Thermal Conductivity Model of Powders under Vacuum Based on Experimental Studies

Introduction: The thermal conductivity of powdered media is characteristically very low in vacuum, and is effectively dependent on many parameters of their constituent particles and packing structure. Understanding of the heat transfer mechanism within powder layers in vacuum and theoretical modeling of their thermal conductivity are of great importance for several scientific and engineering problems. In the context of planetary sciences, thermal conductivity of regolith layers on air-less planetary bodies controls near-surface temperature. Thermal evolution of porous and dust-aggregated planetesimals depends on their thermal properties. Thermal conductivity of powdered material layers under a vacuum environment depends on many parameters, such as grain size, porosity, compressional stress, and temperature [1]. Under vacuum, effective thermal conductivity is dominated by “solid conductivity” originating from thermal conduction through inter-particle contact, and “radiative conductivity” originating from thermal radiation through void spaces between the particles. Because both the solid and radiative conductivity vary widely depending on intricately interconnected parameters and the relationship between them has not been systematically investigated, it has been difficult to predict the effective thermal conductivity of powders under vacuum. A model that comprehensively relates the thermal conductivity of powders to their physical parameters and ambient conditions is required. In this study, we developed a comprehensive model for the thermal conductivity of powdered materials under vacuum conditions based on systematic experimental studies using analogue materials. We report on the experimental results to reveal heat taransfer mechanism in powders under vacuum. Theoretical modeling of the effective thermal conductivity of powdered materials and comparison with our experimental data are also presented. Experiments: Six types of glass beads with different particle size were used as analogue materials. Table 1 shows some sample properties. Five FGB glass beads were used for investigating the effect of the grain size. EMB glass beads had highly adhesive nature, so that they were used to investigate the effect of the packing porosity as well as the grain size. Thermal conductivity of these samples was measured by the line heat source method. A nichrome wire (180 μm in diameter) was suspended in a sample conttainer and its temperature during the heating was measured by a K-type thermocouple. Vacuum level during the measurements was less than 10 Pa. A vacuum chabmer was placed in a thermostatic chamber so that we could control temperature of the whole system from 250 to 330 K. Temperature dependent thermal conductivity data were fitted by a theoretical equation of k(T) = A km(T) + B T, where T is temperature, km(T) is a thermal conductivity of solid materials given in Table 1, A and B are fitting variables. The first term represents solid conductivity, and the second is radiative conductivity. This fitting procedure enabled us to evaluate solid and radiative conductivity separately for each sample, and to investigate the effect of the grain size and porosity on the solid and radiative conductivities. Experimental data: We briefly describe the experimental results. The data were shown in Fig. 2 in terms of the grain size and porosity, together with our model estimations. Solid conductivity of the FGB glass beads appeared to be either independent of the particle size or slightly increased with the particle size. However, EMB glass beads had higher solid conductivity than the FGB glass beads by an order of magnitude. This large discrepancy is expected to be caused by strong adhesive nature of the small EMB particles, which enhanced inter-particle contact area by the adhesive (van der Waals) force in addition to self-weighted compressional force. Moreover, we found microscopic roughness on FGB particles by SEM images, which reduces the contact area or solid conductivity. Radiative conductivity of FGB glass beads increased with increasing the grain size. In addition, we also found that the radiative conductivity becomes higher with increasing the porosity from the data for Table 1: Sample properties. km(T) is temperature-dependent thermal conductivity of constituent glass. ID Grain size [μm] Porosity km(T) [W/mK] FGB-20 710-1000 0.42