This work applies fractal percolation theory to examine the impact of
anomalous diffusion in short time-scale applications of random media.
It is shown that there exist three regimes of heat transport correspon
ding to transport over the basic percolation unit (particle), the frac
tal cluster, and the homogeneous medium. Scaling is performed to deter
mine the characteristic rime scales of anomalous diffusion. The depend
ence of these time scales on both material properties and structure is
examined to assess the impact of the anomalous diffusion regime on sh
ort time-scale energy transport. Additional criteria that determine th
e importance of anomalous diffusion relative to other transport phenom
ena and properties, such as radiation and thermal boundary resistance,
are established.