A scaling law for heat conductivity in sheared granular materials

School of Civil Engineering, J05, The University of Sydney - Sydney, New South Wales 2006, Australia

Corresponding author: prognon@usyd.edu.au

Received: 13 January 2010
Accepted: 23 February 2010

Abstract

We investigate the heat transfer through the contact network of a sheared granular material using the standard Discrete Element Method. Elastic and frictional grains are subjected to steady and uniform plane shear. The effective conductivity tensor is expressed through the sum of contact conductances, which enables instantaneous measurements without simulating the actual heat transfer. We show that the conductivity i) does not depend on the inertial number I which controls the shear state, ii) increases with grain deformations (higher confining stress or lower Young's modulus) and iii) decreases for higher friction coefficients. We extract a robust semi-empirical scaling which quantitatively relates the conductivity to the contact density, Young's modulus and the part of the stresses that carries only the normal forces.