Boming Yu

A fractal permeability model for bi-dispersed porous media

Abstract In this paper a fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the media. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. An analytical expression for the pore area fractal dimension is presented by approximating the unit cell by the Sierpinski-type gasket. The pore area fractal dimension and the tortuosity fractal dimension of the porous samples are determined by the box counting method. This fractal model for permeability does not contain any empirical constants. To verify the validity of the model, the predicted permeability data based on the present fractal model are compared with those of measurements. A good agreement between the fractal model prediction of permeability and experimental data is found. This verifies the validity of the present fractal permeability model for bi-dispersed porous media.

Analysis of Flow in Fractal Porous Media

The flow in porous media has received a great deal of attention due to its importance and many unresolved problems in science and engineering such as geophysics, soil science, underground water resources, petroleum engineering, fibrous composite manufacturing, biophysics (tissues and organs), etc. It has been shown that natural and some synthetic porous media are fractals, and these media may be called fractal porous media. The flow and transport properties such as flow resistance and permeability for fractal porous media have steadily attracted much attention in the past decades. This review article intends to summarize the theories, methods, mathematical models, achievements, and open questions in the area of flow in fractal porous media by applying the fractal geometry theory and technique. The emphases are placed on the theoretical analysis based on the fractal geometry applied to fractal porous media. This review article shows that fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media. A few remarks are made with respect to the theoretical studies that should further be made in this area in the future. This article contains 220 references.

A new model for heat conduction of nanofluids based on fractal distributions of nanoparticles

In this paper we report a new model for predicting the thermal conductivity of nanofluids by taking into account the fractal distribution of nanoparticle sizes and heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids. The proposed model is expressed as a function of the average size of nanoparticles, fractal dimension, concentration of nanoparticles, temperature and properties of fluids. The model shows the reasonable dependences of the thermal conductivity on the temperature of nanofluids, nanoparticle size and concentration. The parameter c introduced in thermal boundary layer depends on fluids, but is independent of nanoparticles added in the fluids. The model predictions are in good agreement with the available experimental data. The model also reveals that there is a critical concentration of 12.6% of nanoparticles at which the contribution from heat convection due to the Brownian movement of nanoparticles reaches the maximum value, below which the contribution from heat convection decreases with the decrease in concentration and above which the contribution from heat convection decreases with the increase in concentration.

A generalized model for the effective thermal conductivity of porous media based on self-similarity

A generalized model for the effective thermal conductivity of porous media is derived based on the fact that statistical self-similarity exists in porous media. The proposed model assumes that porous media consist of two portions: randomly distributed non-touching particles and self-similarly distributed particles contacting each other with resistance. The latter are simulated by Sierpinski carpets with side length L = 13 and cutout size C = 3, 5, 7 and 9, respectively, depending upon the porosity concerned. Recursive formulae are presented and expressed as a function of porosity, ratio of areas, ratio of component thermal conductivities and contact resistance, and there is no empirical constant and every parameter has a clear physical meaning. The model predictions are compared with the existing experimental data, and good agreement is found in a wide range of porosity of 0.14-0.80, and this verifies the validity of the proposed model.

Fractal Models for the Effective Thermal Conductivity of Bidispersed Porous Media

Two fractal models for determination of the effective thermal conductivity of bidispersed porous media are developed based on the fractal theory and electrical analogy technique. The theoretical predictions from the proposedfractalthermalconductivitymodelsarecomparedwiththosefromthepreviouslumped-parametermodel and from experimental data. Theresults from the proposed fractal models are shown to bein good agreement with both the lumped-parameter model and the experimental data.

The scaling laws of transport properties for fractal-like tree networks

The scaling laws of transport properties are very important for understanding the transport mechanisms of the fractal-like tree networks, which have received extensive attention recently. In this paper, we analyze the transport properties including electrical conductivity, heat conduction, convective heat transfer, laminar flow, and turbulent flow in the networks and also derive the scaling exponents of the transport properties in the networks. We show that the scaling laws are different for different transport processes and the scaling exponents are sensitive to microstructures of the networks. The models and results we present here may shed light on the transport mechanisms of the networks such as the natural systems, nanotube networks, microelectronic cooling networks, organisms, fracture networks in oil/water reservoirs, seepage flow in porous networks/media, etc., and might provide guidance for design of composites with the tree structures.

An analytical solution for transverse thermal conductivities of unidirectional fibre composites with thermal barrier

In this paper, an analytical expression for transverse thermal conductivities of unidirectional fibre composites with thermal barrier is derived based on the electrical analogy technique and on the cylindrical filament-square packing array unit cell model (C-S model). The present analytical expressions both with and without thermal barrier between fibre and matrix are presented. The present theoretical predictions without thermal barrier are found to be in excellent agreement with the existing analytical model and nomogram from the finite difference method (FDM), and in good agreement with existing experimental data. Furthermore, the present analytical predictions with thermal barrier can best fit the experimental data and can provide a higher accuracy than the finite element method (FEM). The validity of the present analytical solution is thus verified for transverse thermal conductivities of unidirectional fibre composites with thermal barrier.

A self-similarity model for effective thermal conductivity of porous media

A new model, the self-similarity model, for effective thermal conductivity of porous media is proposed based on the thermal–electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and contact resistance. A recursive algorithm for the thermal conductivity is obtained using the proposed model and is found to be quite simple. The predictions of the model are compared with those of other models and with existing measurements and good agreement was found. This proves that the proposed model is a valid one.

Fractal geometry model for effective thermal conductivity of three-phase porous media

An approximate model, a fractal geometry model, for the effective thermal conductivity of three-phase/unsaturated porous media is proposed based on the thermal-electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and saturation. The recursive algorithm for the thermal conductivity by the proposed model is presented and found to be quite simple. The model predictions are compared with the existing measurements. Good agreement is found between the present model predictions and the existing experimental data. This verifies the validity of the proposed model

A Fractal Model for Nucleate Pool Boiling Heat Transfer

A fractal model for nucleate pool boiling heat transfer is developed based on the fractal distribution of sites (areas) of nucleation sites on boiling surfaces. Algebraic expressions for the fractal dimension and area fraction of nucleation sites are derived