Lattice Boltzmann simulation and fractal analysis of effective thermal conductivity in porous media

Heat transfer in porous media has been attracting wide attention in a variety of scientific researches and engineering applications over the past decades. Due to the complexity of pore-solid microstructural features, an accurate simulation of heat transport process and evaluation of effective thermal conductivity in saturated porous media remain a great challenge. In this work, the lattice Boltzmann method (LBM) simulation of fluid-solid coupling heat transfer and a fractal model are adopted to study the thermal transport property in three-dimensional porous media. The accuracy and reliability of the proposed LBM simulation is validated by the effective thermal conductivity of a straight capillary tube, which analytical solution is available. The relation between effective thermal conductivity in porous media with different geometrical parameters based on the LBM simulation and fractal model are analyzed and discussed extensively. The result shows that the proposed LBM fluid-solid coupling simulation is an efficient tool to describe the heat transfer in complex porous media and the fractal dimension not only has an important effect on accurately estimating the effective thermal conductivity but also may be a useful parameter to determine the representative elemental volume (REV) of porous media. It is also found that compared with LBM simulation, the fractal model over predicates the effective thermal conductivity and the Maxwell model under predicates the effective thermal conductivity. The proposed LBM simulation and fractal model may reveal a better understanding for the thermophysical mechanisms of heat transfer in porous media.