Mingqing Zou

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 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

Fractal Model for Thermal Contact Conductance

A random number model based on fractal geometry theory is developed to calculate the thermal contact conductance (TCC) of two rough surfaces in contact. This study is carried out by geometrical and mechanical investigations. The present study reveals that the fractal parameters D and G have important effects on TCC. The predictions by the proposed model are compared with existing experimental data, and good agreement is observed by fitting parameters D and G. The results show that the effect of the bulk resistance on TCC, which is often neglected in existing models, should not be neglected for the relatively larger G and D. The main advantage of this model is the randomization of roughness distributions on rough surfaces. The present results also show a better agreement with the practical situation than the results of other models. The proposed technique may have the potential in prediction of other phenomena such as friction, radiation, wear and lubrication on rough surfaces.

Permeability of the fractal disk-shaped branched network with tortuosity effect

In this Brief Communication, the effective permeability of the fractal disk-shaped branched networks is derived and the relationship between the effective permeability and the geometry structures is analyzed in detail. It is found that the tortuosity has significant influence on transport properties of the network and that small variations in the geometrical structures can induce very large variations in the effective permeability. The effective permeability approaches zero as the diameter ratio β<0.5 for different length ratios γ. A comparison of the fractal disk-shaped branched network with the traditional parallel net indicates that the fractal disk-shaped branched network has a much stronger capability of fluid transport. The conductivity scaling law for the fractal disk-shaped branched network is obtained to be Ke∼Va, where the scaling exponent a=−(1∕2)ln(N∕γ)∕ln(γβ2), and the scaling exponent a depends on the microstructures of the network in a very wide range and a=1∕2 under the area-preserving con...

FRACTAL ANALYSIS OF HYDRAULICS IN POROUS MEDIA WITH WALL EFFECTS

The analytical expressions for the normalized average mass flux and pressure drop for power law fluids for wall effects in porous media are presented by using the fractal theory and technique for porous media. The proposed models are expressed as functions of power law index and structure parameters. These model predictions show that the proposed models can provide a good agreement with the experimental and other analytical results. This indicates that the fractal models may be helpful to much better understand the mechanisms of flow than other analytical models for porous media.

An Investigation on Transport Properties Near the Wall in Porous Media by Fractal Models

A comprehensive investigation on the wall effects on the transport properties, permeability, thermal conductivity, and thermal dispersion conductivity is performed, based on the fractal models for these properties and the porosity variations near the wall in porous media. The results show that the fractal models for transport properties of porous media can provide good agreement with the conventional models in the region near the wall in porous media. This indicates that the fractal models for transport properties of porous media also hold in the region near the wall in porous media if the wall effects are taken into account.

Fractal analysis of permeability near the wall in porous media

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahramis method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

A honeycomb model for tortuosity of flow path in the leaf venation network

A honeycomb model is designed according to the leaf veins, which is expressed as a function of porosity and tortuosity, and there is no empirical constant in this model. We mainly applied it to the leaf venation network, and the prediction in our model are compared with that from available correlations obtained by matching the numerical results, both of which are consistent with each other. Our model and relations may have important significance and potential applications in leaf venation and porous media. They also have a certain guiding significance to fluid heat transfer and thermal diffusion, as well as biotechnology research, e.g. veins and the neural networks of human.