Numerical and Experimental Study of Anisotropic Effective Thermal Conductivity of Particle Beds under Uniaxial Compression

Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mechanical and Aerospace Engineering


Dr. Heng Ban


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.


This work made publicly available electronically on July 30, 2012.

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