were averaged to obtain a heat flow value for each side (top, bottom, left, and right)
and an overall average value. Nusselt and Rayleigh numbers were then calculated
using the surface conductances obtained using the average interior surface tem-
perature for material properties and the temperature difference between the aver-
age pipe and average insulation surface temperatures, for each side and for the
The following equations developed from data in Raznjevic (1976) were used for
calculating material properties.
Viscosity of air (ft/s2)
υ = 1.27573E - 04 + 6.1411E - 07TAVG .
Density of air (lbm/ft3)
ρair = 8.42416E - 02 - 1.93863E - 04TAVG + 4.16195E - 07TAVG .
Volumetric specific heat of air (Btu/ft3F)
Cv = 0.241ρair .
Coefficient of thermal expansion (1/F)
β = 2.177E - 03 - 4.74865E - 06TAVG + 9.42743E - 09TAVG
- 1.04328E - 11TAVG
Thermal conductivities (Btu/fthrF)
kair = 0.01309 + 2.14766E - 05TAVG
kEPS = (0.214583 + 5.36829E - 04TAVG )/12
kpipe insul = (0.196851e0.00211687TAVG )/12 .
TAVG is the average temperature of the two pertinent surfaces, i.e., for air the
average is that of the inside EPS surface and the pipe or pipe insulation surface
The hypothetical gap width was used as the length parameter in the Nusselt
and Rayleigh number calculations; these values and other enclosure dimensions
values for the numerical experiments. Three sets of emissivity values were used;
two different values for EPS were chosen to represent new (0.6) and old (0.9) insu-
lation.* For the pipe and pipe insulation the two values were for aluminized paint
(0.5) and no paint (0.9).
* Personal communication , Stephen N. Flanders, U.S. Army Cold Regions Research and Engineer-
ing Laboratory, 1994.
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