Permeability of fractal porous media by Monte Carlo simulations

The permeability of the fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size distribution in porous media, the probability models for pore diameter and for permeability are derived. Taking the bi-dispersed fractal porous media as examples, the permeability calculations are performed by the present Monte Carlo method. The results show that the present simulations present a good agreement compared with the existing fractal analytical solution in the general interested porosity range. The proposed simulation method may have the potential in prediction of other transport properties (such as thermal conductivity, dispersion conductivity and electrical conductivity) in fractal porous media, both saturated and unsaturated.     

Analysis of effective thermal conductivity for circular tubes made with porous media based on fractal theory

Accurately evaluating the relation between heat transfer performance and the complex structure of porous media is still a difficult task. Most previous fractal models of effective thermal conductivity (ETC) are developed to describe the heat-conducting characteristics of a unit cell or a representative elementary volume in porous media, and few models have paid attentions to the ETC for practical circular tubes made with a porous structure based on fractal theory. This paper proposes a new ETC model for a circular tube made with porous media based on fractals, and the validity of the present model is proved by previous models and testing data in the literature, then the effects of intrinsic thermo-physical properties of each component and pore structures on the ETC are discussed. The analysis results indicate that a circular tube made with porous media can improve its heat-insulating performance by about 25% compared with a common parallel circular tube. This can supply an alternative scheme for pipe insulation design in cold/hot fluid supplying systems or air conditioning systems.     

Fractal model for prediction of effective thermal conductivity of gas diffusion layer in proton exchange membrane fuel cell

The process of heat transfer within porous media is usually considered as a transport through large numbers of straight channels with uniform pore sizes. For the prediction of effective thermal conductivity of gas diffusion layer (GDL), morphological properties such as the tortuosity of channels and pore-size distribution of this porous layer should be considered. Thus in this article, novel parallel and series-parallel prediction models of effective thermal conductivity for the GDL in proton exchange membrane fuel cell (PEMFC) have been derived by fractal theoretical characterization of the real microstructure of GDL. The prediction of fractal parallel model for carbon paper, a basal material of the GDL, is in good agreement with the reference value supplied by Toray Inc. The prediction results from the proposed models are also reasonable because they are distributed between the upper and lower bounds. Parametric effect has been investigated by using the presented models in dimensionless formalism. It can be concluded that dimensionless effective thermal conductivity (k^′eff${k^{\prime }}_{\text{eff}}$) has a positive correlation with effective porosity (?) or the pore-area fractal dimension (D_p) when k_s/k_g < 1; whereas it has a negative correlation with ? or D_p when k_s/k_g > 1 and with tortuous fractal dimension (D_t) whether k_s/k_g < 1 or not. Furthermore, these fractal models have been modified by considering the effect of polytetrafluoroethylene (PTFE) incorporated into the pore spaces of carbon paper, and the corresponding model prediction shows that there is an increase in the effective thermal conductivity due to the filling of PTFE that has high thermal conductivity.     

含湿非饱和多孔介质的完全分形传热研究

为了探究在含湿情况下多孔介质有效导热率的变化,基于分形理论,考虑多孔介质在含湿时加热过程中相变的影响,结合加热过程中的热量守恒方程和傅里叶导热定律推导出计算有效导热率的新公式。将该模型相关数据代入进行计算,分析了孔隙率、含湿率、面积分形维数和迂曲分形维数对有效导热率的影响。研究发现,孔隙率与有效导热率呈负相关,含湿率与有效导热率呈正相关,分形维数与有效导热率呈负相关。该研究能够反映多孔介质内的传热进程,对于探究微孔结构物质的传热具有一定的指导意义。     

Study on effective thermal conductivity for porous media using fractal techniques

In this paper, the geometric structure of porous media is described using fractal techniques, and a section particle area fractal dimension d of a porous medium with various porosities is considered with a simplified model. Also an expression of the effective thermal conductivity for soil is presented via a fractal dimension and a model of heat transfer in soil. The results obtained in this paper indicate the effectiveness of the method for determining the effective thermal conductivity by using the section area dimension. © 2000 Scripta Technica, Heat Trans Asian Res, 29(6): 491–497, 2000     

多孔介质导热的分形模型

多孔介质中热量传递与多孔介质内部的几何结构有密切的关系，讨论了多孔介质的分形结构和相关的分形维数，利用能量方程，导出了分形维数为D的有限尺度多孔介质中的广义热传导方程，在此基础上，假定热量在多孔介质中的传导路线也是一种分形结构，提出了一个筒化的多孔介质并联通道分形导热模型，求出了基于分形理论的多孔介质有效导热系数表达式。     

Analysis of the effective thermal conductivity of fractal porous media

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.     

Simulation of laminar impinging jet on a porous medium with a thermal non-equilibrium model

This work shows numerical simulations of an impinging jet on a flat plate covered with a layer of a porous material. Macroscopic equations for mass and momentum are obtained based on the volume-average concept. Two macroscopic models are employed for analyzing energy transport, namely the one-energy equation model, based on the Local Thermal Equilibrium assumption (LTE), and the two-energy equation closure, where distinct transport equations for the fluid and the porous matrix follow the Local Non-Thermal Equilibrium hypothesis (LNTE). The numerical technique employed for discretizing the governing equations was the finite volume method with a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure–velocity coupling. Parameters such as porosity, porous layer thickness, material permeability and thermal conductivity ratio were varied in order to analyze their effects on flow and heat transport. Results indicate that for low porosities, low permeabilities, thin porous layers and for high thermal conductivity ratios, a different distribution of local Nusselt number at the wall is calculated depending on the energy model applied. The use of the LNTE model indicates that it is advantageous to use a layer of highly conducting and highly porous material attached to the hot wall.     

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Abstract

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2?D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.     

Asymptotic behaviors of heat transfer in porous passages with axial conduction

As reported in the literature, a sufficiently small Peclet number requires the inclusion of axial conduction within a fluid flowing in a duct. In fluid saturated porous ducts, this phenomenon greatly increases the heat transfer rate within the thermal entrance region. Axial conduction effects near the thermal entrance regions in parallel-plate ducts and in circular ducts are emphasized in this study. Having metallic foams as porous materials can cause the effective thermal conductivity to increase and this decreases the Peclet number. Here, a simple solution is being used for determination wall heat flux near the thermal entrance location and the result leads to a relatively simple correlation for determination of the bulk temperature.     

Effect of Conjugate Heat Transfer on MEMS-Based Thermal Shear Stress Sensor

ABSTRACT

The effect of conjugate heat transfer resulting from a microelectromechanical systems (MEMS)-based thermal shear stress is investigated. Due to the length-scale disparity and large solid–fluid thermal conductivity ratio, a two-level computation is used to examine the relevant physical mechanisms and their influences on wall shear stress. The substantial variations in transport properties between the fluid and solid phases and their interplay with regard to heat transfer and near-wall fluid flow structures are investigated. It is demonstrated that for state-of-the-art sensor design, the buoyancy effect can noticeably affect the accuracy of the shear stress measurement.     

The effect of the position of the heated thin porous fin on the laminar natural convection heat transfer in a differentially heated cavity

Laminar natural convection heat transfer in a differentially heated cavity with two thin porous fins attached to the hot wall and bottom insulated surface was studied numerically for various pertinent parameters. Such parameters include Richardson number, Darcy number, thermal conductivity ratio, and location of the porous fin. The left wall of the cavity is assumed to be uniformly heated while the right wall is kept at a lower temperature. In addition, the horizontal walls of the cavity were considered insulated. Furthermore, the governing transport equations within the porous media were written according to the volume-average theory. The governing equations are solved using a finite element formulation based on the Galerkin method of weighted residuals. The results of this investigation showed that the presence of a horizontal porous fin increases the average Nusselt number when compared with the differentially heated cavity for various Richardson numbers and thermal conductivity ratios. However, a vertical porous fin attached to the bottom insulated surface exhibited a lower average Nusselt number than the no-fin case.     

Simulation of a Turbulent Impinging Jet into a Layer of Porous Material Using a Two–Energy Equation Model

This article presents numerical results for a turbulent jet impinging against a flat plane covered with a layer of permeable and thermally conducting material. Distinct energy equations are considered for the solid porous material attached to the wall and for the fluid that impinges on it. Parameters such as Reynolds number, porosity, permeability, thickness, and thermal conductivity of the porous layer are varied in order to analyze their effects on the local distribution of Nu. The macroscopic equations for mass, momentum, and energy are obtained based on volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted nonorthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure-velocity coupling. Results indicate that inclusion of a porous layer eliminates the peak in Nu at the stagnation region. For highly porous and highly permeable material, simulations indicate that the integral heat flux from the wall is enhanced when a thermally conducting porous material is attached to the surface.     

多孔介质特性参数对燃烧温度及压力影响的数值模拟研究

考查了两段式多孔介质内预混气燃烧的温度与压力分布情况。建立了甲烷／空气预混气体在多孔介质内燃烧的二维数学模型,运用FLUENT软件求解瞬态控制方程的方法计算出燃烧稳定后多孔介质内的温度、与压力分布,并考查了不同当量比、多孔介质辐射衰减系数和导热系数对温度和压力分布的影响。结果表明,甲烷／空气预混气体在多孔介质中燃烧,当量比越大温度峰值越高,压力梯度越大;小孔介质辐射衰减系数的改变对温度分布和压力分布没有明显的影响,而大孔介质辐射衰减系数对温度分布和压力分布有较大的影响;增加多孔介质的导热系数,会使固相与气相温度均有所升高,燃烧区域压力降低。     

Non-Darcian Effects on the Mixed Convection Heat Transfer in a Metallic Porous Block with a Confined Slot Jet

The present numerical investigation addresses non-Darcian effects on the mixed convection heat transfer in a metallic porous block with a confined slot jet. The generalized model of the momentum equation, which is also known as the Forchheimer-Brinkman extended Darcy model, was used in representing the fluid motion inside the porous layer. The local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Our results revealed that the heat transfer performance of the slot jet was 2.4 times as large as that without the presence of a porous block. In addition, the average Nusselt number was found to increase with a decrease in porosity and an increase in the thermal conductivity ratio. The present results illustrate that the average Nusselt number increases with a decrease in the dimensionless height of the porous layer up to H _porous =  0.05 , after which the Nusselt number decreases.     

WALL HEAT CONDUCTION EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM

ABSTRACT

A numerical analysis has been made of the conjugate natural convection in a rectangular enclosure filled with a fluid-saturated porous medium and surrounded with four solid walls. The conductance of the walls is assumed to be much greater than that of the cavity filled with a porous medium. The main objective was to investigate the influences of the ratio of thermal conductivity of the wall to that of the fluid-porous matrix composite, the Darcy-modified Rayleigh number, the Prandtl number, and the aspect ratio. The streamlines and isotherms are presented; also, the local and average Nusselt numbers are presented along the interface between walls and cavity. A non-Darcian model was employed and the numerical method was SIMPLE-C. The numerical results indicate that the wall heat conduction effects decrease the heat transfer rate. When the wall heat conduction is considered, the greater the conductance of the solid walls surrounding the cavity, the greater is the rate of heat transfer.     

Analysis of two‐dimensional porous fins with variable thermal conductivity

Analysis of porous fins for their higher heat transfer in comparison with solid fins with identical volumes has attracted significant attention. In this paper, a two‐dimensional thermal analysis of a porous fin having variable thermal conductivity coefficient is performed using finite difference method. Heat transfer through porous media is simulated using passage velocity from Darcy's model. The thermal conductivity of the solid phase is considered as a linear function of temperature. It is found that the temperature profile of the fin is completely two‐dimensional even for high Rayleigh and Darcy numbers (Ra = 10³～10⁴, Da = 0.01), because the temperature changes significantly along the transverse axis especially for lower Rayleigh and Darcy numbers. Also, the effects of important nondimensional parameters such as Rayleigh and Darcy numbers, porosity, Nusselt, thermal conductivity, and aspect ratio on the temperature profile are investigated. The results demonstrate that the temperature distribution is strongly dependent on the Rayleigh and Darcy numbers.     

Optimization of Thermal Insulation Performance for the Porous Materials

ABSTRACT

Porous materials are widely used in porous media filtration, membrane separation, catalyst substrates, solid fuel cells, insulation, and other fields. When the porous material used in the field of insulation, heat transfer characteristics become its most important performance parameters. The heat transfer characteristics of porous material is a complex issue affected not only by solid elements and porosity, it is also affected by composite structures. Therefore, how to optimize the heat transfer properties of porous materials is a problem to be urgently solved. In this paper, the numerical method is used to study the effects of pore size, pore shape, pore connectivity, porosity and so on. It is found that pore shape, pore connectivity and gas conductivity have great impacts on the heat transfer of porous materials. The effect of pore arrangement is very little. The design optimization of porosity is affected by porous material mechanical property.     

Effect of solid thermal conductivity and particle–particle contact on effective thermodiffusion coefficient in porous media

Transient mass transfer associated to a thermal gradient through a saturated porous medium is studied experimentally and theoretically to determine the effect of solid thermal conductivity and particle–particle contact on thermodiffusion processes. In this study, the theoretical volume averaging model developed in a previous study has been adopted to determine the effective transport coefficients in the case of particle–particle contact configurations. The theoretical results revealed that the effective thermodiffusion coefficient is independent of the thermal conductivity ratio for pure diffusive cases. In all cases, even if the effective thermal conductivity depends on the particle–particle contact, the effective thermodiffusion coefficient remains independent of the solid phase connectivity. We also found that the porosity can change the impact of dispersion effects on the thermodiffusion coefficients. For large values of the thermal conductivity contrast, dispersion effects are negligible and the effective thermal conductivity coefficients are the same as the ones for the pure diffusion case.Experimental results obtained for the purely diffusive case, using a special two-bulb apparatus, confirm the theoretical results. These results also show that, for non-consolidated porous media made of spheres, the thermal conductivity ratio has no significant influence on the thermodiffusion process for pure diffusion. Finally, the particle–particle contact also does not show a considerable influence on the thermodiffusion process.     

Interfacial heat transfer coefficient for non-equilibrium convective transport in porous media

The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal non-equilibrium assumption. Macroscopic time-average equations for continuity, momentum and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). Interfacial heat transfer coefficients are numerically determined for an infinite medium over which the fully developed flow condition prevails. The numerical technique employed for discretizing the governing equations is the control volume method. Preliminary laminar flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.