138
3 Experiments in Pebble Bed Heat Transfer
Fig. 3.10 Temperature curves of five azimuthal sets of the first (a) and the second (b) vacuum test,
the first (c) and the second (d) helium test (30 lines)
3.3.2.1 Derivation of Effective Thermal Diffusivity and Conductivity
Under Vacuum and Helium Conditions
As stated above, the effective thermal diffusivity and conductivity in a porous pebble
bed represent a combined heat transfer effect of solid heat conduction inside or
between fuel elements, thermal radiation between surfaces of adjacent spheres, and
helium-gas heat convection. The definition of the diffusivity is derived from the heat
conduction equation in the beginning. With a mixture-substance heat transfer, the
energy equation of control volume can be written as
d Q
dt
= ρ g V g C p,g
dT
dt
+ ρ v V v C p,v
dT
dt
(3.39)
where subscripts g and v indicate the graphite and void, respectively. The v will be
replaced as h for helium mixture. ρ and V are the density and volume, respectively,
and c p is the specific heat capacity. T is the temperature of this substance, and t is the
time. Q is the heat absorbed by the substance of volume V g + V v . In vacuum tests, the
void means the interspace of the graphite pebbles so that ρ v and c p,v are zero in the