title: Anisotropic Compressive Pressure-Dependent Effective Thermal Conductivity of Granular Beds
Creators: name: Garrett, R. Daniel
Publisher: name: Utah State University
Year: 2011

description: In situ planetary effective thermal conductivity measurements are typically made using a long needle-like probe, which measures effective thermal conductivity in the probe‟s radial (horizontal) direction. The desired effective vertical thermal conductivity for heat flow calculations is assumed to be the same as the measured effective horizontal thermal conductivity. However, it is known that effective thermal conductivity increases with increasing compressive pressure on granular beds and horizontal stress in a granular bed under gravity is related to the vertical stress through Jaky‟s at-rest earth pressure coefficient. No research has been performed previously on determining the anisotropic effective thermal conductivity of dry granular beds under compressive uniaxial pressure.
The objectives of this study were to examine the validity of the isotropic property assumption and to develop a fundamental understanding of the effective thermal conductivity of a dry, noncohesive granular bed under uniaxial compression. Two experiments were developed to simultaneously measure the effective vertical and horizontal thermal conductivities of particle beds. One measured effective thermal conductivities in an atmosphere of air. The second measured effective thermal conductivities in a vacuum environment. Measurements were made as compressive vertical pressure was increased to show the relationship between increasing pressure and effective vertical and horizontal thermal conductivity. The results of this experiment show quantitatively the conductivity anisotropy for different materials.
Based on the effective thermal conductivity models in the literature and results of the two experiments, a simple model was derived to predict the increase in effective vertical and horizontal thermal conductivity with increasing compressive vertical applied pressure of a granular bed immersed in a static fluid. In order to gain a greater understanding of the anisotropic phenomenon, finite element simulations were performed for a vacuum environment. Based on the results of the finite element simulations, the simple derived model was modified to better approximate a vacuum environment. The experimental results from the two experiments performed in this study were used to validate both the initial simple model and the modified model. The experimental results also showed the effects of mechanical properties and size on the anisotropic effective thermal conductivity of granular beds.
This study showed for the first time that compressive pressure-dependent effective thermal conductivity of granular beds is an anisotropic property. Conduction through the fluid has been shown to have the largest contribution to the effective thermal conductivity of a granular bed immersed in a static fluid. Thermal contact resistance has been shown to have the largest influence on anisotropic effective thermal conductivity of a granular bed in a vacuum environment.
Finally, a discussion of future work has been included.