The material properties of the fluid (air) can be held constant or reevaluated

between iterations using an average temperature obtained using a number of

schemes. FECOME averages the temperatures of the zero velocity nodes (the

inside surfaces of the enclosure) and calculates new air properties based on this

average temperature between each iteration.

Large temperature differences can sometimes exist between utilidor steam lines

and the utilidor walls. Temperature differences between surfaces cause heat flow

(radiosity) between surfaces is described by this equation:

1 - ε j *Q*j

δ kj

(

)

∑

= ∑ Fk - j σ *T*k4 - *T*j4

- *F*k - j

(113)

ε j *a*j * j *=1

where σ = Boltzmann's constant,

Fkj = viewfactor of surface *k *to *j*,

δkj = 1 if *k *= *j*, and = 0 if *k *≠ *j*.

The calculation of the radiation heat flux requires the cal-

a

1

b

culation of the radiation viewfactors between each radia-

tion surface. There are a number of procedures to make

5

these calculations (Siegel and Howell 1992). Emery et al.

(1991) made accuracy comparisons between several numeri-

2

4

cal approaches. However, none of the procedures are trivial

for complex geometries. For the two-dimensional analysis

of utilidors, the surfaces should be considered infinite in

3

depth. By using the finite element boundaries as the edges

c

of infinite strips, a special case of two-dimensional geom-

6

d

etry is obtained.

A relatively simple method can be used to obtain the

viewfactors for the case of infinite strips; known as Hottel's

crossed-string method (Siegel and Howell 1992), the procedure is developed as

follows. To obtain the viewfactor between surfaces 1 and 6 in Figure 10, first form

the triangle *abc *with the infinite strips 1, 2, and 3. The viewfactors between these

three surfaces can be written as

(114)

(115)

(116)

Multiply each equation by the area of its surface:

(117)

(118)

20

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