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5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.31 Effective thermal conductivity for particle radiation of short-range radiation model and
empirical correlations
Fig. 5.32 Sub-cell of the
particle and the Voronoï cells
(a) and the face-face thermal
radiation (b)
were very close to each other (see Fig. 5.31b), only the Face-Centered Cubic (FCC)
packing was applied in Sub-Cell radiation Model (SCM). The particle and the Voronoï
cell were divided into 12 identical parts, which is shown in Fig. 5.32.
The radiation flux between the two surfaces (surface 1 and surface 2) was assumed
to be independent of any others. Thus, surface 3 shown in Fig. 5.32b is a reradiating
surface. The thermal resistances of the face-to-face radiation are shown in Fig. 5.33
and the total thermal resistance can be expressed as
R =
1 − ε r,1
ε r,1 A 1
+
1
A 1 V 12
−1
+
1
A 1 V 13
+
1
A 2 V 23
−1
−1
+
1 − ε r,2
ε r,2 A 2
(5.104)
The view factor should be V 12 + V 13 = 1 and V 13 + V 23 . Thus, the thermal radiation flux between the two surfaces is