The Emergent Behaviour of Thermal Networks and its Impact on the Thermal Conductivity of Heterogeneous Materials and Systems

The properties of thermal networks are examined to understand the effective thermal conductivity of heterogeneous two-phase composite materials and systems. At conditions of high contrast in thermal conductivity of the individual phases (k1 and k2), where k1 << k2 or k1 >> k2, the effective thermal conductivity of individual networks of the same composition was seen to be highly sensitive to the distribution of the phases and the presence of percolation paths across the network. However, when the contrast in thermal conductivities of the two phases was modest (k1 / k2 ~ 10-2 to 102) the thermal networks were observed to exhibit an emergent response with a low variability in the effective thermal conductivity of mixtures of the same composition. A logarithmic mixing rule is presented to predict the network response in the low variability region. Excellent agreement between the model, mixing rule and experimental data is observed for a range two-phase porous and granular media. The modelling approach provides new insights into the design of multi-phase composites for thermal management applications and the interpretation or prediction of their heat transfer properties.