Numerical calculations of the thermal conductivities of composites; A 3-D model

A 3-D numerical finite-difference model to calculate the thermal conductivity of a composite with two or more constituents has been developed to better understand how the relative quantities and distributions of the component materials within a sample affect the whole sample conductivity. It is found that different distributions of similar components within a sample can yield whole sample conductivity differences greater than a factor of 2. Comparisons are made between the numerical model results and the geometric and real-space renormalization group theory (RSRG) models and the effective medium approximation (EMA) for random distributions. Although good agreement exists between the numerical model and the EMA for the ranges of constituent conductivities considered, the geometric and RSRG models give lower values.