A numerical method is used to investigate the effects of particle sizes and orientations on the thermal conductivities of two-component composites. The method is based on a finite-difference simulation of the divided-bar thermal conductivity measuring device, and solves the steady-state heat-flow equation in two dimensions throughout a region representing the divided bar with included sample. Calculations are made for two-component particle sizes for two orientations and for random distributions. The results are compared with those from a geometric model in which the conductivity of the composite depends on the volume fractions of the different components and with conductivities calculated using real-space renormalization group theory (RSRG) and the effective medium approximation (EMA). The results show substantial differences between samples with different particle orientation and sizes. For the particular distributions examined here, differences of up to a factor of one and one-half occur in some instances.