Civil Engineering Reference
In-Depth Information
In the case of a bare tube, if the outside surface is taken as reference, the
abovementioned relationships (with
n
¼
1) are modified as follows:
t
i
t
o
Q
¼
A
R
th
where
r
2
¼
r
o
,
A
¼
2
π
L
r
o
r
o
r
o
ln
r
2
r
o
r
o
ln
r
r
i
þ
R
th
¼
h
i
1
r
i
þ
k
1
r
1
þ
h
o
¼
1
h
i
1
r
i
þ
k
1
1
h
o
If the thickness (
r
o
r
i
) of the pipe is small (
r
o
r
i
<
0.1
r
i
), this expression
can be approximated to the following, as for a flat surface:
1
h
i
þ
r
o
r
i
k
1
þ
1
h
o
R
th
¼
ð
simplified formula
Þ
Notice that 1/
h
i
is usually the lowest term in the case of pipelines, because of the
moving fluid inside the pipe.
For insulated pipelines with one insulation layer, there follows:
t
i
t
o
Q
¼
A
R
th
where
A
¼
2
π
L
r
i
1
r
i
ln
r
2
r
i
ln
r
3
1
r
i
R
th
¼
h
i
þ
k
1
r
1
þ
k
2
r
2
þ
h
o
r
o
,
j
¼
2;
r
1
¼
r
i
;
r
3
¼
r
o
If
r
1
¼
r
i
is assumed to be equal to
r
2
(small thickness of the pipe) there follows:
1
h
i
þ
r
i
k
2
ln
r
3
1
h
o
r
i
r
o
R
th
¼
r
2
þ
If the thickness of the insulation layer is small in comparison with the bare pipe
radius, that is (
r
3
r
2
)
<
0.1
r
2
¼
0.1
r
i
and (
r
i
/
r
o
)
>
0.9 the expression given
above can be approximated as follows:
1
h
i
þ
r
3
r
2
k
2
þ
1
h
o
r
i
r
o
R
th
¼
Table
8.5
shows heat losses from a composite metal pipeline to still air.
Notice that insulation reduces heat transfer through the layers to roughly
10 %.
Attention must be paid to surface conditions such as film deposits, surface
scaling, and corrosion. A fouling factor can be introduced to take account of
these phenomena as an additional term in the overall thermal resistance
R
th
(see
also Chap.
15
).
