SIMULATED EFFECTIVE THERMAL CONDUCTIVITY OF SINTERED, RANDOMLY PACKED SPHERES AND STATISTICAL STRUCTURES OF PACKINGS

Effective thermal conductivity of sintered spherical particles is estimated by a computer simulation. The simulation consists of (i) simulated random packing of equal spheres by a method of "rigid sphere free fall into a virtual box," (ii) finite element method (FEM) estimation of the thermal resistance of a "sintered" pair of spheres, and (iii) simulated heat conduction tests of a "random network, " as a model of sintered particles, of thermal resistors with the estimated resistance; these tests yield the effective conductivity of sintered spherical particle aggregates. Statistical structures of the random packings of spheres are examined. The random packings constructed are standard "loose random packings. " The cumulative diameter distribution of circles appearing on cross-sections of the packings is in complete agreement with the theoretical prediction for all three orthogonal directions, implying that the packing structures are isotropic. And, despite this result, the zenithal distribution of branch orientations deviates from a uniform one; more spheres are in contact with their neighbors at the zenithal angles of theta approximate to 45 degrees. The effective conductivities obtained are not isotropic but transversely isotropic, which is due to the deviation of branch orientations.