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     

Determination of effective thermal conductivity for real porous media using fractal theory

INTRODUCTIONPorousmediaisacompositemediathatincludessolidframeandfluidandexistedwidelyintheeajrthbiosphere.Heatandmasstransferinporousmediaisbothanaturalphenomenoninearthbiosphereandaphysicalchemistryprocessinindustries,agricultureandhumanlife.Thusthestudyonheatandmasstransferinporousmediahasbecomeanimportanttasktoscielltistsandengineers.Heatandmasstransferinporousmediaisaverycomplexobject.Therearestillmanydifficultiestodescribethecoupledheatandmasstransferphenomena.Amongthesedifficultie…     

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.     

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.     

Influence of moisture content on measurement accuracy of porous media thermal conductivity

The thermal conductivity measurement accuracy of sand was experimentally studied with a hot disk thermal constant analyzer and water morphologies, distribution, and evolution at the pore scale were observed with a charge coupled device (CCD) combined with a microscope. It was found that thermal conductivities of samples with low moisture content (<25%) could not be accurately measured. For samples with low moisture content, the analysis showed that the water in the region adjacent to the analyzer sensor mainly existed as isolated liquid bridges between/among sand particles and would evaporate and diffuse to relatively far regions because of being heated by the sensor during measurement. Water evaporation and diffusion caused the sample constitution in the region adjacent to the sensor to vary throughout the whole measurement process, and accordingly induced low accuracy of the obtained thermal conductivities. Due to high water connectivity in pores, the rate of water evaporation and diffusion in porous media of high moisture content was relatively slow when compared with that of low moisture content. Meanwhile, water in the relatively far regions flowed back to the region adjacent to the sensor by capillary force. Therefore, samples consisting of the region adjacent to the sensor maintained the constant and thermal conductivities of porous media with relatively high moisture content and could be measured with high accuracy. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20272     

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。     

Effective thermal conductivity of highly porous two-phase systems

A theoretical expression for predicting effective thermal conductivity (ETC) of highly porous two-phase systems has been developed. The porous system has been assumed to contain particles of irregular shape, being dispersed randomly within the continuous medium. The concept of averaging the temperature field within different phases has been used. Resistor model has been applied to determine ETC of two-phase porous systems, as a porous medium is neither composed of slabs parallel nor perpendicular to the heat flux. It is proposed to use slabs inclined at an angle θ with the heat flux lines. An effort is made to correlate angle of inclination θ in terms of the ratio of thermal conductivity of the constituent phases and the physical porosity. Best-fitted expression so obtained for θ is used in the derived model and found that the predicted values of ETC are quite close to the experimental results.     

超级绝热材料气凝胶的纳米孔结构与有效导热系数

根据气凝胶的纳米孔结构特点,采用由小球体构成的立方阵列单元体结构,建立了描述纳米孔超级绝热材料气凝胶的气固耦合导热模型。计算结果表明气凝胶的纳米孔结构和固体颗粒纳米尺寸效应以及高的比表面积值是导致材料具有极低导热系数的主要因素。气凝胶存在具有最低导热系数的最佳密度。在高温下辐射传热是气凝胶传热的主要方式,通过渗碳等遮光处理会显降低气凝胶在高温下的导热系数。     

Influence of 2-D nanofillers on the thermal conductivity of composite PCMs

为了探究两种不同二维纳米填料对复合相变材料导热系数的影响,分别制备了以石墨烯纳米片和六方氮化硼纳米片为填料的石蜡基复合相变材料.采用瞬态平面热源法在20 ℃时测量了不同添加量下复合相变材料的导热系数.结果显示,石蜡基复合相变材料的导热系数随纳米填料添加量近似线性增长;六方氮化硼纳米片对复合相变材料导热系数的提升远低于石墨烯纳米片.此外,利用基于有效介质模型的预测公式与试验值进行了比较,计算发现形状,大小和导热系数相近的两种纳米材料,六方氮化硼纳米片的界面热阻却高出石墨烯纳米片两个数量级,是后者具有更显著强化效果的原因之一.     

A simple analytical model for calculating the effective thermal conductivity of nanofluids

A simple mathematical model for calculating the effective thermal conductivity of nanofluids has been developed based on the thermal resistance approach. The model is developed by considering both effects of a solid‐like nanolayer and convective heat transfer caused by Brownian motion which have not been considered simultaneously by most available models in the literature. In addition the correlation of Prasher and Phelan for the convective heat transfer coefficient is modified to take into account the effect of the solid‐like nanolayer. In addition a general value for n (different from the one presented by Tillman and Hill) is introduced to modify the thickness of the solid‐like nanolayer. The latter is done by considering both conduction and convection heat transfer mechanisms. Comparisons with previously published experimental results and other mathematical models show that the presented model could well predict a nanofluids effective thermal conductivity as a function of the nanoparticles mean diameter, volume fraction, and temperature for different kinds of nanofluids. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20290     

Enhanced thermal conductivity of copper-doped polyethylene glycol/urchin-like porous titanium dioxide phase change materials for thermal energy storage

A composite phase change material (PCM) of copper-doped polyethylene glycol (PEG) 2000 impregnated urchin-like porous titanium dioxide (TiO₂) microspheres (PEG/TiO₂) was successfully synthesised. The urchin-like porous TiO₂ structures contain hollow cavities that can provide a high PEG loading capacity of up to 80 wt%. Copper nanoparticles were uniformly dispersed on the outer and inner surfaces of the 0.8PEG/TiO₂ as additives to enhance the thermal conductivity of the composite PCM. The latent heat of the Cu/PEG/TiO₂ porous composite PCM reached 133.8 J/g, and the thermal conductivity was 0.58 W/(mK), which was 152.2% higher than that of TiO₂ and 38.1% higher than 0.8PEG/TiO₂. Moreover, the Cu/PEG/TiO₂ porous composite PCM has excellent thermal stability and reliability.     

Permeability and effective thermal conductivity of bisized porous media

In the region of minimum porosity of particulate binary mixtures, heat exchange and permeability were found to be higher than the ones obtained with a mono-size packing built with the same small size particles used in the binary packing. This effect was noticed in the range of the particles size ratio 0.1–1.0.The obtained improvement on thermal performance is related to the increase of effective thermal conductivity (ETC) in the binary packing and to the increase in transversal thermal dispersion due to the porosity decrease and tortuosity increase.Permeability can increase by a factor of two, if the size ratio between small and large spheres of a loose packing stays in the range 0.3–0.5.     

Measurement of dough effective thermal conductivity using an integrated thermocouple during the bread baking process

The present study produced an integrated thermocouple in order to gain an understanding of the heat transfer mechanism during baking. The thin film thermocouple was made by depositing copper‐nickel on a polyimide sheet base, and five hot junctions were arranged at regular intervals. Thermal electromotive force was proportional to the temperature difference between the reference and hot junctions. The study also used the integrated thermocouple to investigate heat transfer properties during baking that are equivalent to effective thermal conductivity, which include latent heat transport, water vapor diffusion, and heat conduction. The effective thermal conductivity crumbs increased according to the latent heat transportation effect caused by water vapor diffusion, and the thermal conductivity of crust was in agreement with its effective thermal conductivity value measured by the steady state parallel plate method. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 373–385, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20165     

A comprehensive study on thermal conductivity of the lithium-ion battery

The reliable thermal conductivity of lithium-ion battery is significant for the accurate prediction of battery thermal characteristics during the charging/discharging process. Both isotropic and anisotropic thermal conductivities are commonly employed while exploring battery thermal characteristics. However, the study on the difference between the use of two thermal conductivities is relatively scarce. In this study, the isotropic and anisotropic thermal conductivities of the four commercially available lithium-ion batteries, ie, LiCoO₂, LiMn₂O₄, LiFePO₄, and Li (NiCoMn)O₂, were reviewed and evaluated numerically through the heat conduction characteristics inside the battery. The results showed that there are significant differences in the temperature distribution in the battery caused by the isotropic and anisotropic thermal conductivities, which could affect the layout and cooling effectiveness of battery thermal management system. Furthermore, the effective thermal conductivities of porous electrodes and separator were determined to establish thermal conductivity bounds of lithium-ion batteries combined with the thicknesses of battery components. The thermal conductivity bounds could be applied to evaluate the rationality of the thermal conductivity data used in battery thermal models.     

高孔隙率泡沫金属复合相变材料有效热导率的预测

基于十四面体泡沫金属的单元晶胞结构,提出了一种高孔隙率开孔泡沫金属复合相变材料有效热导率的预测模型。热量沿热流方向在金属骨架和填充介质中并行传递,推导得出包含结构参数f(节点边长与韧带半径之比)和d(韧带半径与韧带长度之比)的有效热导率计算式。在孔隙率0.889 0≤ε≤0.977 0,针对单元晶胞的十六分之一结构,采用数值模拟的方法并结合实验数据的对比分析,校正了与有效热导率紧密相关的两个无量纲参数f和d,并以孔隙率的二阶多项式拟合出f变量的函数关系,以孔隙率的三阶多项式拟合出d变量的函数关系,从而确定出有效热导率的预测模型。通过与其他几种预测模型和实验数据的比较分析,结果表明：验证了当前预测模型具有较高的正确性和有效性,与实验值的平均相对误差ARD和相对均方根误差RMS分别为2.93%和3.50%,相对其他模型具有更高的预测精度。     

A novel method used to study growth of ash deposition and in situ measurement of effective thermal conductivity of ash deposit

Ash deposition always brings boilers some trouble due to fouling or slagging. In this paper, a completely controlled system was developed to study the growth of ash deposit. A novel sampling probe was designed to online measure the heat flux through ash deposit. Additionally, the thickness of ash deposit can be obtained by an online figure collecting system. The results of this research showed that as the thickness of ash deposit increased, the heat flux decreased. It was also found that at the initial stage of ash deposition when the thickness of ash deposit is approximately 1 mm, the heat flux through ash deposit had a sharp reduction. An effective method was attempted to situ measure the effective thermal conductivity of the ash deposit in the simulated combustion flue gas. It was found that temperature of the ash deposit layer had no obvious effect on its value. It was concluded that the structure of ash deposit had no obvious change in a short deposition time of 30 min with varied surface temperatures of the probe head between 400 °C and 600 °C.     

Numerical simulation of the effective thermal conductivity of wet clothing materials

Clothing materials may be considered composite materials composed of fiber, air, and moisture. For this paper, effective thermal conductivities of wet clothing materials were analyzed numerically using a proposed heat transfer model. The following simplifications were introduced. The clothing material fiber is woven with a single yarn, there is no air movement between fibers, and mass transfer is neglected. Numerical calculations were made using finite difference equations for steady three-dimensional heat conduction for several composite materials representing wet clothing materials. The main results obtained were as follows. The effective thermal conductivity of wet clothing material increases as the thermal conductivity of the yarn and the moisture content increase. We found that our numerical results agree qualitatively with those previously measured. The effective thermal conductivity of a wet layered material depends on the distribution of moisture and attains a maximum in the wet layer. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(3): 243–254, 1998     

Investigation on the thermal performance of phase change material/porous medium‐based battery thermal management in pore scale

With the latent heat, the phase change material (PCM) is widely used in battery thermal management (BTM) to control the temperature. In this paper, the porous medium is employed to enhance the heat transfer of PCM. The lattice Boltzmann model for PCM/porous medium in pore scale is considered, where the mesh system with porous medium (fixed point) is generated by quartet structure generation set (QSGS) method. The effects of the Rayleigh number and porosity on the heat transfer process in BTM are investigated. The results show that decreasing the porosity will accelerate the melting rate. When the porosities are 0.9, 0.8, 0.7, and 0.6, the total melting times are decreased by 23.7%, 43.3%, 58.0%, and 75.4%, compared with pure PCM. The heat is transferred through the high‐conductivity framework. The natural convection in the porous medium is weak, and the conduction is the dominated heat transfer. As a result, the area of solid–liquid interface will be increased, and the heat‐transferred rate is accelerated. However, when the Rayleigh number is raised to 10⁵, applying the porous medium with porosity of 0.9 will increase the total melting time, resulted from the stronger natural convection of PCM. The present study is helpful for design of PCM/porous medium‐based BTM.     

Numerical study of effective parameters on the drying process in a vertical porous channel

Comprehensive understanding of evaporation in porous channels is important for the design of modern heat exchangers and thermal systems such as heat pipes. This paper presents a numerical study of evaporation in a vertical porous channel. The volume of the fluid method was applied to capture the interface between phases. The multi‐dimensional limiter for explicit solution method, in which there are additional constraints based on the flux‐corrected transfer method, was used to solve the interface transfer equation. Pressure drop, Nusselt number, and the drying rate were considered as performance parameters. Comparing simulation results with experimental data showed that this new solver can precisely solve the thermal phase change in a porous medium. The influence of parameters effective on the drying process, such as porosity, permeability, the dynamic contact angle was investigated. Based on the results of the pressure profile in the final state, four different regions are visible. Because of the close fit of the wall temperature to the average cross‐sectional temperature, the Nusselt number increases sharply at transition points from the liquid to the vapor phase. By increasing the dynamic contact angle, the average drying rate in the channel is reduced.     

Effective thermal conductivity analysis of xonotlite-aerogel composite insulation material

A 3-dimensional unit cell model is developed for analyzing effective thermal conductivity of xonotlite-aerogel composite insulation material based on its microstructure features. Effective thermal conductivity comparisons between xonotlite-type calcium silicate and aerogel as well as xonotlite-aerogel composite insulation material are presented. It is shown that the density of xonotlite-type calcium silicate is the key factor affecting the effective thermal conductivity of xonotlite-aerogel composite insulation material, and the density of aerogel has little influence. The effective thermal conductivity can be lowered greatly by composite of the two materials at an elevated temperature.