Thermal Lagging in Amorphous Media

Abstract

The lagging behavior of heat transport in amorphous media results from the finite time required for the significantly longer conducting path that energy carriers have to follow and the finite time required for establishing thermal equilibrium between the solid and the gaseous phases. As compared to heat transfer in a continuum, the presence of interstitial gases/fluids in amorphous media prevents the energy carriers from moving from hot to cold sides along a straight line. Instead of interpreting anomalous diffusion in amorphous media by fracton transport through percolating network in non-Euclidean geometry as in the past, the dual-phase-lag model is extended to describe the anomalous diffusion in terms of the ratio of the two phase lags (τ T and τ q ). The threshold values of τ T and τ q are determined for a number of amorphous media where the experimental data are available. The dual-phase-lag model is proven capable in describing the much slower rate of heat transport during anomalous diffusion, the non-Fourier but Fourier-like diffusion during the very early transient, as well as temperature overshooting in recovering Fourier diffusion at long times. It also offers an energy equation that can be used to optimize the conditions in thermal processing on amorphous media, exemplified by the proportional control posted at the end to suppress the unexpected temperature rise.Amorphous materials are noncrystalline in nature. Typical examples include the roughness layer in carbon samples, random assemblies of metal spheres, silica aerogels, and silicon dioxide. Unlike continuous structures in which heat transport is dominated by the characteristic length on a macroscopic level, heat transport in amorphous materials is dictated by the averaged size of holes and clusters, measured by the correlation length, which spans from mesoscale to microscale (from millimeters to nanometers). As compared to sand discussed in Chapter 6, where finer particles still exist and fill the interstitial gaps among the larger particles, amorphous media have more distinct solid and gaseous phases. The continuum models are not expected to reflect the mechanisms in microscale when used for describing the fast-transient behavior of heat transport in this type of medium, owing to the percolating networks that make the concept of macroscopic average difficult. In contrast to crystalline materials, amorphous materials do not possess a periodic lattice structure. The microscopic models assuming periodicity of lattices, therefore, are not expected to work either.