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

Abstract

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.

Electroosmosis in homogeneously charged micro- and nanoscale random porous media

“…Similar algorithms have been found in soil researches, named Markov chain Monte Carlo methods, which also created two-dimensional structures with satisfactory agreements with various scanned real soil structure images [43,44]. Borrowing the spirit of cluster growing theory [45,46], Wang et al have recently developed a random generation-growth method to generate random microstructures of various multiphase micro porous media including granular porous media [47,48] and fibrous porous media [49]. The generated structures have been used to predict effective thermal properties of porous materials and good agreements have been obtained with the existing experimental data [47,48].…”

“…The generated microstructure may be different from a real one in detail, but they have same structure characteristics in statistics. Several methods have been proposed to generate random porous structures in the past few years [36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Here we follow the random generation-growth model for reproducing multiphase granular porous microstructures [47,48] and develop the algorithm into three dimensional cases.…”

“…We extend the random generation-growth method for reproducing microstructures of random porous media, for granular porous media as examples [47,48], and the lattice Poisson-Boltzmann algorithm [62,63,65] into three dimensional cases. The present numerical set is then employed to analyze the influences of statistical characteristics of solid-media morphology, fluid phase property and surface potential on the EOF behavior in random porous media.…”

Transport properties of functionally graded materials

“…For instance, of dielectric permittivity of porous glass with different fillers reported by Sen et al 47 We have noticed that the measurement technique used by them was based on the twoelectrode method and it is equivalent to the hot probe technique found in thermal conductivity measurement. Early work has proved that such axis-symmetrical techniques are essentially two-dimensional techniques 48 so that the experimental data thus obtained are comparable to twodimensional predictions. We performed a two-dimensional QSGS process to regenerate the structure, and solved the corresponding governing equations by a D2Q9 LBM.…”

Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media

“…However, one can notice from the available data and images that the lowest-energy law is, but not always, the rule dominating the phase distributions of porous media where random factors may play more important roles, especially in micro porous media [18]. Wang et al [21,22] proposed a multi-parameter random generation-growth method, termed quartet structure generation set (QSGS), to replicate randomly distributed multi-phase granular porous media based on the cluster growth theory [7,23] and then investigated the thermal conductivity of isotropic porous media.…”