Heat conduction in granular porous media is a phenomenon that is relevant to a broad spectrum of problems in science and engineering disciplines including physical, earth, and biological sciences, to name a few. Effective thermal conductivity in granular porous media is a function of morphological features of the medium such as grain shape, grain size, and geometrical structure. Thermal contact resistance can also affect heat conduction due to topological features such as the surface profile of the grain. Furthermore, the compressive pressure and presence of different fluids in the pore space along with partial saturation can also dictate the nature of the effective thermal properties.
To study the effect of all these factors on the effective thermal conductivity of granular porous medium, we simulate heat conduction by developing a two-dimensional, parallel and thermal Lattice Boltzmann Method (T-LBM) simulator using existing open source libraries. We use this simulator on a digitally reconstructed, two-dimensional granular porous medium that is generated with an existing packing algorithm. We then conduct a progressive investigation by first, introducing thermal contrast resistance as surface roughness on the grains and study its effect on thermal conductivity. Second, we introduce thermal anisotropy in the system by inclusion of elliptical grain packing in the medium. Third, we investigate the effect of partial saturation of water and air in pore space. We use an LBM single component multiphase model to simulate phase segregation in the pore space. We also incorporate elastic deformation of grains based on an existing model, which depicts the surface topology of grains as a self-affine fractal function. This elastic deformation is a function of Young's modulus of the grains and the external compressing pressure.
Based on our investigation, we observe that thermal contact resistance due to the surface roughness of grains reduces effective thermal conductivity. Elliptical packing of grains, manifest thermal anisotropy in the system and causes local heat flux deviations especially when the grain orientation angle changes. External compressive pressures cause elastic deformation of the grain surface and enhance the thermal conductivity of grains with lower Young’s modulus. Introducing partial saturations of water and air in the pore space offsets the effective contribution in heat conduction from the grains as well as the effect of compressing pressure. All of these observations are further accentuated if the thermal contrast ratio of the granular porous medium is changed. We also compare results for selected observations for consistency. A qualitative agreement is obtained with the existing experimental data.
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