Modeling of heat transfer by fractal structures in porous media

Thermal conductivity plays a significant role in the heat transfer problems. Modeling of effective thermal conductivity of heterogeneous or composite materials is areas of interest. There are a lot of developed expressions for modeling of thermal conductivity in the literature. Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite difference and finite volume methods. The influences of the thermal conductivity of solid, the thermal conductivity of fluid, the porosity, the size and spatial distribution of pores on the effective thermal conductivity of these structures are analyzed in detail. The calculated results indicate that the relation of effective thermal conductivity with thermal conductivity of solid and thermal conductivity of fluid conforms to a power function, and the relation of effective thermal conductivity with porosity conforms to an exponential function. The porosity 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. Effective thermal conductivity values are obtained from finite difference and finite volume methods. The numerical results are compared with the available empirical formulas, and are verified by these empirical formulas.Key Words: Effective thermal conductivity, fractal model, porosity