Flow Past an Impulsively Started Semi-infinite Flat Plate in the Presence of a Magnetic Field

The solution of the motion of a viscous electrically conductingfluid past a semi-infinite flat plate, which is started impulsivelyfrom rest with a constant velocity parallel to itself, in thepresence of an applied magnetic field which is parallel to theplate at infinity, is investigated. The governing partial differentialequations can be written in similarity form and reduced to aset of coupled, non-linear, singular parabolic partial differentialequations. Numerical methods have been developed previouslywhich deal with uncoupled equations. The analytical work forlarge time indicates that the steady state solution is approachedexponentially when the equations uncouple but a simple extensionof this analysis is not possible when the equations are coupled.     

Adaptive Wavelet Simulation of a Flow around an Impulsively Started Cylinder Using Penalisation

We present an adaptive wavelet method to integrate the velocity–vorticity formulation of the two-dimensional Navier–Stokes equations coupled with a penalisation technique to handle efficiently solid boundaries of arbitrary shape. We demonstrate the validity of this method, called coherent vortex simulation (CVS), to compute the flow around an impulsively started cylinder at high Reynolds number and compare the results with a classical vortex method.     

Effect of Second Order Chemical Reaction on MHD Free Convective Radiating Flow over an Impulsively Started Vertical Plate

An attempt has been made to study laminar convective heat and mass transfer flow of an incompressible, viscous and electrically conducting fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in presence of transverse magnetic field. The influence of both second order chemical reaction and heat generation are taken into account. The governing coupled partial differential equations are solved by Crank-Nicolson method. The effects of important physical parameters on the velocity, temperature and concentration have been analyzed through graphs. The results of the present study agree well with the previous solutions. Applications of the present study are shown in material processing systems and different industries. The important findings of present study are: chemical reaction parameter acts as resistive force to reduce the velocity whereas heat source parameter enhances the velocity.     

The Rolling Motion of A Viscous Fluid On and Off a Rigid Surface

An analytical solution is obtained for the local flow field near a point of steady attachment to or detachment from a rigid boundary. The possible free surface shapes depend on the capillary number.     

突然起动双圆柱绕流初期流场的研究

本文推广Bar Lev M.等人在1975年提出的求解突然起动单圆柱初期流场的方法,研究了双圆柱的相应问题,对流函数φ采用匹配渐近展开法求出直到二级近似的分析解。     

Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.     

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.     

The Excitation of a Fluid-loaded Plate Stiffened by a Semi-infinite Array of Beams

The excitation of an infinite, fluid-loaded plate with parallel,equally spaced stiffening beams reinforcing one half of it isstudied. The problem is formulated in terms of a discrete convolutionequation for the displacement at the beam positions and is solvedby discrete Fourier transforms coupled with the Wiener-Hopftechnique. The basic ideas are introduced through a reconsiderationof the excitation of an infinite, fluid-loaded plate, stiffenedby a periodic array of beams. As an example, asymptotic expressionsare derived for the reflected, transmitted and scattered fieldsgenerated when a free wave in the unstiffened half of the plateimpinges upon the semi-infinite array. It is shown, in particular,that the far-field motion in the stiffened half of the platehas the form of a Floquet wave. Numerical results for reflectionand transmission coefficients, and for the pressure field radiatedinto the fluid, are presented graphically. Finally, a briefoutline is given of a number of related problems that are solubleby similar techniques.     

Uniform Flow Past an Axially Uniform Viscous Vortex

It is believed that the flow past a tornado causes the formation of smaller vortices which produce the “suction spots” observed along the path of destruction. Here we develop a greatly simplified mathematical model to investigate this phenomenon. An axially uniform vortex is developed by visualizing a circular tube with uniform surface suction of fluid possessing circulation at infinity. This vortex is then perturbed by a uniform flow past it. An inner asymptotic expansion of an E^1/3 radial boundary layer is matched to an outer expansion to obtain a solution. The results show that a stagnation point developing into a secondary vortex is formed in a free shear layer at critical flow conditions. However, it is difficult to apply our results quantitatively because of the difficulty in comparing the axially uniform vortex with a real tornado vortex.     

Nonuniqueness of a Solution to the Problem on Motion of a Rigid Body in a Viscous Incompressible Fluid

This paper is devoted to the problem on motion of a rigid body in a viscous incompressible fluid. It is proved that there exist at least two weak solutions of this problem if collisions of the body with the boundary of the flow domain are allowed. These solutions have different behavior of the body after the collision. Namely, for the first solution, the body goes away from the boundary after the collision. In the second solution, the body and the boundary remain in contact. Bibliography 15 titles.To Vsevolod Alekseevich Solonnikov on the occasion of his jubilee__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 199–209.     

Resonant Flow of a Rotating Fluid Past an Obstacle: The General Case

We consider the flow of a rotating fluid past an antisymmetric obstacle placed on the axis of a cylindrical tube, for the case when the upstream flow is nearly resonant, or critical, so that the speed of a free linear long wave is nearly zero in the frame of reference of the obstacle. The perturbed flow is dominated by the resonant mode, whose amplitude satisfies a forced Korteweg—de Vries equation in this general case when the upstream flow contains radial shear andjor radially dependent angular velocity.     

Predominantly Unidirectional Flow of a Viscous Fluid

Journal of Applied and Industrial Mathematics - We consider the problem of the flow of a viscous fluid in the presence of solid bodies (namely, the two walls and a permeable plate) under...     

Attractors of an Autonomous Model of Nonlinear Viscous Fluid

Doklady Mathematics - For an autonomous model of the motion of a nonlinear viscous fluid, we study the limiting behavior of its weak solutions as time tends to infinity. Namely, the existence of...     

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.     

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。     

The Magnetogasdynamic Boundary Layer on a Thermally Insulated Flat Plate

This paper examines the effect of compressibility on the flowin the boundary layer on a semi-infinite, thermally insulatedflat plate placed at zero incidence to a uniform stream of electricallyconducting gas, with an aligned magnetic field at large distancesfrom the plate. The present discussion is limited to small values of the conductivityparameter = 4µv, and the Prandtl number is taken to beunity. The latter assumption permits a simplification of theanalysis, and the former allows the dependence of the flow onthe parameters ß = µH²/4U² and M = U/cto beadequately illustrated without excessive computation. A seriessolution valid for small values of the conductivity parameterand for Mach numbers not too large is derived. Values of ß = 0.3 and 0.5, = 0.01 and 0.1 are consideredand for those values the skin friction decreases with increasingMach number, similar to the case when ß = 0. The analysissuggests that for larger values of ß the skin frictionmight even increase with the Mach number initially. This iscertainly the case with the tangential component of the magneticfield, which for ß = 0.5 exhibits a maximum at approximatelyunit Mach number. The reason for this behaviour lies in thefact that, in view of the temperature changes taking place inthe flow, the electrical conductivity and thereby the localvalue of can change by more than an order of magnitude. Thishas the effect of giving results which are akin to those forarbitrary large in incompressible flow even though the valueof based on the main stream gas properties remains low.