Expression for ETC of the solid phase of randomly packed granular materials

•An expression for ETC of the solid phase of granular material is derived.•ETC is expressed in terms of grain size distribution and compressive strain.•The predicted ETC is compared with the numerical result obtained by FEM.

Effective thermal conductivity (ETC) is an important parameter describing the thermal behavior of particulate materials, and has been extensively examined in the past decades. In this paper, a theoretical model called parallel-column model is proposed and based on this model, an analytical expression is developed to predict the ETC of the solid phase of granular materials. The ETC is expressed in terms of particle size distribution, the compressive strain and thermal conductivity of individual particle. Different types of contact force models and grain size distribution is incorporated into the parallel-column model and the expression for ETC is derived for different types of contact force models and grain size distribution.

Graphical abstract(a) The schematic of thermal and mechanical boundary conditions imposed on the granular sample. (b) The schematic of pipe-network model. (c) Schematic of the parallel-column model.Figure optionsDownload full-size imageDownload as PowerPoint slide