空间分数阶非Newton流体本构及圆管流动规律研究

对非Newton流体的本构及流动规律进行研究是分析、预测和控制非Newton流体在管道中流动的关键.实验表明非Newton流体在流动过程中具有历史记忆性,基于空间分数阶微积分方法,建立了分数阶非Newton流体本构模型;并推导了该模型在圆管中的流速分布、流量、平均流速、压降、平均Reynolds数等管道流动参数;提出了分数阶非Newton流体圆管流态判别准则.研究表明非Newton流体的圆管流层间的切应力可以通过流速的轴向分布大小来描述.对于不含屈服切应力的分数阶非Newton流体,分数阶的阶数越大,断面流速分布越均匀,记忆能力越强.分数阶的阶数大小反映了流体对全域空间的记忆性强弱;而对于含有屈服切应力的分数阶非Newton流体,分数阶的阶数越大,速梯区流速分布越均匀,流核区速度越小.分数阶的阶数大小反映了局部空间记忆性强弱.该研究为非Newton流体的记忆特征提供了一种新的建模方法.     

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.     

NGLM:一类全局收敛的Newton-GMRES方法

本文提出了一类具有全局收敛性质的Newton-GMRES方法—NGLM方法．该方法是对经典Newton—GMRES方法的推广．NGLM方法的全局策略是当在非精确Newton方向上后退不能成功时，转而在一个子空间上运用信赖域方法确定迭代步长．理论分析与数值实验均表明，NGLM方法改善了Newton—GMRES方法的强健性．     

非Newton流体的物质点法模拟研究

准确模拟非Newton流体的运动特性具有重要的工程意义.物质点法作为一种相对新兴的粒子型算法,其结合了Lagrange算法和Euler算法的双重优势,已广泛有效地应用于各个工程领域.基于物质点法,结合人工状态方程,分析了两种非Newton流体(cross流体和幂律流体)在平板Poiseuille流和Couette流情况下的流动特性.结果表明:对Newton流体,物质点模拟结果与理论值一致;对非Newton流体,物质点法可准确模拟其剪切稀化和剪切稠化现象.表明了物质点法在模拟非Newton流体流动问题时的适用性,拓展了物质点法的应用范围.     

非Newton流体在多孔介质中沿竖直面作自由对流时应力屈服和Soret效应对其传热/传质的影响

对饱和的非Newton幂律流体,流经多孔介质中竖直平板时的自由对流,在出现应力屈服和Soret效应时,研究化学反映对传热/传质的影响.用相似变换,将边界层控制方程及其边界条件转换为无量纲的形式,然后通过有限差分法求解该方程.给出并讨论了浓度曲线,以及本问题各种参数值时的Nusselt数和Sherwood数.发现化学反应参数γ、化学反应级m、Soret数Sr、浮力比N、Lewis数Le及无量纲流变参数Ω对流场有着显著的影响.     

喷涂于运动边界上液体薄膜射流的流变效应

采用非Newton流体的二阶流体模型分析了相对高温的液体熔体薄膜由模口喷出并涂于运动的固体膜上. 讨论了由自由面上温度梯度驱动的非Newton液体薄膜的热毛细流动, 考虑热毛细流动的流变效应. 分析是基于润滑理论近似和摄动理论近似. 得到了液体高度方程和非Newton液体薄膜的热流体力学过程描述, 具体求解了弱流变流体效应的情况.     

具有参数平方收敛的线性插值迭代类

提出了一类具有参数平方收敛的求解非线性方程的线性插值迭代法,方法以Newton法和Steffensen法为其特例,并且给出了该类方法的最佳迭代参数.数值试验表明,选用最佳迭代参数或其近似值的新方法比Newton法和Steffensen方法更有效.     

Newton-非Newton幂律流双区复合水平井压力动态特征分析

聚合物驱油在提高原油采收率方面具有重要作用，水平井在薄层油田的开发过程中占有重要优势.根据聚合物驱油过程，基于点源函数基本理论，建立了Newton-非Newton双区复合水平井试井解释数学模型.利用Laplace积分变换和Fourier有限余弦积分变换方法，获得了Laplace空间Newton-非Newton双区复合水平井试井解释数学模型的解析解.通过Stehfest数值反演得到了典型无因次井底压力、压力导数特征曲线.研究表明:幂律指数越小，外区压力、压力导数曲线上翘越明显，且压力导数曲线呈斜率为(1-m)/(3-m)的直线；当幂律指数为1时，该模型简化为水平井常规双区复合模型；水平井水平段长度越长，早期径向流阶段结束的时间越早； 内外区流度比越大、 内区半径越小， 外区压力和压力导数曲线位置越高， 且始终保持斜率为(1-m)/(3-m)的直线.     

超平方收敛的2步法公式

给出3个求解非线性方程的迭代公式,它们均是2步法计算公式,就函数值的计算量来看,它们和Newton法一样,但它们却具有超平方收敛性,其中2个公式的收敛阶约为2．414,另一个公式的收敛阶约为2．732．     

微极流体向受热面的MHD驻点流动

分析了有均匀横向磁场作用时,导电微极流体垂直冲击受热面时形成的二维驻点流动问题．应用适当的相似转换,将连续、动量、角动量及热量的控制方程,及其相应的边界条件,简化为无量纲形式．然后,利用以有限差分离散化为基础的算法,求解简化了的自相似非线性方程．用Richardson外推法,进一步求精其结果．以图表形式表示磁场参数、微极性参数、Prandtl数对流动和温度场的影响,说明了其解的重要特性．研究表明,随着磁场参数的增大,速度和热边界层厚度变小了．与Newton流体相比较,微极流体的剪应力和传热率出现明显的减少,这对聚合物生产过程中流体的流动和热量控制是有益的．     

Boundary layer flow of power-law fluids past arbitrary profiles

Two-dimensional steady-state boundary layer equations of power-lawfluids are derived using a special coordinate system which makesthe equations independent of the body shape immersed in theflow. In deriving the boundary layer equations, the method ofmatched asymptotic expansions is used. It is shown that thesimilarity solutions for power-law fluids are much the sameas those of Newtonian fluids. Similarity solutions correspondingto the case of parallel flow past a flat plate and stagnation-pointflow are presented. Finally, the shear stress is calculatedfor different geometries.     

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudo-similarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.     

Free vibration of four-parameter functionally graded moderately thick doubly-curved panels and shells of revolution with general boundary conditions

This paper aims to present a unified vibration analysis approach for the four-parameter functionally graded moderately thick doubly-curved shells and panels of revolution with general boundary conditions. The first-order shear deformation theory is used in this formulation. The functionally graded panels structures consists of ceramic and metal which are set to vary continuously in the thickness direction according to the general four-parameter power-law distribution, and six types of power-law distributions are considered for the ceramic volume fraction. The admissible function of the FG panels and shells of revolution is obtained by the improved Fourier series with the help of the governing equations and the boundary conditions. The solution is obtained by using the variational operation in terms of the unknown expanded coefficients. By a great many numerical examples, the rapid convergence and good reliability and accuracy of the proposed approach are validated. A variety of new results for vibration problems of the FG doubly-curved shells and panels with different elastic restraints, geometric and material parameters are presented. The effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data in the research and the actual production process.     

Isoperimetric estimates of the solutions of a class of pseudodifferential equations and their application to crack problems

Isoperimetric estimates are obtained of solutions of boundary value problems for a class of pseudodifferential equations. This class of equations includes the equation of problems on plane normal discontinuity cracks located in a homogeneous linearly elastic space and an inhomogeneous space whose Young's modulus has a power-law dependence on the distance to the plane of the crack. As it applies to crack problems, the established inequalities yield, in particular, isoperimetric estimates of the maximum opening of the crack and its volume under arbitrary loads.     

A new reformulation of vibration suppression equations of functionally graded magnetorheological fluid sandwich beam

This article presented a new reformulation of governing equations of functionally graded magnetorheological fluid (FGMRF) sandwich beams using new auxiliary functions. This technique led to the decoupled vibration equations of the FGMRF sandwich beams and also to the analytical solutions for the in-plane and out of plane displacement fields by considering the Euler-Bernoulli beam theory (EBBT). The material properties of top and bottom layers were changed through the layer thickness according to a power-law distribution of the volume fraction of the constituents. Complex shear modulus of the magnetorheological fluid was varied continuously as a quadratic function of magnetic field intensity. Natural frequencies and corresponding loss factors were calculated with high accuracy in comparison with those available in literature. The effects of boundary conditions, geometric and material properties and the magnetic field intensity on vibrational modes were investigated. Results revealed that unlike the natural frequencies, the loss factors were more affected by the magnetic field.     

Bending analysis of size-dependent functionally graded annular sector microplates based on the modified couple stress theory

In the present paper, a non-classical model for functionally graded annular sector microplates under distributed transverse loading is developed based on the modified couple stress theory and the first-order shear deformation plate theory. The model contains a single material length scale parameter which can capture the size effect. The material properties are graded through the thickness of plates according to a power-law distribution of the volume fraction of the constituents. The equilibrium equations and boundary conditions are simultaneously derived from the principle of minimum total potential energy. The system of equilibrium equations is then solved using the generalized differential quadrature method. The effects of length scale parameter, power-law index and geometrical parameters on the bending response of annular sector plates subjected to distributed transverse loading are investigated.     

MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet

This article presents a numerical solution for the magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a semi-infinite non-isothermal stretching sheet with internal heat generation/absorption. The flow is caused by linear stretching of a sheet from an impermeable wall. Thermal conductivity is assumed to vary linearly with temperature. The governing partial differential equations of momentum and energy are converted into ordinary differential equations by using a classical similarity transformation along with appropriate boundary conditions. The intricate coupled non-linear boundary value problem has been solved by Keller box method. It is important to note that the momentum and thermal boundary layer thickness decrease with increase in the power-law index in presence/absence of variable thermal conductivity.     

反平面塑性V形切口尖端应力和位移渐近解

提出了一种确定幂硬化材料反平面V形切口尖端应力和位移渐近解的主导项和高阶项的有效方法。首先通过在弹塑性理论基本方程中引入V形切口尖端应力场和位移场的渐近级数展开,建立以应力和位移为特征函数的非线性和线性常微分方程组。然后采用插值矩阵法求解常微分方程组,可得到多阶应力特征指数和其相对应的特征函数。该方法具有通用性强、精度高等优点,可处理任意开口角度和应变硬化指数的V形切口。典型算例验证了该方法的准确性和有效性。     

弹性力学问题解唯一的边界积分方程

从积分方程式出发,应用基本解的特性分析,说明在力边值问题中,位移边界积分方程和面力边界积分方程的位移解不唯一.提出了位移解唯一的条件,建立了唯一解的位移边界积分方程和面力边界积分方程.实例计算结果表明唯一解的边界积分方程是有效的.     

Singularly perturbed boundary value problems with a power-law boundary layer

We consider boundary value problems for second-order singularly perturbed equations whose solution has a power-law boundary layer that occurs because the degenerate equation has multiple roots.