This paper describes a three-dimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of poly-dispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20-30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and inter-particle contact areas controlled by confining stress are explored as variables to underscore the effects of micro- and macro-scales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The inter-particle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss-Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20-30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the inter-particle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particle-scale mechanism in macro-scale manifestation.
Bibliographical noteFunding Information:
Support for this research was provided by the basic science research program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0002414), the basic research project of the Korea Institute of Geoscience and Mineral Resources (KIGAM) funded by the Ministry of Knowledge Economy of Korea (No. 2010-8-0350), and the Yonsei University Research Fund of 2009 (No. 2009-1-0193) and North Carolina State University.
All Science Journal Classification (ASJC) codes
- Geotechnical Engineering and Engineering Geology
- Computer Science Applications