keff
= (9.5031 + 9.9585r)e0.00373TAVG .
(141)
kair
Table 11 presents comparisons at three air temperatures for eq 134 through 138,
and 141. The poorest comparisons are with eq 135 and 137, which have differences
of 19 and 17% at an air temperature of 100F.
The results from three numerical experiments were next compared with corre-
sponding numerical experiments in which the conductivity of air was specified
using eq 141 and treated as a solid (without radiation); the same FE meshes were
used in both cases. Table 12 contains the parameters and description of each com-
parison. Figures 4550 compare the inside surface temperatures and temperature
contours for each comparison.
In the figures above, it can be seen that using an effective conductivity in lieu of
the full convection solution will produce inaccurate temperature distributions in
the air. In some cases, the predicted interior surface temperatures agree, but the
quality of agreement depends on which surface (top, bottom, or side) is being con-
sidered. Better agreement is seen when a small temperature difference exists within
the "air," and when the pipe is insulated. Average inside surface temperatures
Table 11. Comparison of effective conductivity
correlations.
Pipe radius (ft)
0.1875
0.27083 0.09896 0.18229
0.35416
TAVG
Equation 141, keff/kair
20
12.25
13.15
11.30
12.20
14.04
60
14.22
15.26
13.12
14.16
16.30
100
16.51
17.72
15.23
16.44
18.92
Equations, keff/kair
134
135
136
137
138
20
12.79
11.62
10.57
13.65
14.31
60
14.48
13.13
12.46
16.47
16.58
100
16.39
14.84
14.70
19.88
19.21
Residuals
20
0.543
1.523
0.732
1.450
0.273
60
0.257
2.127
0.655
2.314
0.284
100
0.124
2.874
0.531
3.448
0.291
% differences
20
4.2
13.1
6.9
10.6
1.9
60
1.8
16.2
5.3
14.1
1.7
100
0.8
19.4
3.6
17.3
1.5
Table 12. Conditions for comparisons between numerical conduc-
tion and convection solutions.
Pipe
Outside
Estimated
keff
temp. (F)
temp. (F)
TAVG (F)
(Btu/hr ft2F)
Name*
Pipe radius (ft)
sq4ib65a
150
85
0.27083
100
0.26995
sq2d35c
80
45
0.09896
60
0.18865
sq2ic65a
150
85
0.18229
100
0.25045
*Names correspond to file names in Appendix B.
44
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