A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.