An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

Effect of ion slip on the time-varying Hartmann flow of a non-Newtonian viscoelastic fluid with heat transfer

Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.     

On unsteady hydromagnetic flows of a dusty fluid between two oscillating plates

An initial value investigation is made of the motion of an incompressible viscous conducting fluid with embedded small spherical particles bounded by two infinite rigid non-conducting plates. The flow is generated in the fluid-particle system due to rectilinear oscillations of given frequencies superimposed on the plates in presence of an external transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities and the wall shear stress. It is shown that the effect of the dust particles on the fluid velocity depends on the time periods of the oscillating plates. When the time-periods are small, i.e., when the plates oscillate with high frequency, the fluid motion is found to be retarded by the particles. However, when the plates oscillate with larger time periods (smaller frequencies), the fluid velocity is increased by the presence of the particles at the early stage of the motion, and this effect persists until the equilibrium is reached when the particles exert their influence to resist the flow.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Steady MHD Couette flow with temperature-dependent physical properties

The influence of variation in physical variables on the steady magnetohydrodynamic (MHD) Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal as well as electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures, and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing nonlinear coupled equations of motion and the energy equation is obtained. The effect of the temperature-dependent viscosity, thermal conductivity, and electrical conductivity on both the velocity and temperature distributions is examined. H.A. Attia - On leave from: Dept. of Eng. Mathematics and physics, El-Fayoum University, El-Fayoum, Egypt     

Stagnation-point viscous flow of an incompressible fluid between porous plates with uniform blowing

The axially-symmetric laminar flow of an incompressible viscous fluid resulting from uniform injection through two parallel porous plates is analyzed. An exact numerical solution as well as asymptotic solutions for high and low Reynolds numbers are obtained. It is found that the velocity component normal to the porous plates is everywhere independent of radial position. This property of uniform accessibility may make this flow geometry a useful experimental tool analogous to the rotating disc. The analysis of high Peclet number mass transfer across the center plane of this geometry is presented as an example.     

Thermal stability for a reactive viscous flow in a slab

The paper deals with the effect of dimensionless non-Newtonian coefficient on the thermal stability of a reactive viscous liquid in steady flow between parallel heated plates. It is assumed that the liquid is symmetrically heated and the flow fully developed. Approximate analytical solution is obtained for the velocity of the flow and the criterion for which this solution is valid is determined. After the velocity distribution is known, the temperature distribution may be calculated. Disappearance of criticality (transition values) are obtained in the following cases: (i) bimolecular (ii) Arrhenius and (iii) sensitized temperature dependence. We have observed that non-linear effect from velocity and temperature fields introduced decaying for the transitional values of the dimensionless central temperature. Other effects of this non-linearity are reported. The results help to enhance understanding of the interplay between Newtonian and non-Newtonian thermal explosions.     

Instabilities of a gas-liquid flow between two inclined plates analyzed using the Navier–Stokes equations

The paper is devoted to a theoretical analysis of a counter-current gas-liquid flow between two inclined plates. We linearized the Navier–Stokes equations and carried out a stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. As a result, we found two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral disturbances varying the liquid and gas Reynolds number. The first mode is a “surface mode” that corresponds to the Kapitza's waves at small values of the gas superficial velocity. We found that the dependence of the neutral disturbance wavelength on the liquid Reynolds number strongly depends on the gas superficial velocity, the distance between the plates and the channel inclination angle for this mode. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase and there is a critical value of the gas Reynolds number for this mode. We obtained that this critical Reynolds number weakly depends on both the channel inclination angle, the distance between the plates and the liquid flow parameters for the conditions considered in the paper. Despite a thorough search, we did not find the unstable modes that may correspond to the instability in frame of the viscous (or inviscid) Kelvin–Helmholtz heuristic analysis.     

Two fluid flow and heat transfer in an inclined channel containing porous and fluid layer

Convective flow and heat transfer in an inclined channel bounded by two rigid plates held at constant different temperatures with one region filled with porous matrix saturated with a viscous fluid and another region with a clear viscous fluid different from the fluid in first region is studied analytically. The coupled nonlinear governing equations are solved using regular perturbation method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Results have been presented for a wide range of governing parameters such as Grashof number, porous parameter, angle of inclination, ratio of heights of the two layers and also the ratio of viscosities.     

Autorotation dynamics of a low aspect-ratio rectangular prism

This paper presents two previously unreported aspects of the autorotation dynamics of low aspect ratio rectangular prisms, observed during an experimental study of the dynamics of helicopter underslung loads. Low-speed wind tunnel tests of a simplified container model free to rotate on a fixed axis demonstrated (a) that autorotation rate can lock-in to a structural mode and (b) that static hysteresis in autorotation rate can occur at low speeds. Autorotation lock-in behaves in a similar manner to vortex-shedding lock-in, suggesting that a similar feedback flow process between vortex wake dynamics and body motion is operating, and may provide a partial explanation for the complex changes in behaviour of rotating slung loads at high airspeeds. Static hysteresis at low speeds results in a bifurcation diagram for autorotation which is similar to that for cross-wind galloping of a square prism, including the effects of friction and inertia. The similarity in bifurcation behaviour seems likely to indicate similar dynamics rather than flow physics, suggesting that it may be possible to apply techniques developed to model the effect of non-linear damping characteristics in galloping to the modelling of autorotation.     

Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated.The plate exchanges heat with an external fluid.Both conditions of equal and different reference temperatures of the external fluid are considered.First,the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically.Then,the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter.To relax the conditions on the perturbation parameter,the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique.The velocity,temperature,skin friction,and Nusselt numbers at the plates are discussed numerically and presented through graphs.     

暖季强降雨对多年冻土南界斜坡路基稳定性影响分析

为阐明表面活性剂水溶液的减阻作用,使用LDV对零压梯度的二维湍流平板边界层中的CTAB 表面活性剂水溶液的湍流特性进行了实验研究. 结果表明：与牛顿流体相比,CTAB水溶液边 界层的粘性底层增厚;主流时均速度分布有被层流化的趋势,对数分布域上移;主流方向速 度湍动强度峰值减小,且远离壁面,在靠近边界层中部,出现第2峰值;垂直于主流方向的 速度湍动强度受到了大幅度抑制,雷诺应力沿着边界层厚度方向几乎为零. 结果说明CTAB 水溶液具有减弱湍流湍动各个成分相关度的作用,从而能够使雷诺应力降低、湍流能量生成 项减小最终降低流体的输送动力.     

Viscosity-stratified flow in a Hele–Shaw cell

A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow the interpretation of the Saffman–Taylor instability is given. A kinematic-wave model of viscous fingering taking into account friction between the fluid layers is proposed. Comparison with calculations on the basis of two-dimensional equations shows that this model allows to determine the propagation velocity of the viscous fingers.     

Mathematical modeling of fractional derivatives for magnetohydrodynamic fluid flow between two parallel plates by the radial basis function method

Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years, owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena. In this paper, the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic field. The magnetohydrodynamics coupled stress fluid flows between two parallel plates, with the bottom plate being stationary and the top plate moving at a persistent velocity. We compared the radial basis function approach to the numerical method (fourth-order Range-Kutta) in order to verify its validity. The findings demonstrated that the discrepancy between these two techniques is quite negligible, indicating that this method is very reliable. The impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is illustrated. Eventually, the velocity parameter is compared for diverse conditions α, Reynolds and position (y), the maximum of which occurs at α = 0.4. Also, the maximum velocity values occur in α=0.4 and Re=1000 and the concavity of the graph is less for α=0.8.     

Design method for fluid viscous dampers

A basic design method of doubly acting fluid viscous dampers with double guide bars is presented. The flow of the viscoelastic fluid between two parallel plates, one of which is started suddenly and the other of which is still, is analyzed. According to this solution, the velocity and the shear stress of the fluid at the fringe of the piston are solved approximately. A mathematical model of viscous dampers is derived, and the shock test is carried out. From experimental results, the parameters of the mathematical model are determined. Consequently, a semi-empirical design equation is obtained. Applying this equation to a certain practical damper, the damping material is chosen and the physical dimensions of the damper are determined. Shock tests using this damper are performed. Theoretical results are in good agreement with experimental results, which validates the reliability of the calculated physical dimensions of the specimen damper and the validity of the basic design equation. An erratum to this article can be found at     

Diffusion velocity for a three-dimensional vorticity field

A discussion is presented on the existence of a diffusion velocity for the vorticity vector that satisfies extensions of the Helmholtz vortex laws in a three-dimensional, incompressible, viscous fluid flow. A general form for the diffusion velocity is derived for a complex-lamellar vorticity field that satisfies the property that circulation is invariant about a region that is advected with the sum of the fluid velocity and the diffusion velocity. A consequence of this property is that vortex lines will be material lines with respect to this combined velocity field. The question of existence of diffusion velocity for a general three-dimensional vorticity field is shown to be equivalent to the question of existence of solutions of a certain Fredholm equation of the first kind. An example is given for which it is shown that a diffusion velocity satisfying this property does not, in general, exist. Properties of the simple expression for diffusion velocity for a complex-lamellar vorticity field are examined when applied to the more general case of an arbitrary three-dimensional flow. It is found that this form of diffusion velocity, while not satisfying the condition of circulation invariance, nevertheless has certain desirable properties for computation of viscous flows using Lagrangian vortex methods. The significance and structure of the noncomplex-lamellar part of the viscous diffusion term is examined for the special case of decaying homogeneous turbulence.     

Oberbeck convection flow of a couple stress fluid through a vertical porous stratum

The flow and heat transfer characteristics of Oberbeck convection of a couple stress fluid in a vertical porous stratum is investigated. The perturbation method of solution is obtained in terms of buoyancy parameter N valid for small values of N. This limitation is relaxed through numerical solutions using the finite difference technique with an error of 0.1×10^-7. The effect of increase in the values of temperature difference between the plates, permeability parameter and couple stress parameter on velocity, temperature, mass flow rate, skin friction and rate of heat transfer are reported. A new achievement is explored to analyse the flow for strong, weak and comparable porosity with the couple stress parameter. It is noted that both the porous parameter and the couple stress parameter suppress the flow. Higher-temperature difference is required to achieve the mass flow rate equivalent to that of viscous flow.     

The computational fluid dynamics modelling of the autorotation of square,flat plates

This paper examines the use of a coupled Computational Fluid Dynamics (CFD) – Rigid Body Dynamics (RBD) model to study the fixed-axis autorotation of a square flat plate. The calibration of the model against existing wind tunnel data is described. During the calibration, the CFD models were able to identify complex period autoration rates, which were attributable to a mass eccentricity in the experimental plate. The predicted flow fields around the autorotating plates are found to be consistent with existing observations. In addition, the pressure coefficients from the wind tunnel and computational work were found to be in good agreement. By comparing these pressure distributions and the vortex shedding patterns at various stages through an autorotation cycle, it was possible to gain important insights into the flow structures that evolve around the plate. The CFD model is also compared against existing correlation functions that relate the mean tip speed ratio of the plate to the aspect ratio, thickness ratio and mass moment of inertia of the plate. Agreement is found to be good for aspect ratios of 1, but poor away from this value. However, other aspects of the numerical modelling are consistent with the correlations.     

Transverse motions of a single sphere in hanging or swing configurations under a longitudinal flow

As a result of the reporting of casual observations of the oscillation or rotation of the beacons in transmission line guard cables, some attention has been paid to the stability of the guard cables with beacons.The relatively more frequent observation of these motions has been explained in recent papers dealing with the elastic part of the problem as a consequence of the increasing number of resonant frequencies (one for each additional beacon) that can be excited by appropriate aerodynamic loads. But a model that could explain the aerodynamic forces that can give rise to this motion is still lacking.In this paper we consider the transverse motions of a single sphere in two simplified configurations, (1) hanging (tethered at one point), and (2) swing (tethered at two points) under a longitudinal flow, performing small amplitude swinging oscillations or circular-orbit autorotation about an axis parallel to the main flow direction. The dynamic model here presented is based on the motion equations, which also include a model for the aerodynamic lift and drag forces on the sphere in transverse motion, which considers the effect of changes of flow around the sphere due to the cable interference. These forces are contained in the symmetry plane of the flow relative to the sphere, and, when projected on the lateral direction, give rise to a lateral force, which can explain the existence of the azimuthal motion even at a large reduced velocity, outside the vortex induced vibration (VIV) range The conditions for stable small oscillation motion and circular-orbit autorotation of a sphere in a swing configuration are given.The results for the aerodynamic loads in transverse motion have also been applied to the case of a circular-orbit autorotation of a hanging sphere (spherical pendulum) under a vertical flow. The angular rotation speed and the orbit radius (or cable angle) have been determined as a function of aerodynamic coefficients and configuration parameters.