Nu
keq =
(34)
Nucond
where the Nusselt numbers are averaged values for the overall heat transfer around
the cylindrical surfaces, and are based on Do. RaDi is the Rayleigh number based
on Di and RaDo is that based on Do. The temperature difference in Ra is the differ-
ence between the inner (Ti) or outer (To) surface temperatures and the average fluid
temperature (Tb) between the inner and outer cylinder boundary layers. Tb can be
determined from φb, the average dimensionless fluid temperature between bound-
ary layers. An iterative solution to the correlation will be required to obtain the
Nusselt numbers. What is significant about this correlation is that the conductances
for both surfaces can be obtained along with the mean fluid temperature.
Lunardini (1990) conducted experiments using a conduit system used at many
government installations (Fig. 3). He identified four ways to evaluate the thermal
1
Ra =
(35)
2π ri h
from the Federal Guide Specification (1981), where the convective coefficient (h)
assumes a constant value of 3 Btu/hr ft2F, or
r
ln ci
rri
Ra =
(36)
2π keff
where
keff = 0.11Ra L.29 kair
0
(37)
obtained from Grober et al. (1961), or from his own data
keff = 1.463Ra L.123 kair ,
0
(38)
which includes radiation effects, or
keff = 0.68Ra L.157 kair ,
0
(39)
Carrier Pipe
which has had the effect of
Pipe Insulation
rci
the effective conductivity of
Outer Conduit
air, rci is the inner radius of
ri
the outer conduit, and ri is
the outer radius of the insu-
lation. The air gap thickness
is used as the characteristic
length in the Rayleigh num-
ber.
Boyd (1981) combined
data from concentric circu-
Figure 3. Cross section of a concentric pipe conduit.
lar cylinders with data from
7
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