滑移垂直壁面驻点附近的混合对流边界层流动

就粘性不可压缩流体,研究垂直壁面的滑移,对壁面驻点附近稳定混合对流边界层流动的影响.假定表面温度和外部流动速度与到驻点的距离呈线性变化.首先,将偏微分的控制方程,转变为常微分方程组,然后应用打靶法进行数值求解.对不同数值的控制参数,按分顺流和逆流两种情况,分析和讨论了流动特性和热传导特征.结果表明,逆流时,在浮力参数的某一范围内出现双解;顺流时,解是唯一的.一般而言,速度滑移导致壁面热传导率增大,而热滑移使之减小.     

微极流体蠕动泵经由滑移边界管道输送的Stokes流动

计及管道边界条件滑移的影响,研究微极流体蠕动泵,经由圆柱形管道输运的Stokes流动.壁面运动的控制方程为正弦波方程.使用润滑理论,得到了轴向速度、微转动向量、流函数、压力梯度、摩擦力和机械效率的解析数值解.用图形表示出构成参数,如像耦合参数、微极参数和表征蠕流泵特性的滑移参数、摩擦力和俘获现象的影响.数值计算表明,当耦合参数较大时,需要蠕动泵的压力更大,而微极参数和滑移参数正相反.俘获团块的大小随耦合参数和微极参数的减小而缩小,而随滑移参数的增大而缩小.     

三维与二维晶体生长控制方程的精确解

本文通过将未知函数展开成复数形式的Fourier级数,求出了一类二阶偏微分方程的三角级数形式的解析解,并严格证明了其收敛性．三维稳态与二维稳态和二维非稳态晶体生长控制方程都是这类二阶偏微分方程特例．利用这一特点,本文求出了三维稳态与二维稳态和二维非稳态晶体生长控制方程的解析解．理论结果有助于揭示稳态晶体生长的本质特性．本文还给出了三维非稳态晶体生长控制方程的解析解．     

基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

研究了多孔介质中带二阶滑移边界的不可压缩MHD粘性流体在可渗透指数延伸壁面上的驻点流问题.通过相似变换将描述驻点流的控制方程转换为非线性常微分方程,并利用MATLAB的bvp5c函数求解非线性问题.分析并讨论了一、二阶滑移参数,抽吸/喷注参数以及渗透参数对速度分布和壁面剪切力的影响.结果显示在多孔介质中当壁面延伸速度小于外界主流速度时,随着一阶滑移参数、二阶滑移参数绝对值、抽吸/喷注参数以及渗透参数的增大,速度增大,壁面剪切力减小且均为正数;而当壁面延伸速度大于外界主流速度时形成一个反边界层,速度减小,壁面剪切力绝对值也减小且均为负数;二阶滑移参数对速度剖面和壁面剪切力的影响略大于一阶滑移参数的影响,抽吸/喷注参数对速度剖面和壁面剪切力的影响明显大于渗透参数或磁场参数的影响.     

在有一级化学反应时粘弹性流体流经无限竖直多孔平板时的边界层流动

在有一级化学反应时,研究不可压缩的粘弹性流体,在竖直多孔连续运动平板上的不稳定自然对流.控制方程用隐式有限差分法进行数值求解.与解析解的结果比较,证明所选用的数值方法有效.详细图示了速度分布的数值结果.研究了粘弹性参数、无量纲化学反应参数和平板运动速度,对稳定的速度分布、与时间相关的摩擦因数、Nusselt数和Sherwood数的影响.     

精确的磁流体动力学汇流解析解

就一个特殊的磁流体动力学(MHD)流动,即速度幂指数为-1时的汇流,得到著名的Falkner-Skan方程精确的解析解.解析解是封闭的,并有多重解分支.分析了磁场参数和壁面伸长参数的影响.发现了有趣的速度分布现象:即使壁面固定,回流区域依然出现.在一个罕见的FalknerSkan MHD流动中,得到了一组解,以精确封闭的解析公式表示,极大地丰富了著名的Falkner-Skan方程的解析解,也加深了对这重要又有趣方程的理解.     

轴向变速运动弦线的非线性振动的稳态响应及其稳定性

研究具有几何非线性的轴向运动弦线的稳态横向振动及其稳定性．轴向运动速度为常平均速度与小简谐涨落的叠加．应用Hamilton原理导出了描述弦线横向振动的非线性偏微分方程．直接应用于多尺度方法求解该方程．建立了避免出现长期项的可解性条件．得到了近倍频共振时非平凡稳态响应及其存在条件．给出数值例子说明了平均轴向速度、轴向速度涨落的幅值和频率的影响．应用Liapunov线性化稳定性理论,导出倍频参数共振时平凡解和非平凡解的不稳定条件．给出数值算例说明相关参数对不稳定条件的影响．     

传导-辐射和磁流体组合对磁化可渗透平板自然对流影响的数值解法

研究粘性、不可压缩、导电流体,在磁化可渗透竖直平板上作自然对流时,数值地分析辐射和磁流体组合的影响.采用两种方法数值地求解非相似的控制方程:1)对所有吸入参数值ξ,采用有限差分法;2)为小数值和大数值的吸入参数值ξ,分别建立起级数的渐近解.用图形和列表形式,给出Prandtl数Pr,磁Prandtl数Pm,磁力参数S,辐射参数Rd,壁面温度θw的变化,对壁面摩擦因数、热交换率和电流密度的影响.最后分析上述物理参数对速度分布、温度分布和磁场横向分量的影响.     

考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析

采用微分求积方法（DQ方法）讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题．导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件．进一步推广并运用新的分析技术简化了非线性方程的计算．为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响A·D2还考察了几何、材料参数及横向剪切效应对正交各向异性板非线性弯曲的影响．分析结果表明横向剪切效应对正交各向异性中厚板的影响是显著的．     

高zeta势下Phan-Thien-Tanner(PTT)流体的电渗微推进器北大核心CSCD

在高的壁面zeta电势下,考查了Phan-Thien-Tanner(PTT)黏弹性流体在平行板微通道中的电渗推进器问题.在没有考虑Debye-Hückel线性近似的条件下,求解了非线性Poisson-Boltzmann方程,得到了高zeta电势下电势的解析解.通过求解PTT流体满足的Cauchy动量方程,获得了Navier滑移条件下微推进器速度的数值解.进而通过数值积分得到了电渗微推进器的性能分布,包括比冲、推力、效率和推力-功率比.最后,详细分析了黏弹性参数、壁面zeta电势、滑移系数和双电层厚度对速度分布及推进器性能的影响.结果表明,与Newton流体相比,PTT流体作为推进剂有利于推进器性能的提高,比如,流体速度随着黏弹性参数的增大而增大,导致推进器性能也呈增大的趋势.此外,当前推进器比冲为800~1000 ms时,推力可达0~250μN,效率为6%~12%,推力-功率比为0~20 mN/W.     

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.     

Nano boundary layers over stretching surfaces

In this paper, we present similarity solutions for the nano boundary layer flows with Navier boundary condition. We consider viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. The resulting nonlinear ordinary differential equations are solved analytically by the Homotopy Analysis Method. Numerical solutions are obtained by using a boundary value problem solver, and are shown to agree well with the analytical solutions. The effects of the slip parameter K and the suction parameter s on the fluid velocity and on the tangential stress are investigated and discussed. As expected, we find that for such fluid flows at nano scales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter K.     

等宽多孔介质壁面管道中磁流体的流动

研究等宽管道中,磁场、可渗透壁面、Darcy速度和滑动参数,对流体稳定流动的综合影响.假设管道中流动的流体是均匀的、不可压缩的Newton流体.利用Beavers-Joseph滑动边界条件,得到控制方程的解析解.详细地讨论了磁场、可渗透性、Darcy速度和滑动参数对轴向速度、滑动速度和剪应力的影响.可以看出,Hartmann数、Darcy速度、多孔参数和滑动参数,在改变流动方向,进而改变剪应力方面,起着至关重要的作用.     

Entropy Generation and Thermal Radiation Effects on Nanofluid over Permeable Stretching Sheet

In the present paper, effects of entropy generation and nonlinear thermal radiation on Jeffery nanofluid over permeable stretching sheet with partial slip effect were analyzed. The suitable similarity transformation is utilized for the reduction of a set of governing equations, which are solved by using Differential Transformation Method (DTM) with the help of symbolic software MATHEMATICA. The accuracy of impact of slip parameter on coefficient of skin friction by using DTM and numerical method (Shooting technique with fourth-order Runge-Kutta) is illustrated and good agreement is found. Further, velocity, temperature, nanoparticle volume fraction and entropy generation profiles are shown graphically and studied in detail for various physical parameters. We notice that, as slip parameter rises the velocity and entropy generation profile rises. Enhancement in the effect of nonlinear thermal radiation reduces the entropy generation.     

Free vibration analysis of circular plates by differential transformation method

This study analyses the free vibrations of circular thin plates for simply supported, clamped and free boundary conditions. The solution method used is differential transform method (DTM), which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the governing differential equations are reduced to recurrence relations and its related boundary/regularity conditions are transformed into a set of algebraic equations. The frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate. Numerical results for the dimensionless natural frequencies are presented and then compared to the Bessel function solution and the numerical solutions that appear in literature. It is observed that DTM is a robust and powerful tool for eigenvalue analysis of circular thin plates.     

Unsteady Slip Flow and Heat Transfer Analysis of Oldroyd-B Fluid Over the Stretching Wedge北大核心CSCD

研究了在速度滑移现象存在下,上随体Oldroyd-B流体绕加热的楔形体的非稳态流动。采用松弛-延迟热通量模型,模拟了传热过程和热延迟时间对传热的影响,通过考虑浮升力、热辐射和对流换热边界条件,进一步研究了流动及传热特性。利用同伦分析方法获得常微分方程组的近似解析解,发现滑移参数的增大可以促进流体的流动,以及流体的温度随热辐射参数增大而升高。此外还发现,温度场在热松弛时间和热延迟时间中出现相反的变化趋势。     

Falkner-Skan equation for flow past a stretching surface with suction or blowing: Analytical solutions

The simultaneous effects of suction and injection on tangential movement of a nonlinear power-law stretching surface governed by laminar boundary layer flow of a viscous and incompressible fluid beneath a non-uniform free with stream pressure gradient is considered. The self-similar flow is governed by Falkner-Skan equation, with transpiration parameter γ, wall slip velocity λ and stretching sheet (or pressure gradient) parameter β. The exact solution for β = −1 and three closed form asymptotic solutions for β large, large suction γ, and λ → 1 have also been presented. Dual solutions are found for β = −1 for each value of the transpiration parameter, including the non-permeable surface, for each prescribed value of the wall slip velocity λ. The large β asymptotic solution also dual with respect to wall slip velocity λ, but do not depend on suction and blowing. The critical values of γ, β and λ are obtained and their significance on the skin friction and velocity profiles is discussed. An approximate solution by integral method for a trial velocity profile is presented and results are compared with the exact solutions.     

Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip

The entrained flow and heat transfer of a non-Newtonian third grade fluid due to a linearly stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that the slip and the third grade fluid parameter have opposite effects on the velocity and the thermal boundary layers.     

Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall

The influences of Hall current and slip condition on the MHD flow induced by sinusoidal peristaltic wavy wall in two dimensional viscous fluid through a porous medium for moderately large Reynolds number is considered on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for the outer and inner flows for various values of the Reynolds number, slip parameter, Hall and magnetic parameters are drawn. The inner and outer solutions are matched by the matching process. An interesting application of the present results to mechanical engineering may be the possibility of the fluid transportation without an external pressure.