Measurements of in situ planetary thermal conductivity are typically made using long needle-like probes inserted in a planet's surface, which measure effective thermal conductivity (ETC) in radial direction (parallel to surface). The desired vertical (perpendicular to surface) ETC is assumed to be the same as the horizontal. However, ETC of particle beds in vertical and horizontal directions is known to be an anisotropic property under low compressive pressures. This study further examines the anisotropy of bed ETC under low and high compressive pressures in both vacuum and air environments. The ratio of vertical to horizontal stress, K0, is measured for the particles used in these experiments. A resistance network heat transfer model has been developed in predicting the vertical and the horizontal ETC as a function of applied compressive pressure. The model predicts vertical ETC by using only macro-contact thermal resistances for both high and low applied compressive pressure regimes. It is proposed that the vertical and horizontal ETC of particle beds under uniaxial compression is related by compressive pressures in each direction. The horizontal compressive pressure, which is perpendicular to the applied compressive pressure, can be calculated with the use of at-rest pressure coefficient and subsequently used in macro-contact thermal resistance to predict the horizontal ETC. The vertical ETC is obtained using the same model by substituting vertical compressive pressure into macro-contact thermal resistance. A two-dimensional axisymmetric finite element model in the COMSOL Multiphysics software package has been developed to simulate heat transfer coupled with structural deformation of spheres under compressive pressures in a simple cubic (SC) packing arrangement. The numerical model is used as a tool to predict the lower limit of bed ETC as well as validating thermal contact resistance used in the theoretical model. The predictions from the numerical model can be extended to particle beds with different packing arrangements.

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.