微极液体在两个多孔圆盘间的MHD流动及其热传导

两个平行的无限大多孔圆盘,圆盘表面有均匀注入时,数值地研究圆盘间不可压缩导电微极流体,在横向外加磁场作用下的轴对称稳定层流.运用von Krmn的相似变换,将非线性运动的控制方程转化为无量纲形式.使用基于有限差分格式的算法,在相应的边界条件下,求解简化后耦合的常微分方程组.讨论Reynolds数、磁场参数、微极参数和Prandtl数,对流动速度和温度分布的影响.在特殊情况下,所得结果与已有文献的工作有着很好的一致性.研究表明,圆盘表面的传热率随着Rynolds数、磁场参数和Prandtl数的增加而增加;剪切应力随着注入的增加而减少,但它随着外部磁场的加强而增加.和Newton流体相比较,微极流体的剪切应力因素较弱,有利于聚合体加工过程中流动和温度的控制.     

流过半无限竖直可渗透壁面时的磁流体动力学自由对流

研究不可压缩粘性导电流体,流过半无限竖直可渗透平板时,将其偏微分形式的流动和传热的基本控制方程,应用适当的相似变换,简化为非线性的常微分方程组．对两种抽吸参数:大的和小的抽吸参数,采用摄动法得到变换后方程的近似解．数值结果表明,随着磁场参数和抽吸参数的增大,任意点的速度场在减小;磁场参数的影响,引起热边界层厚度的增大;速度和温度场随着热汇参数的增大而减小．     

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。     

生物磁粘弹性流体的流动:应用动脉电磁过热评估血液的流动,癌症治疗进程

利用生物磁流体动力学(BFD)原理,在生物磁流体经由遭受磁场作用的多孔介质时,研究其流动的基本理论.所研究流体的磁化强度随温度而变化.流体被认为是非Newton流体,其流动由二阶梯度流体方程所控制,并考虑了流体的粘弹性效应.假设管道壁是能够伸展的,管壁表面的速度与到坐标原点的纵向距离成正比.首先将问题简化为包括7个参数的、耦合的非线性微分方程组的求解.将血液看作生物磁流体,并用上述方法分析,目的是计算某些血液的流动参数,并配以适当的数值方法,导数用差分格式近似.计算结果用图形给出,从而在磁场作用下,得到过热状态中关系血液的、血流动力学流动的理论预测.结果清楚地表明,在电磁过热治疗进程期间,磁偶极子对动脉中血液流动特征的影响起着重大作用.该研究引起了临床医学的关注,其结果有益于癌症病人采用电磁过热的治疗.     

竖板表面温度的变化对磁流体动力学流动的影响

在横向磁场作用下,不可压缩的粘性导电流体,流经一个半无限的竖板,完成了壁面温度变化对磁流体动力学流动的分析.假定由粘性耗散和感应磁场产生的热量可以忽略不计.无量纲的控制方程为二维非稳态耦合的非线性方程.结果显示,磁场参数对空气和水的速度有着抑制作用.     

朝向产热或吸热伸展平面的MHD驻点流动

分析了微极流体朝向加热伸展平面的磁流体动力学(MHD)驻点流动,考虑了粘性耗散和内部产热/吸热对流动的影响.讨论了指定表面温度(PST)和指定热通量(PHF)两种情况,采用同伦分析方法(HAM)求解边界层流动和能量方程.通过图表的显示,研究了感兴趣物理量的变化.注意到高伸展参数时解的存在与外加应用磁场密切相关.     

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.     

流经有热源多孔平板并伴有化学反应的传热传质混合对流MHD流动

对流经无限竖直多孔平板的不可压缩粘性导电流体,稳定的传热传质混合对流MHD流动问题,给出了精确解和数值解.假定均匀磁场横向作用于流动方向,考虑了感应磁场及其能量的粘性和磁性损耗.多孔平板有恒定的吸入速度并均匀地混入流动速度.用摄动技术和数值方法求解控制方程.得到了平板上速度场、温度场、感应磁场、表面摩擦力和传热率的分析表达式.相关参数取不同数值时,用图形表示出问题的数值结果.讨论了从平板到流体的Hartmann数、化学反应参数、磁场的Prandtl数,以及包括速度场、温度场、浓度场和感应磁场等其它参数的影响.可以发现,热源/汇或Eckert数的增大,极大地提高了流体的速度值.x-方向的感应磁场随着Hartmann数、磁场的Prandtl数、热源/汇和粘性耗散的增大而增大.但是,研究表明,随着破坏性化学反应(K0)的增大,流动速度、流体温度和感应磁场将减小.对色谱分析系统和材料加工的磁场控制,该研究在热离子反应堆模型、电磁感应、磁流体动力学传输现象中得到了应用.     

均匀自由流动的非牛顿流体中连续表面上的磁流体动力学流动和热传递

分析在平行自由流动的非牛顿黏弹性导电流体中,连续平展表面移动时的稳态流和热传递特性,该流动处于横向均匀磁场作用下.以二阶流体构建它的本构方程,得到了速度分布和温度断面图的数值结果.讨论了诸如黏弹性参数、磁场参数和Prandtl数等不同物理参数对诸种动量和热传递特性的影响,并给出相关图示.     

微极流体薄膜层通过以滑移速度移动的可渗透无限平板时流体特性变化和热辐射对流动和热传导的影响

微极流体薄膜层通过按滑移速度移动的可渗透无限竖直平板时,研究热辐射对混合对流薄膜层流动和热传导的影响.假定流体粘度和热传导率变化是温度的一个函数.对一些典型的可变参数值,应用Chebyshev谱方法,数值求解流动的控制方程.将所得结果与已发表文献的结果进行比较,结果是一致的.绘出并讨论了可变参数对速度、微旋转速度、温度分布曲线、表面摩擦因数和Nusselt数的影响.     

On the dynamical reduction of the Vlasov equation

The elimination of a fast-time scale from the Vlasov equation by Lie-transform methods is an important step in deriving a reduced Vlasov equation such as the drift-kinetic Vlasov equation or the gyrokinetic Vlasov equation. It is shown here that this dynamical reduction also leads to the introduction of polarization and magnetization effects in the reduced Maxwell equations, which ensure that the reduced Vlasov–Maxwell equations possess an exact energy–momentum conservation law.     

二阶流体在旋转坐标系中的三维管道流动

就两个水平板构成的旋转系统,在磁场作用下分析二阶磁流体在其间的流动.下表面是一块可伸展的平面,上面是一块多孔的固体平板.选用合适的变换,将质量和动量的守恒方程,简化为耦合的非线性常微分方程组.应用最强大的分析技术,即同伦分析法(HAM),得到该非线性耦合方程组的级数解.结果用图形给出,并详细地讨论了无量纲参数Re,λ,Ha2,α和K2对速度场的影响.     

UNSTEADY NATURAL CONVECTIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER OF FRACTIONAL SECOND-GRADE NANOFLUIDS WITH DIFFERENT PARTICLE SHAPES

The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes. Nonlinear boundary layer governing equations are formulated with time fractional derivatives in the momentum equation. The governing boundary layer equations of continuity, momentum and energy are reduced by dimensionless variable. Numerical solutions of the momentum and energy equations are obtained by the finite difference method combined with L1-algorithm. The quantites of physical interest are graphically presented and discussed in details. It is found that particle shape, fractional derivative parameter and the Grashof number have profound influences on the the flow and heat transfer.     

Modelling and analysis of the natural oscillations of a prismatic elastic beam based on a projection approach

A regular approach to the construction of mathematical models describing the natural motions of beam-type elastic bodies within the limits of the linear theory of elasticity is developed using the method of integrodifferential relations. By employing the integral form of the equations of state, relating the stresses and strains and also the velocities and momenta, the system of partial differential equations is reduced to a denumerable system of ordinary differential-algebraic equations. A polynomial representation of the unknown functions of the displacements, stresses and momentum density along two spatial coordinates is used for this purpose. The effect of the geometric and mechanical parameters of the system on the frequencies and modes of the natural oscillations of a rectilinear elastic beam is investigated.     

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the porous upper plate is investigated and an analysis is made to determine the heat and mass transfer. The unsteady Navier–Stokes equations are reduced to a generalization of the Proudman–Johnson equation retaining the effect of wall motion using a suitable similarity transformation. The analytical solution for stream function and heat transfer characteristics are obtained by employing homotopy analysis method. The effects of various physical parameters like expansion ratio, Prandtl number, Reynolds number on various momentum and heat transfer characteristics are discussed in detail.     

Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts

For a Chaplygin sleigh on a plane, which is a paradigmatic system of nonholonomic mechanics, we consider dynamics driven by periodic pulses of supplied torque depending on the instant spatial orientation of the sleigh. Additionally, we assume that a weak viscous force and moment affect the sleigh in time intervals between the pulses to provide sustained modes of the motion associated with attractors in the reduced three-dimensional phase space (velocity, angular velocity, rotation angle). The developed discrete version of the problem of the Chaplygin sleigh is an analog of the classical Chirikov map appropriate for the nonholonomic situation. We demonstrate numerically, discuss and classify dynamical regimes depending on the parameters, including regular motions and diffusive-like random walks associated, respectively, with regular and chaotic attractors in the reduced momentum dynamical equations.     

Cattaneo–Christov heat flux model for three-dimensional flow of a viscoelastic fluid on an exponentially stretching surface

ABSTRACT

In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier’s law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied.     

Numerical and analytical simulation of peristaltic flow of a Jeffrey-six constant fluid

This paper describes the Peristaltic flow of a Jeffrey-six constant fluid in an endoscope. The two-dimensional equation of Jeffrey-six constant fluid is simplified by making the assumptions of long wave length and low Reynolds number. The reduced momentum equations are solved with three methods, namely (i) Perturbation method, (ii) Homotopy analysis method, and (iii) shooting method. The comparison of the three solutions shows a very good agreement between the three results. The expressions for pressure rise and frictional forces per wave length have been also computed numerically. Finally, the pressure rise, frictional forces are plotted for different parameters of interest.     

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.