A unit cell model for predicting the thermal conductivity of a granular medium containing an adhesive binder

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A unit cell model is proposed which can be used to predict the effective thermal conductivity of a granular medium composed of sand particles, a thermal binder, and air. The unit cell model is described by three dominant thermal conductances which account for the heat transport across the interfaces among the components comprising the medium. The stereological concept of contiguity is used to quantitatively link the macroscopic effective thermal conductivity to the microscopic interfacial contact area among the components. Utilizing a geometric model of a representative contact between two particles, an analytical expression for the contiguity is developed. This expression is used in the unit cell model to calculate the effective thermal conductivity of the medium as a function of the thermal conductivity of the components and their volumetric concentration. The predictive accuracy of the unit cell model for sand-like media is verified with numerous quantitative microscopic measurements and thermal conductivity data obtained with the transient, cylindrical probe technique. The unit cell model is applied to the design of thermal backfill materials. Both analysis and experiment demonstrate that thermally coupling contiguous sand particles with a binder can significantly increase the effective thermal conductivity of dry sand. Four basic microstructure regimes of the medium are identified, and these regimes are quantitatively related to the volume fraction of the binder. The greatest increase in the effective thermal conductivity with respect to the volume fraction of the binder is shown to occur in a regime where the sand particles become thermally coupled with the binder. The unit cell model identifies quantitative guidelines for the thermal conductivity and volume fraction of the binder that can be used to produce the greatest increase in the effective thermal conductivity of dry sand. Thus, the results of this study have practical application to the design and development of thermal backfill materials for increasing the heat transfer between the earth and underground heat sources such as buried electric power cables and ground source heat pump coils.