The scope of this paper is to demonstrate the ability of a radial temperature model for spherical particles to allow for the calculation of the thermal behavior of granular assemblies with large particle numbers using Discrete Element simulations. The model efficiently accounts for inner particle heat transfer and is based on an analytical solution of the differential equation of heat conduction for a solid spherical particle with time and radius as independent parameters. It avoids the high computational costs of a numerical solution as well as the shortcoming of the assumption of uniform temperature profiles. To account for conduction due to multiple particle-particle or particle-wall contacts, each particle is divided into segments. Contact heat transfer on the particle scale is analyzed, comparisons with numerical solutions of Siu and Lee  for a contact of two spheres and a contact of a sphere with a wall were made for the adjustment and verification of the model. Results of a Discrete Element simulation using the radial temperature model for spheres stirred by moving walls are presented.
A New Approach to Simulate Transient Heat Transfer Within the Discrete Element Method
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Rickelt, S, Wirtz, S, & Scherer, V. "A New Approach to Simulate Transient Heat Transfer Within the Discrete Element Method." Proceedings of the ASME 2008 Pressure Vessels and Piping Conference. Volume 4: Fluid-Structure Interaction. Chicago, Illinois, USA. July 27–31, 2008. pp. 221-230. ASME. https://doi.org/10.1115/PVP2008-61522
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