Three-dimensional effect on the effective thermal conductivity of porous media

A three-dimensional mesoscopic method is developed for predicting the effective thermal conductivity of multiphase random porous media. The energy transport equations are solved by a lattice Boltzmann method for multiphase conjugate heat transfer through a porous structure whose morphology is characterized by a random generation-growth algorithm. Our numerical results show that the cell number in the third dimension influences the resulting effective thermal conductivity of three-dimensional porous media. The predicted effective thermal conductivity varies with the cell number in the third dimension following an exponential relationship, and it requires in the examples at least 10 cells along the third dimension before the predictions stabilize. Comparisons with the experimental data show that the effective thermal conductivities measured by the hot-probe and hot-wire techniques agree well with the predicted results by the two-dimensional model, whereas those measured by the transient comparative method agree more with the three-dimensional predictions.