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In this paper, a fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media is derived. The determined imbibition height and imbibition mass of capillary rise are in satisfying agreement with the existing models reported in the literature. It is found that the imbibition height and imbibition mass of capillary decreases with increasing relative roughness. Besides, it is observed that the equilibrium time in a single tortuous capillary with roughened surfaces decreases with an increase in relative roughness. In addition, it is seen that the imbibition height and imbibition mass of capillary rise increases with imbibition time. With the proposed fractal model, the physical mechanisms of capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media are better elucidated. One advantage of our fractal analytical model is that it contains no empirical constant, which is usually required in previous models.

The properties of nanoparticles and its aggregation as well as convective heat transfer of nanofluids have received great attentions over the last few decades. It is well certified that nanoparticles and its aggregation can be successfully described by fractal geometry theory and technology. In this review, the fractal properties of nanoparticle and its aggregation are firstly introduced, and then the recent investigations on the fractal models and fractal-based approaches that applied for effective thermal conductivity, convective heat transfer, critical heat flux and subcooled pool boiling of nanofluids, fractal clusters and yield stress property of nanoparticle aggregation are summarized.