Figure 54 compares the measured and calculated interior insulation surface
temperatures. Fair agreement is obtained for all surfaces except the bottom,
where temperatures are much warmer than measured. It can also be observed that
the temperatures are not very sensitive to changes in the effective conductivity.
The case chosen was that which had the greatest temperature difference across the
air gap, and this should be considered when comparing the temperatures. It could
also be noted that closeness of the outside boundary conditions to the compared
temperatures are ensuring reasonable results. In defense of this, in an actual utilidor
design the wall thickness would be much greater, but with well-known thermal
properties. Because conduction solutions can be obtained with a high degree of
confidence, then temperatures in similar locations will in most cases be known
fairly well.
SUMMARY
Three approaches to the thermal analysis of utilidors were investigated: the tra-
ditional or currently accepted practice of one-dimensional analysis, numerical
analysis with modeling of convection and radiation, and numerical conduction
analysis using an effective conductivity to account for convection and radiation
effects. Each method has limitations and advantages.
The one-dimensional analysis did not produce good results when uninsulated
pipes were modeled; only some correlations can account for multiple pipes, off-
center locations, or other two-dimensional design possibilities. However, the
method is easy to use, and good agreement with overall heat losses was observed
with insulated pipes.
Numerical modeling with convection and radiation was demonstrated, produc-
ing good comparisons of heat loss with the experimental data; however, large
geometries and/or large temperature differences across the air gap were difficult
to model. The inclusion of radiation is required, and effects of surface emissivity
values can be observed. Numerical data were obtained only for relatively small
utilidors, the primary limitation being related to computational memory require-
ments and the matrix solution methods. Future improvements in computational
methods and storage hardware may make this analysis method practical.
Numerical conduction analysis using an effective conductivity produced rea-
sonable approximations to temperature distributions on inside surfaces; the method
was easy to use, and the solutions were all obtained on a personal computer. Two-
dimensional effects can be differentiated, but the information regarding tempera-
ture distribution within the air gap is inaccurate. The method seems to be most
accurate for small temperature differences across the air gap and is relatively
insensitive to minor changes in the effective conductivity value.
CONCLUSIONS AND RECOMMENDATIONS
Average heat losses can be calculated reliably for insulated pipes using one-
dimensional analysis, and these results will compare well with full (convection
and radiation) numerical solutions (of average heat loss).
A full numerical solution will provide the best two-dimensional analysis. How-
ever, the current model may not be able to converge to a solution given reason-
able computer resources. Ignoring radiation in a numerical convection model of
49
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