ
α
from the insulation to air, linearly interpolated
= 10 W/(m
2
values are used between
α
K) for
k'
= 0.2 W/(m K) and
α
=
15.5 W/(m
2
K) for
k'
= 0.5 W/(m K).
The example of the previous section is also used here to calculate the
circulation losses of a 20-m-long 15
1-mm copper pipe (
d
P
= 15 mm). The
= 10 W/(m
2
surface coefficient of heat transfer is taken to be
α
K). The heat
transition coefficient for an insulation thickness of 30 mm (
d
I
= 0.075 m)
and a thermal conductivity of
= 0.040 W/(m K) can be estimated from
Equation (3.29) as
k'
= 0.1465 W/(m K). Hence, the piping circulation losses
at an ambient temperature of
λ
ϑ
A
= 20°C for a heat transfer fluid temperature
of
ϑ
HTF
= 50°C for a circulation time of
t
circ
= 8 h become:
Q
circ
= 703 Wh.
The circulation losses of a 20-m-long pipe with a diameter of 22 mm and an
insulation thickness of 10 mm for a temperature difference between heat
transfer fluid and ambient air of 40°C and a circulation time of 10 h are as
high as
Q
circ
= 2500 Wh. This demonstrates clearly that the insulation should
be as good as possible to avoid loosing the majority of the heat on the way to
the storage tank. Also, pipe lengths should be kept as short as possible and
pipe clips must be attached without forming heat bridges. When laying pipes,
it must be considered that they expand as a result of temperature changes.
If the regulator stops the circulation in the collector cycle, the pipes and
the heat transfer medium cool down again. At a time
t
1
with an ambient
temperature of
ϑ
A
and a heat transfer fluid temperature of
ϑ
HTF
(
t
1
), the stored
heat in the pipes is:
(3.30)
This heat is reduced by the heat flow:
(3.31)
The
stored heat
at time
t
2
becomes:
