Discrete Modeling of Heat Conduction in Granular Media

This thesis addresses heat conduction in granular systems both under static and slow flow conditions with and without the presence of astagnant interstitial fluid. A novel discrete simulation technique for granular heat transfer, the Thermal Particle Dynamics (TPD) method hasbeen developed. By modeling particle-particle interactions, bed heterogeneities -- e.g., mechanical and thermal -- are directly accountedfor and transient temperature distribution are obtained at the particle level. This technique, based on the Discrete Element Method, not onlysheds light on fundamental issues in heat conduction in particulate systems, but also provides a valuable test-bench for existingcontinuous theories. Computational results, as well as supporting experiments coupled with existing theoretical models are used to probethe validity of the proposed simulation technique. Studies on heat conduction through static beds of particles indicate that stress and contact heterogeneities -- due primarily to theexistence of localized ``chains' of particles which support the majority of an imposed load (stress chains) -- may cause dramaticchanges in the way that heat is transported by conduction. It is found that by matching the microstructure of an experimental system onlyqualitatively, quantitatively accurate estimates of effective properties are possible, without requiring adjustable parameters. Onekey result in this study reveals that an important consideration has been missing from previous granular conduction studies -- the stressdistribution in the particle bed. Extensions of TPD to incorporate the ability to model heat transfer in particulate systems in the presenceof an interstitial fluid indicate that a good qualitative and quantitative agreement between measured and calculated values of theeffective thermal conductivity for a wide variety of materials in the presence of both liquid and/or gas are possible. Simulation results for slow granular flows -- e.g., simple shear cell and a rotating drum -- indicate that in both cases there is anenhancement of the effective thermal conductivity with increase in the shear rate due to enhanced mixing of the particles. These results arein agreement with previous theoretical and experimental investigations. In contrast to the behavior found at high shear rates, where the thermal conductivity is proportional to the shear rate, a complex non-linear relation is found for the effective conductivity in granular flows at low shear rates. This observation has not beenpreviously reported. It is argued that a balance between heat conduction and convection is necessary to explain these observations