G. Buonanno et A. Carotenuto, The effective thermal conductivity of packed beds of spheres for a finite contact area, NUM HEAT A, 37(4), 2000, pp. 343-357
The upper and lower bounds of the effective thermal conductivity range of p
acked beds of spheres is evaluated using the theoretical approach of the vo
lume averaging method for a two-phase system. The solid mechanics and therm
al problems are resolved by considering the effects of superficial roughnes
s and pressure. The numerical solutions to the problem of thermal conductio
n through the periodic regular arrangement of stainless steel and aluminum
spheres in the air are determined using the finite element method. As regar
ds to the aluminum spheres, the influence of oxide stratum on the effective
thermal conductivity is also considered. Finally, empirical equations are
proposed for periodic regular arrangements of stainless steel and aluminum
spheres.