The effective thermal conductivity of packed beds of spheres for a finite contact area

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.