tions yield Nusselt numbers within 20% of each other with the exception of

Ghaddar 's (eq 42), which is about 260% higher than the mean value of the other

equations at a Rayleigh number of 108. This could be due to the pipe location (*E *=

0.52 using eq 50), which agrees with the findings of Babus'Haq et al. (1986) that

more heat transfer occurs from hot pipes when placed lower in the enclosure (posi-

tive values of *E*).

Currently accepted practice by Federal agencies, for the thermal analysis of the

utilidors shown generically in Figure 8, is presented by Smith et al. (1979) and by

the U.S. Army (1987). Two assumptions are made: (1) the air temperature inside

the utilidor is uniform and (2) interior air film resistance can be ignored. The pro-

cedure consists of determining the thermal resistances by assuming that the rect-

angular enclosures can be treated as circular by using a radius calculated from the

mean perimeters (*P*L and *P*E in Fig. 8). If the interior pipes are insulated, the con-

duction resistance of the air gap is neglected. If the interior pipes are uninsulated,

then the resistance may be based on both the air film and pipe material. For mul-

tiple pipes with differing temperatures, all of the resistances and pipe tempera-

tures are included to obtain an interior air temperature.

It is also possible to determine an effective conductivity of the air that includes

all the film resistances, radiation, and natural convection effects. These procedures

depend upon estimates of rectangular enclosures as circular and neglecting any

effects of eccentricity of the pipe location. These approaches are illustrated as fol-

lows: Using the square enclosure in Figure 8, the heat loss per unit length is

∆*T*

(51)

∑R

With the assumption that the square enclosure can be treated as a cylinder of equal

perimeter, the resistances are determined as

(52)

Thermal Lining

Insulated or Bare

T3

T2

Ta

T1

T0

T3

T2

T1

PL

PE

Exterior Casing

11

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