多孔介质热弥散系数的分形模型北大核心CSCD

热弥散系数是与流体的物性和多孔介质结构有关的,表征多孔介质传热传质强弱的重要参数.该文建立了分形多孔介质的孔喉结构模型,研究了在孔喉结构处流体由湍流状态变为层流状态的局部水头损失和速度弥散效应,在考虑微观孔喉结构和速度弥散效应的影响下,推导了热弥散系数关系式.研究表明,热弥散系数与孔喉比、孔喉结构个数和迂曲分形维数成正比,与孔隙率和面积分形维数成反比.进一步研究发现,孔喉比在1~150范围内对速度弥散效应有显著影响,流体在孔喉结构处存在局部水头损失,导致速度弥散效应增强,热弥散系数增大.     

化学反应对竖直平板边界磁流体动力学微极流体滑流的影响

对半无限竖直平板为边界的多孔介质，研究了传热、传质对微极流体不稳定滑流的影响，其化学反应是一级均匀的。均匀磁场垂直作用于可以吸收微极流体的多孔表面，吸引速度随着时间而变化。自由流动的速度随着微小扰动而呈指数增大或减小。采用近似方法获得了微极流体的速度、微转动、温度、浓度的表达式，还得到了在不同流体特征和流动条件下，壁面的摩擦系数、耦合应力系数、传热率和传质率。     

非Darcy多孔介质中的非线性对流

利用温度-浓度-密度关系,研究非Darcy多孔介质中的自由对流问题.对于不同的惯性参数、传递参数、Rayleigh数、Lewis数、Soret数和Dufour数,分析了非线性温度参数和浓度参数对非线性对流的影响.浮力对对流起着辅助的附加作用,当惯性作用不计时,切向速度随着非线性温度和浓度的增加而急剧地增加.然而,当惯性效应不为0时,非线性温度和浓度对切向速度的影响是有限的.对两个传递参数、惯性影响参数以及控制非线性温度和浓度的其他参数,取不同的数值时,浓度分布有点儿变化,并在不同的范围内传播.随着非线性温度和浓度的增加,传热/传质在很大的范围内变化,这取决于是Dacry多孔介质,还是非Darcy多孔介质.当所有的影响(惯性的影响、两个传递系数的影响、Soret和Dufour的影响)同时为0/不为0,在非线性温度/浓度参数以及浮力的共同作用下,分析了传热/传质的变化.发现在Darcy多孔介质中,温度和浓度以及它们的交叉扩散,对传热/传质的影响,要比非Darcy多孔介质要大.发现了浮力的负面作用,随着非线性温度系数的增加,传热/传质率是提高的,而随着非线性浓度系数的增加,传热/传质率是下降的.     

解析法确定含蜡原油热质耦合的蜡分子扩散速率

蜡分子扩散过程是在热和质的广义热力学"力"耦合驱动下产生广义热力学"流"的结果,其实质是传热和传质同时存在的复杂耦合不可逆过程.基于非平衡态热力学的基本原理,推导出含蜡原油管输过程蜡分子扩散热质传递的线性唯象方程组;依据质量和能量的守恒关系,得到蜡分子扩散的传热一传质微分方程组,利用拉普拉斯变换求解到其解析解,探讨促使蜡分子扩散的动力学原因,分析输量和季节变化的不同工况对扩散速率的影响.     

C60-Ag薄膜高、低温粗糙表面的标度行为和粗糙化机理的实验研究

利用原子力显微镜和透射电子显微镜对沉积在NaCl衬底上的C₆₀-Ag复合薄膜的表面形貌和微结构进行了研究 .结果表明薄膜表面的粗糙度依赖于衬底的温度 ,当衬底温度从 - 80℃上升到 1 2 0℃ ,薄膜表面发生从粗糙→光滑→粗糙的变化过程 .由于高温和低温条件下 ,薄膜表面的粗糙化机理不同 .高低温的表面虽然具有类似的rms粗糙度 ,但却具有不同的分形标度行为 .同时探讨了标度行为、微结构和粗糙化机理之间的关系     

基于动态热湿传递的纺织材料孔隙率决定的反问题

除纺织材料的厚度与导热系数外,其孔隙率也是影响人体热湿舒适性的一个重要因素.基于动态热湿传递模型,作者提出了满足人体热湿舒适性的纺织材料孔隙率决定反问题.通过吉洪诺夫正则化方法将纺织材料孔隙率决定反问题归结为目标函数极小值问题.应用巴拿赫不动点理论证明了正问题解的存在唯一性,揭示了织物内热湿传递变化规律.应用L-曲线方法获得了正则化参数的最优选择,采用粒子群最优化算法随机搜索目标函数极小值点,得到反问题的广义解.数值模拟结果验证了纺织材料孔隙率决定反问题提法的合理性和算法的有效性.     

矩形域上分形插值研究

该文给出了矩形域上分形插值数学模型, 分形插值曲面的计算公式, 证明了分形插值曲面迭代函数系唯一性定理, 导出了分形插值曲面的维数定理,并应用实际数据进行了分形插值曲面的实例研究. 为工程中长期寻求的粗糙表面模拟提供了理论基础和实用方法.     

变温度荷载作用下半无限成层饱和介质的热固结分析

对半无限成层饱和多孔介质作用随时间变化的温度荷载的热固结问题进行解析求解．其中,热-水-力耦合线性弹性控制方程考虑了热渗效应和等温热流效应的影响．先采用Laplace变换求其在变换域上的解,然后用数值方法求逆变换．对半无限体表面作用呈指数衰减热荷载的双层体系进行研究,分析了两层介质热固结系数、弹性模量等的差异性对热固结特征的影响．研究表明:位移场和应力场对温度场的耦合作用可以忽略,而热渗效应对温度和孔压有显著影响．     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

发汗冷却系统的控制及其特性*

本文给出热层三维发汗冷却控制系统的数学模型.在一般情形下,它是一个可变域上分布参数和集中参数混合的非线性控制系统.本文指出:在冷却剂渗流是一维不可压缩的(或一维定常的)条件下,热层的传热和烧蚀问题可以单独求解.针对热防护层的表面烧蚀问题,本文讨论了系统控制方案,阐明简化的条件,研究了一维发汗冷却系统点控制的特性,给出了冷却剂无相变和有相变两种情形的平衡状态解.     

Non-Newtonian phase-change heat transfer of nano-enhanced octadecane with mesoporous silica particles in a tilted enclosure using a deformed mesh technique

In the present study, the melting phase-change heat transfer of nano-enhanced phase-change octadecane by using mesoporous silica particles is investigated in an inclined cavity, theoretically. The presence of mesoporous silica particles induces non-Newtonian effects in the molten octadecane. A phase-change interface-tracking approach, deformed mesh technique, is employed to track the phase-change interface and heat transfer in the cavity. The Arbitrary Lagrangian-Eulerian (ALE) moving mesh technique along with the finite element method is adopted to solve the governing equations for conservation of mass, momentum, and energy during the phase-change process. A re-meshing technique and an automatic time step control approach are employed to control the quality of the deformed mesh and the computed numerical solution. The effect of various mass fractions of nanoparticles and various inclination angles of the enclosure on the heat transfer and phase-change behavior of nano-enhanced octadecane are addressed. The outcome reveals that using the mesoporous silica particles diminish the heat transfer in the enclosure. Although the presence of nanoparticles improved the conductive heat transfer, a reduction in the phase-change heat transfer performance of the enclosure can be observed, which is due to the increase of the viscosity (consistency parameter) of the liquid and suppression of natural convective flows. Moreover, the presence of nanoparticles reduces the latent heat capacity of octadecane as they do not contribute to the phase-change energy storage. Dispersing 5% mass fraction of nanoparticles in octadecane can reduce the heat transfer up to 50% and increase the consistency parameter by three folds. The angle of inclination of the cavity also plays an important role in the heat transfer characteristics. Tilting the cavity by -75° leads to an 80% reduction in the heat transfer.     

On turbulence in fractal porous media

We examine three fundamental equations governing turbulence of an incompressible Newtonian fluid in a fractal porous medium: continuity, linear momentum balance and energy balance. We find that the Reynolds stress is modified when a local, rather than an integral, balance law is considered. The heat flux is modified from its classical form when either the integral or local form of the energy density balance law is studied, but the energy density is always unchanged. The modifications of Reynolds stress and heat flux are expressed directly in terms of the resolution length scale, the fractal dimension of mass distribution and the fractal dimension of a fractal’s surface. When both fractal dimensions become integer (respectively 3 and 2), classical equations are recovered.     

On turbulence in fractal porous media

We examine three fundamental equations governing turbulence of an incompressible Newtonian fluid in a fractal porous medium: continuity, linear momentum balance and energy balance. We find that the Reynolds stress is modified when a local, rather than an integral, balance law is considered. The heat flux is modified from its classical form when either the integral or local form of the energy density balance law is studied, but the energy density is always unchanged. The modifications of Reynolds stress and heat flux are expressed directly in terms of the resolution length scale, the fractal dimension of mass distribution and the fractal dimension of a fractal’s surface. When both fractal dimensions become integer (respectively 3 and 2), classical equations are recovered.      

On the heat flux vector for flowing granular materials—Part I: effective thermal conductivity and background

Heat transfer plays a major role in the processing of many particulate materials. The heat flux vector is commonly modelled by the Fourier's law of heat conduction and for complex materials such as non‐linear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematical parameters such as temperature, shear rate, porosity or concentration, etc. In Part I, we will give a brief review of the basic equations of thermodynamics and heat transfer to indicate the importance of the modelling of the heat flux vector. We will also discuss the concept of effective thermal conductivity (ETC) in granular and porous media. In Part II, we propose and subsequently derive a properly frame‐invariant constitutive relationship for the heat flux vector for a (single phase) flowing granular medium. Standard methods in continuum mechanics such as representation theorems and homogenization techniques are used. It is shown that the heat flux vector in addition to being proportional to the temperature gradient (the Fourier's law), could also depend on the gradient of density (or volume fraction), and D (the symmetric part of the velocity gradient) in an appropriate manner. The emphasis in this paper is on the idea that for complex non‐linear materials it is the heat flux vector which should be studied; obtaining or proposing generalized form of the thermal conductivity is not always appropriate or sufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

On the heat flux vector for flowing granular materials—part II: derivation and special cases

Heat transfer plays a major role in the processing of many particulate materials. The heat flux vector is commonly modelled by the Fourier's law of heat conduction and for complex materials such as non‐linear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematical parameters such as temperature, shear rate, porosity or concentration, etc. In Part I, we will give a brief review of the basic equations of thermodynamics and heat transfer to indicate the importance of the modelling of the heat flux vector. We will also discuss the concept of effective thermal conductivity (ETC) in granular and porous media. In Part II, we propose and subsequently derive a properly frame‐invariant constitutive relationship for the heat flux vector for a (single phase) flowing granular medium. Standard methods in continuum mechanics such as representation theorems and homogenization techniques are used. It is shown that the heat flux vector in addition to being proportional to the temperature gradient (the Fourier's law), could also depend on the gradient of density (or volume fraction), and D (the symmetric part of the velocity gradient) in an appropriate manner. The emphasis in this paper is on the idea that for complex non‐linear materials it is the heat flux vector which should be studied; obtaining or proposing generalized form of the thermal conductivity is not always appropriate or sufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

煤层注水非线性渗流方程的解析解及应用

本文运用流体力学,多孔介质流体动力学,渗流理论等理论知识,结合实验室和现场试验,从理论上对煤层注水预湿煤体机理进行了研究.分析了煤层注水过程,建立起了煤层注水的数学模型;对煤层注水的边界条件进行了描述.由于描述煤层注水的方程组为非线性的,为简化它们,利用了因次分析理论,引入了注水压力,渗透速度,煤水份增加量等无因次量.之后讨论了其解析和近似解.另外:结合实际煤层注水的科研项目,说明了该理论指导煤层注水及设计的作用和重要性.     

粗糙面分形计算理论研究进展

为提出一种工程上适用可靠的粗糙面分形维数计算方法,在分形曲线的维数计算方法(码尺法,盒维法)基础上,先后提出了星积分形曲面的维数计算方法、三角形棱柱表面积法、投影覆盖法、立方体覆盖法、改进的立方体覆盖法、分形的增变量描述法等曲面分形维数理论.鉴于上述方法的共有缺陷——获取三维坐标的激光表面仪器的扫描尺度限制,研究者提出了粗糙面图像维数计算理论,包括二值化图像维数、灰度图像维数、RGB图像维数计算理论.最后,本文展望了分形维数计算理论领域内亟待解决的三大问题.     

Simulated fractal permeability for porous membranes

Fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the membrane. 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. The pore area fractal dimension and the tortuosity fractal dimension of the porous membranes are determined by the box counting method. To verify the validity of the model, the predicted permeability were compared with the experimental data utilizing H₂ gas permeating through porous Pd-alumina, silicalite-1 and B-ZSM-5, and O₂ across perovskite-alumina membranes form the past effort.