Analysis of the effective thermal conductivity of fractal porous media

Abstract

Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite volume method (FVM). The influences of the thermal conductivity of solid k s, the thermal conductivity of fluid k f, the porosity ε, the size and spatial distribution of pores on the effective thermal conductivity k e of these structures are analysed in detail. The calculated results indicate that the relation of effective thermal conductivity k e with thermal conductivity of solid k s and thermal conductivity of fluid k f conforms to a power function, and the relation of effective thermal conductivity k e with porosity ε conforms to an exponential function. The porosity ε is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influence. The numerical results are analysed by comparing with the available empirical formulas from literatures, and provide verification of these empirical formulas.