5.3 Discrete Modeling of Pebble Radiation
297
to-conduction ratio ξ is proposed here for quantifying the relative contribution of
thermal radiation to conduction, which is defined as
ξ =
k r,SCM
k c
(5.136)
When the radiation-to-conduction ratio is higher than 1, i.e., ξ > 1, the radiative
ETC is the dominant part of the heat transfer of the bed. For the cases shown in
Figs. 5.48 and 5.49, ξ are 6.3 and 2.3 at 800
◦ C, respectively. However, for the beds of
small-sized particles, ξ may be far lower than 1 at low temperature ranges, i.e., ξ 1
and the radiation is negligible. Another demonstration case is given in Fig. 5.50. The
densely packed bed filled with FAM-Z02 spheres of 2.0 mm in diameter is operated
in the temperature range of 10–80
◦ C [92]. The emissivity is set at 0.9 in SCM and
k c is about 0.19 W/(m·
◦ C). The radiation-to-conduction ratio ξ is 0.049 at 10
◦ C,
which slightly increases to 0.092 at 80
◦ C. Practically, it can be concluded that the
thermal radiation of the pebble bed is an essential part to be considered when the
radiation-to-conduction ratio ξ > 0.1 for accurate evaluation.
Fig. 5.50 The total effective thermal conductivity and its radiation part for packed bed under low
temperature ranges