多孔饱和矩形管中粘性随温度变化对熵产、热和流体流动的影响

研究了充填流体-饱和多孔介质的矩形管中,随温度变化的粘性对充分发展强迫对流的影响.采用Darcy流动模型并假设粘性-温度为倒线性关系.管壁视为均匀热通量,即Kays和Craw-ford称为的H边界条件.当流体粘性随温度升高而降低时,管壁的Nusselt数增大.求解速度和温度分布时,利用热力学第二定律求解了局部平均熵产率.根据Brinkman数、Péclet数、粘性变化数、无量纲管壁热通量和管道截面宽高比,给出了熵产率、Bejan数、传热不可逆性和流体流动不可逆性的表达式.这些表达式是该类问题参数研究的基础.可以看出,当管道截面宽高比的增大使熵产率减小时,方形管中流动产生的熵大于矩形管,这类似于Ratts和Raut研究的明流(clear flow)情况.     

Richardson数对后台阶流动熵产的影响

后台阶流动是研究伴随有传热现象的分离流动的常用模型．虽然Richardson数的改变会明显影响分离流动的流动和传热特性,但是迄今为止关于Richardson数对后台阶流动熵产影响的研究依然很少．基于求解熵产方程,第一次系统研究Richardson数对后台阶流动熵产的影响．对于求解熵产方程所需的速度和温度等变量,通过格子Boltzmann方法来得到．通过上述工作可以发现,后台阶流动中熵产和Bejan数的分布随Richardson数变化显著．总熵产数是Richardson数的单调减函数而平均Bejan数是Richardson数的单调增函数．     

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.     

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.     

恒温平行板间多孔介质通道中的分层耗散流动

利用Darcy模型,研究了平行板间充填饱和多孔介质的通道中,在热量入口处传热的粘性耗散效应．讨论了等温边界情况．求得热量入口处局部温度和体积计算平均温度随Nusselt数的分布．给出了独立于Brimkman数的经充分发展的Nusselt数应为6A·D2并观察到,若忽略粘性耗散影响,将导致熟知的内流现象,此时Nusselt数等于4.93．还给出了有限差分数值解．结果表明解析法和数值法的结果吻合很好．     

等通量多孔介质内填夹杂时,粘性和Joule传热对磁流体动力学自然对流的影响

当一个等通量多孔介质内填倾斜矩形夹杂物时,数值地研究了粘性和Joule传热对磁流体动力学自然对流热传导的影响.矩形夹杂物的一边为等热通量的加热面,其对边为等热通量的致冷面,另外两边为绝热面.使用一组适当的变量,将能量方程和Darcy-Oberbeck-Boussinesq的Forch-heimer推广式变换为无量纲形式,然后用有限差分法求解.控制参数为磁效应数、修正的Rayleigh数、矩形夹杂物的倾角及其长宽比.结果显示,粘性和Joule传热导致热传导率下降.     

充满多孔介质的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,对4个壁面均为低温、低浓度,内置高浓度发热圆的充满均匀多孔介质的方腔内双扩散自然对流现象进行了数值模拟研究.分析了Darcy(达西)数Da(10-4≤D_a≤10~(-2))和浮升力比B(-5.0≤B≤5.0)对内部发热圆表面平均Nusselt(努赛尔)数Nuav和平均Sherwood(舍伍德)数Shav的影响.模拟结果表明:除B=-1.0时,Nu_(av)和Sh_(av)随D_a的增加而增大;当-5.0B5.0,在D_a=10~(-4)时,Nu_(av)和Sh_(av)几乎不受B变化的影响;在Da=10~(-3)和Da=10~(-2)时,Nu_(av)和Sh_(av)随B的增加先减小后增大,在B=-1.0时取得最小值.     

饱和纳米流体多孔介质中竖直嵌入板上边界层的非Newton流

在层流条件下,对饱和多孔介质中的竖直板,研究幂指数型非Newton流的自由对流热交换.非Newton纳米流体服从幂指数型的数学模型,模型综合考虑了Brown运动和热泳的影响.通过相似变换,将问题的偏微分控制方程组,转化为常微分方程组,得到了常微分方程组的数值解.数值解依赖于幂指数n,Lewis数Le,浮力比Nr,Brown运动参数Nb,以及热泳参数Nt.在n和Le的不同取值下,研究并讨论了对相关流体性质参数的影响和简化的Nusselt数.     

趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析

基于趋旋性微生物和幂律流体模型,研究了在含有非Newton流体饱和多孔介质中生物对流的线性稳定性问题.利用Galerkin数值方法求解了该系统的控制方程,得到生物Rayleigh数的数值解,讨论了非Newton流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh数和生物Lewis数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非Newton流体的幂律指数则有利于系统的稳定性.     

饱和多孔介质的超粘弹性本构理论研究

为了建立能考虑固体材料、多孔固体与流体可逆和不可逆变形的饱和多孔介质超粘弹性理论,以多孔固相为参考构型,以有效应力、材料真实应力和流相真实孔压作为状态变量,结合混合物均匀化响应原理获得各项均符合热力学功共轭特征的饱和多孔介质能量平衡方程,根据非平衡热力学熵分解理论求得熵流和熵产.结果表明,超弹塑性理论是该理论的一个特例;多孔固体的总变形可分为固相间隙和材料变形两部分,间隙应变与Terzaghi有效应力构成功共轭对,材料应变与材料真实应力构成功共轭对.饱和多孔介质的自由能可分为固相和流相两部分.当固相间隙和材料变形解耦时,固相所含的自由能又可分为间隙和材料两部分.证明了Skempton有效应力不是饱和多孔介质的基本应力状态变量.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.