| First, the fractal geometry theory and heat transfer in porous media are addressed. The focuses of this dissertation are involved in developing an analytical model for tortuous fractal dimension, a generalized model for the thermal conductivity of two-phase and three-phase porous media and the thermal conductivity of nanofluids.In Chapter 2, an analytical expression for the fractal dimension for tortuous capillaries in porous media is derived and found to be a function of porosity and microstructures of porous media. There is no empirical constant in the proposed fractal dimension. The present model for the fractal dimension is verified by a comparison with the available analogy model. The present model may have the potential and significance on fractal analysis of transport properties (such as the permeability, dispersion, thermal and electrical properties) in porous media.In Chapter 3, a generalized model for the thermal conductivity of two phase porous media is derived based on the self-similarity existing in porous media and thermal-electrical analogy technique. In this model, the geometry model, Sierpinski carpet, is chosen to approximate the statistically self-similar porous media. The Sierpinski carpets with the same side length L=13 and different cutout sizes C (=3, 5, 7 and 9) and the different fractal dimensions are adopted to model the real porous media in a wide range of porosities, 0.14~0.80. The present model for the thermal conductivity of porous media is found to be a function of the porosity (related to stage n of Sierpinski carpet), the ratio Ant / A of areas, the ratioβof component thermal conductivities, contact thermal resistance t + and microstructures L and C. This model has the least parameters, Ant / A and t +, compared to the other models and every parameter in this model has clear physical meaning. The model predictions are compared with the existing experimental data and other models', and the results show that the present model presents a good agreement with the existing experimental data in a wide range of porosities, 0.14~0.80. Furthremore, the proposed thermal conductivity model for two-phase porous media is then extended to analyze unsaturated/three-phase porous media. The Sierpinski carpets with side length L = 13 and cutout sizes C = 5, 7 and 9, respectively, depending on the porosity concerned. The recursive formulae are presented and expressed as a function of porosity, ratio of areas, ratio of component thermal conductivities, and saturation. The model predictions are compared with those of available experimental data, and good agreement between them in a wider range of porosities 0.14~0.60 is obtained.The effective thermal conductivity of nanofluids is studied in Chapter 4. First, the Monte Carlo simulations combined with the fractal geometry theory are performed. Based on the fractal character of nanoparticles in nanofluids, the probability model for nanoparticle's sizes and the effective thermal conductivity model are derived, in which the effect of the micro-convection due to the Brownian motion of nanoparticles in the fluids is taken into account. The proposed model is expressed as a function of the thermal conductivities of the base fluid and the nanoparticles, the volume fraction, fractal dimension for particles, the size of nanoparticles and the temperature, as well as random number. The predictions by the present Monte Carlo simulations are shown in good accord with the existing experimental data. Then, by taking into account the nanolayer and nanoparticles'aggregation, a new model for the effective thermal conductivities of nanofluids is proposed. This model is expressed as a function of the thickness of nanolayer, the nanoparticle size, the nanoparticle volume fraction and thermal conductivities of suspended nanoparticles and base fluid. The theoretical predictions on the effective thermal conductivities of nanofluids are shown to be in good agreement with the available experimental data. The validity of the proposed model is thus verified.
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