Thermal Conductivity of Two-Phase Solid Bodies

A survey has been made of equations for calculating the thermal conductivity of two-phase solid bodies based on Ohm’s law and the flux laws. Most of these equations can be reduced to the Fricke relationship for a two-phase medium containing the second phase as randomly distributed ellipsoids. Fricke’s relationship is applied to porous uranium dioxide and to cermets UO₂-metal with a structural orientation. First of all, in the case of UO₂, Loeb’s formula based on Ohm’s law is considered. Although physically inadequate, this formula is easily handled and used by almost all of the investigators: the thermal conductivity of UO₂ is corrected by introducing an empirical factor a multiplying the whole porosity of the oxide; a is generally determined by experimental measurements. The most probable value for α is 2.3 ± 0.5. By using the Fricke equation the a factor is justified and calculated. Second, the thermal conductivity of UO₂-Fe, and UO₂-Ni, containing 10, 20, and 30% metal by weight, is calculated, according to the parallel and perpendicular directions of “metallic veins,” using the Fricke mixture equation. Finally. the calculated values are compared with the experimental thermal dif-fusivity data measured along the two previous directions. The Fricke two-phase equation is found not to agree experimentally, especially at low temperatures. This discrepancy is probably due to the insufficiently precise mathematical formulation.