Environmental Engineering Reference
In-Depth Information
transfer
α
2
from the insulation to the ambient air depends on the orientation
of the wall (VDI, 1982).
For a horizontal wall with
heat transfer upwards:
For a horizontal wall with
heat transfer downwards:
For a vertical wall (spherical cap) with
heat transfer to the side:
With
r
and
h
defined in Figure 3.15, the surface of the spherical cap becomes:
(3.43)
The following example calculates the heat losses of a 300-litre storage tank.
The ambient temperature and storage temperature are
ϑ
S
=
90°C, the dimensions of the tank are
l
cyl
= 1.825 m,
d
o
= 0.7 m,
d
i
=0.5m,
r
= 0.45 m,
h
= 0.11 m and
s
= 0.1 m. With the heat conductivity of the
insulation
ϑ
A
= 20°C and
α
= 15.5 W/(m
2
K) in the cylindrical part, the heat transition coefficient is
k'
=
0.64 W/(m K). With the surface area of the spherical cap of
A
sphere
= 0.311
m
2
and the heat transition coefficient of the spherical cap
k
= 0.33 W/(m
2
K), the storage losses become:
λ
= 0.035 W/(m K) and the surface coefficient of heat transfer
The temperature
ϑ
S
of a stationary storage tank decreases with the time
t
.
Thus, the storage losses decrease as well. If no heat is fed into or taken from
the storage tank, the storage temperature
(3.44)
can be calculated as described for the pipes above. The value
(3.45)
is the
time constant
of the storage. It describes the time taken for the
temperature difference to decrease to 1/e = 36.8 per cent of the initial value.
The time constant of the example above is
= 250 h = 10.4 days.
Figure 3.16 shows the storage temperature of a stationary storage tank. It
is obvious that a high portion of the stored heat is emitted again to the
τ
