380
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.119 Effective thermal conductivity of thermal radiation of SC packing with spheres of 60 mm
in diameter at ε r = 1.0
The effective thermal conductivity of thermal radiation k e,struc can be obtained
by Eq. (5.247) without boundary effects in an infinite region or by Eq. (5.249) in
finite region. For the SC packing, the numerical results with ε r = 1.0 are shown in
Fig. 5.119. The computed radiation exchange factor is F = 1.18 with all surrounding
spheres in infinite regions, which is in good agreement with the data given by [46]
with F = 1.13.
In addition, for the beds of BCC and FCC packing in an infinite region, the
radiation exchange factor is F = 0.915 and 0.873, respectively.
Cubic Particle Packing
In addition, in the packed bed of cubic particles (Fig. 5.120), where L is the edge
length and s is the gap width, the thermal radiation becomes a short-range interaction
at s → 0. In this case, based on Eqs. (5.243) and (5.246), the effective thermal
conductivity in the infinite region is formulated as
k e = 4σ ε r T
3 L
(5.255)
and the radiation exchange factor is
F =
k e
4σ ˆ
d p T 3
= ε r
π
6
1
3
(5.256)