5.3 Discrete Modeling of Pebble Radiation
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Fig. 5.35 Effective thermal conductivity for particle radiation of Sub-Cell radiation Model (SCM),
Short-range Radiation Model (SRM), and empirical correlations
Fig. 5.36 Total effective thermal conductivity (a) and radial temperature distribution (b) of the
packed pebble bed
It is shown in Fig. 5.36a that the results of SCM for total effective thermal conductivity (k eff = k r,SUB + k c ) are in good agreement with the experimental data. Both the
natural convection and axial heat transfer can be neglected [21], so one-dimensional
radial heat transfer model is formulated as
Q = −2πr Lk eff (T )
dT (r )
dr
(5.110)
where Q, r , and L are the heat power, radial distance, and height of the bed, respectively. The implicit analytical solution could be written as
T
0
k eff (T )dT =
T 2
0
k eff (T )dT +
Q
2π L
ln
r 2
r
,
(5.111)
where T 2 is the temperature at the outer wall and T 2 = 101.7
◦ C [21]. The radial
temperature profile can be calculated by interpolation, and the radial temperature