热对流环中混沌的控制技术

本文应用谱展开法将描述一维热对流环中流体层流自然对流循环的质量、动量和能量守恒方程化为一组无穷维的常微分方程组;其一阶模态为自封闭的Lorenz方程。应用线性与非线性反馈控制,通过数值模拟发现混饨的线性和非线性反馈控制技术可以明显改变热对流环中流体的运动特征,达到我们所希望的流型,即增强混沌或抑制混沌。     

槽式太阳能集热器内耦合换热特性研究

对槽式太阳能集热器内的耦合换热过程建立了统一求解模型,推导了无量纲控制方程,并进行了耦合求解.结果表明:随Ra增加,管内自然对流形成的涡逐渐向右侧管壁方向移动,等温线中心向下偏移;环形空间内自然对流形成的涡向顶部移动,等温线向下偏转;随管径比增加,管内的混合对流换热系数增加,管外环形空间的换热系数减小.内管内外表面的温度梯度及局部换热系数均随着角度的增加而增加.在θ=π/4和θ=π/2的截面内,环形空间中间区域内温度沿半径方向不降反升,出现偏转;而在θ=3π/4和θ=π的截面内,圆管内部中间区域内的温度沿着径向不升反降,也出现偏转.     

饱和含混多孔介质中环绕水平圆柱的自然对流

本文运用达西流模型，对饱和含湿多孔介质中环绕水平等温圆柱发生的自然对流进行了数值模拟和分析。流函数和温度分布采用傅里叶级数的形式，以联立求解二维流动的控制方程组，傅里叶级数项的系数由一维常微分方程的解得到。文中同时给出局部和平均努谢尔数随修正瑞利数的变化关系以及修正瑞利数处在０．１～１０范围内时二维流场和温度场分布。     

Convection heat transfer in a Maxwell fluid at a non-isothermal surface

Analysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.     

考虑Soret和Dufour效应的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,考虑Soret和Dufour效应,对内置高浓度发热圆的方腔内部双扩散自然对流现象进行数值模拟.高浓度发热圆位于方腔中心,四周壁面均为低温低浓度.在该模型中,用三个独立的LBGK方程分别模拟速度场、温度场和浓度场,并通过Boussinesq近似将它们耦合起来.分析Soret数和Dufour数对方腔内部双扩散自然对流的影响,得到流线图、等温线图、等浓度线图、发热圆表面平均Nusselt数和平均Sherwood数.结果表明：Soret和Dufour效应对方腔内双扩散自然对流影响明显,不能忽略.     

湍流热对流DNS多分辨率并行直接求解方法

依据温度标量场与动量计算的空间和时间计算分辨率不同的特点,采用两套网格,建立多分辨率双网格并行直接求解方法,用以解决极高Ra数湍流热对流DNS模拟巨大计算工作量的难题.在两套网格的数据交换上,根据每个细网格都满足连续方程,设计了速度的守恒平移插值方法.二维极高Ra数湍流热对流的计算结果表明,采用多分辨率双网格并行直接求解方法的DNS计算,可以使计算工作量降低近一个量级.瞬时温度场显示,双网格方法的计算结果可以很好地描述极高Ra数下快速运动的小尺寸漩涡团状羽流,得到的结果与原网格一致,不同方法计算得到的传热Nu数误差不超过1%.     

非牛顿流体沿竖直平板自然对流传热的计算研究

非牛顿幂次流体沿竖直平板层流自然对流为非线性两点边值问题,其速度场与温度场需耦合求解。采用几种数值方法对该问题进行了计算,研究了各种普朗特数(Pr)及不同幂次流体对沿壁面平均努赛尔数(Nu)的影响变化,并与有关文献的结果进行了对比分析。     

高Rayleigh数条件下竖圆环夹层内自然对流换热的实验研究

对内壁维持恒热流和外壁向环境冷却的大高宽比竖圆环夹层内自然对流换热进行了实验研究。实验装置高宽比分别为２３５和６６６７，半径比分别为２．０３和３．９２。实验数据整理考虑了热辐射影响以获得对流规律。由于已有工作均未考虑高Ｒａ数区域，首次得到Ｒａ数高达１０￣９的区域内平均Ｎｕ数的换热准则式。在低Ｒａ数区域，亦取得了与前人工作一致的结论。本文结果改进了高Ｒａ数区域换热规律的预测能力。     

Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations

In this paper, transient and steady natural convection heat transfer in an elliptical annulus has been investigated. The annulus occupies the space between two horizontal concentric tubes of elliptic cross-section. The resulting velocity and thermal fields are predicted at different annulus orientations assuming isothermal surfaces. The full governing equations of mass, momentum and energy are solved numerically using the Fourier Spectral method. The heat convection process between the two tubes depends on Rayleigh number, Prandtl number, angle of inclination of tube axes and the geometry and dimensions of both tubes. The Prandtl number and inner tube axis ratio are fixed at 0.7 and 0.5, respectively. The problem is solved for the two Rayleigh numbers of $10^4$ and $10^5$ considering a ratio between the two major axes up to 3 while the angle of orientation of the minor axes varies from $0^\circ$ to $90^\circ$. The results for local and average Nusselt numbers are obtained and discussed together with the details of both flow and thermal fields. For isothermal heating conditions, the study has shown an optimum value for major axes ratio that minimizes the rate of heat transfer between the two tubes. Another important aspect of this paper is to prove the successful use of the Fourier Spectral Method in solving confined flow and heat convection problems.     

微秒级导通时间等离子体断路开关的二维雪耙模型

 给出了适合微秒级导通时间等离子体断路开关的二维雪耙模型的具体描述，建立了二维雪耙模型的基本方程及其差分格式，对方程进行了显式求解。通过对一个模型的计算，给出了雪耙阵面的传播图像，指出了断路开关的断开位置及附近点密度随时间的变化曲线，在该位置附近出现了等离子体薄化现象。     

Natural convection of CuO–water nanofluid filled in a partially heated corrugated cavity:KKL model approach

In this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for Cu O–water inside a partially heated domain by defining the constraint along the boundaries. For nanofluid analysis, the Koo and Kleinstreuer Li(KKL) model is implemented to deal with the effective thermal conductivity and viscosity. A heated thin rod is placed inside the corrugated cavity and the bottom portion of the corrugated cavity is partially heated. The dimensionless form of nonlinear partial differential equations are obtained through the compatible transformation along with the boundary constraint. The finite element method is executed to acquire the numerical solution of the obtained dimensional system. Streamlines, isotherms and heat transfers are analyzed for the flow field and temperature distribution. The Nusselt number is calculated at the surface of the partially heated domain for various numerical values of emerging parameters by considering the inner obstacle at cold, adiabatic and heated conditions. The computational simulation was performed by introducing various numerical values of emerging parameters. Important and significant results have been attained for temperature and velocities(in both x-and y-directions) at the vertically and horizontally mean positions of the corrugated duct.     

Free transverse vibrations of uniform circular plates and membranes with eccentric holes

An analytical method, based on the transformation of cylindrical wave functions, is presented for calculating the free transverse vibrations of uniform circular plates and membranes with eccentric holes. The wave equations governing the small transverse motion of the plates and membranes are solved exactly to satisfy the boundary conditions at both inner and outer edges, and the associated frequency equations for the plates and membranes are derived. The analysis also includes the vibrations of uniform circular plates and membranes with concentric holes as special cases. Numerical examples are presented to show the dependence of the eigenfrequency on the eccentricity and on the ratio of the inner radius to outer radius. The main purpose of the paper is to illustrate that an exact, analytical solution of the vibrations of eccentric annular plates and membranes can be obtained.     

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret-Dufour Effects

The present study is carried out to see the thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method (OHAM) is best candidate to handle highly nonlinear system of differ-ential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.     

Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet

The steady two-dimensional mixed convection flow of a micropolar fluid over a non-linear stretching sheet is investigated. The governing non-linear equations and their associated boundary conditions are transformed into coupled non-linear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy analysis method (HAM). The convergence of the obtained series solutions is carefully checked. The physical significance of interesting parameters on the flow and the thermal fields are shown through graphs and discussed in detail. The values of wall shear stress, couple wall stress and the local Nusselt number are tabulated. Comparison is also made with the corresponding results of viscous fluid with no mixed convection and an excellent agreement is noted.     

Influence of magnetic field by free convection flow past an impulsively started vertical cylinder in the presence of Dufour and Soret effects

Numerical modeling of two-dimensional, unsteady, laminar, isothermal heat and mass transfer by MHD free convection flow past an impulsively started vertical cylinder in the presence of Dufour and Soret effects is considered. The governing equations of the flow problems, valid in the free convection regime, are transformed into a nondimensional form using appropriate nondimensional parameters. These equations are solved numerically by an efficient, implicit, iterative, finite-difference scheme of Crank-Nicolson type. A parametric study illustrating the influence of the magnetic field, Grashof number, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration, as well as the local and average skin friction, Nusselt and Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.     

Oscillating two-stream instability of a lower hybrid wave in aninhomogenous plasma

The effect of the density inhomogeneity on the oscillating two-stream instability of a lower hybrid pump wave with a finite wavelength is investigated. The density inhomogeneity introduces dephasing that restricts the interaction region where the matching conditions hold. The loss of energy due to convection from this region introduces a certain convection threshold for the onset of this instability. The coupled differential equations are solved in Fourier space by converting them into an uncoupled eigenvalue equation and then applying a quantization condition. Expressions are obtained for the growth rate and the convective threshold, and the results are applied to the Princeton Large Torus parameters     

数值分析环形池硅熔体旋转-热毛细对流及其稳定性

数值模拟了内半径20 mm、外半径40 mm、深5 mm环形池内硅熔体在旋转和热毛细力共同驱动下的热对流,通过线性稳定性分析确定了旋转-热毛细对流失稳的临界Marangoni数等临界条件。研究结果表明,液池低速旋转会降低轴对称热毛细对流的稳定性,而较高速度的旋转能增强热毛细对流的稳定性。临界条件下旋转-热毛细对流耗散结构波纹的传播方向与液池的旋转方向相同,临界周向波数随旋转速度的增加而增加。在较大的旋转速度下,液池底部出现涡胞,底部涡胞对热毛细对流的稳定性具有削弱作用。     

New Generalized Conditional Symmetry Reductions and Exact Solutions of the Nonlinear Diffusion-Convect ion-Reaction Equations

The generalized conditional symmetry method, which is a generalization of the conditional symmetry method, is used to study the nonlinear diffusion-convection-reaction equations. In particular, power law and exponential diffusivities are examined and we derive mathematical forms of the convection and reaction terms which permit a new type of generalized conditional symmetry. Some new exact solutions of the governing equations can be obtained by solving the systems of two or three ordinary differential equations which arise from the compatibility of the generalized conditional symmetries and the governing equations.     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported.The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point.The constitutive relationship for the Casson fluid is used.The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations.Exact solutions of the resulting ordinary differential equations are obtained.The effect of increasing Casson parameter,i.e.,with decreasing yield stress(the fluid behaves as a Newtonian fluid as the Casson parameter becomes large),is to suppress the velocity field.However,the temperature is enhanced as the Casson parameter increases.It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature.The skin-friction coefficient is found to increase as the transpiration parameter increases.