NuL = 0.2 + 0.145 L D Gr 0.25e
-0.02 L D
i
i
for 30, 000 ≤ GrL ≤ 716, 000
(24)
and 0.55 ≤ L D ≤ 2.65
i
where Di is the diameter of the internal cylinder. Gap width, however, does not
provide all the heat transfer information that may be desired, i.e., the conductances
for the two surfaces are not obtained individually, but are lumped together. The
is defined as the ratio of actual heat flow to that due to conduction alone across
the region. For concentric cylinders, the equivalent conductivities based on the
inside and outside surface areas are
( )i
D
Nui
hD
= i i ln o
=
(25)
keq
Di
Nucond
2k
( )o
D
Nuo
hD
= o o ln o
=
(26)
keq
Di
Nucond
2k
where
2
Nucond =
.
(27)
ln (Do Di )
The total energy lost by one cylinder equals that gained by the other (i.e., eq 25
equals eq 26). The subscript i refers to the inner cylinder and o to the outer one,
and Nucond is the Nusselt number for pure conduction between concentric cylin-
ders (Gebhart et al. 1988).
Kuehn and Goldstein (1978) combined a large amount of data and obtained the
following correlations for Pr = 0.7 (air):
2
Nui =
(28)
(
) + (0.12Ra )
15 1/15
15
1/ 4
1/ 3
ln 1 + 2
0.5RaD
Di
i
-2
Nuo =
(29)
(
) (
)
1/ 3 15 1/15
1/ 4 15
+
ln 1 - 2
0.12RaD
RaD
o
o
(
)
Tb - To
Nui
φb =
=
(30)
Nui + Nuo (Ti - To )
-1
1
1
Nuconv =
+
(31)
Nui Nuo
2
Nucond =
(32)
ln (Do Di )
[
]
Nu = (Nucond )
+ (Nuconv )
15 1/15
15
(33)
6
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