A mesoscopic numerical tool has been developed in this study for predictions of the effective thermal conductivities for microscale random porous media. To solve the energy transport equation with complex multiphase porous geometries, a lattice Boltzmann algorithm has been introduced to tackle the conjugate heat transfer among different phases. With boundary conditions correctly chosen, the algorithm has been initially validated by comparison with theoretical solutions for simpler cases and with the existing experimental data. Furthermore, to reflect the stochastic phase distribution characteristics of most porous media, a random internal morphology and structure generation-growth method, termed the quartet structure generation set ͑QSGS͒, has been proposed based on the stochastic cluster growth theory for generating more realistic microstructures of porous media. Thus by using the present lattice Boltzmann algorithm along with the structure generating tool QSGS, we can predict the effective thermal conductivities of porous media with multiphase structure and stochastic complex geometries, without resorting to any empirical parameters determined case by case. The methodology has been applied in this contribution to several two-and three-phase systems, and the results agree well with published experimental data, thus demonstrating that the present method is rigorous, general, and robust. Besides conventional porous media, the present approach is applicable in dealing with other multiphase mixtures, alloys, and multicomponent composites as well.
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.
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