Anomalous Heat Diffusion in a Chain of Large Particles Through Radiative Heat Transfer

Radiative heat transfer in particulate system has many applications in industry. Recently, the anomalous heat diffusion was reported for particulate system in near field thermal radiation heat transfer, and the existence of heat super-diffusive regimes was observed and the spread of heat can be described by Levy flight. In this work, attention is paid to investigate whether there is anomalous heat diffusion in far-field radiative heat transfer or not. Specifically, this study is focused on the radiative heat transport of a system, consisting of optically large particles, in the geometric optic range. Those particles are arranged in a linear chain surrounded by reflective walls and all particles are identical and equally spaced. The effect of the boundary type and particle surface emissivity on the heat diffusion is also investigated. The heat diffusion behavior in the far-field is studied based on Monte Carlo ray tracing method and the fractional diffusion equation in one dimension. The result indicates the existence of anomalous heat diffusion in the far-field by analyzing the asymptotic behavior of radiation distribution function (RDF). It’s shown that the distribution of RDF decays in power law and can be divided into two parts: for near the source particle, heat diffusive regime is super-diffusive (according to the analysis of fractional diffusion equation), while for far from the source particle, heat diffusive regime becomes sub-diffusive. Moreover, the kind of boundary type and particle wall emissivity have a significant influence on the heat diffusion of the far-field radiation heat transfer. This work will help the understanding of radiation heat transfer in particulate system in the far-field.