Influence of radiation on mixed convection over a wedge in non-Darcy porous medium

The influences of radiation on mixed convection flow of an optically dense viscous fluid along an isothermal wedge embedded in non-Darcy porous medium, in the presence of heat source/sink are numerically investigated. The entire mixed convection regime is covered by a single parameter χ from the pure free convection limit (χ=0) to the pure forced convection limit (χ=1). Forchheimer’s extension is employed to describe the fluid flow in the porous medium and the Rosseland diffusion approximation is considered to describe the radiative heat flux in the energy equation. The governing equations, including internal heat source/sink, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by the Keller box method. The effect of the radiation parameter, mixed convection parameter, Forchheimer number and heat source/sink parameter on the velocity and temperature profiles as well as on the local Nusselt number is presented and analyzed. The results are compared with those known from the literature and excellent agreement between the results is obtained.     

Dynamics of a thin film with temperature-dependent viscosity on a rotating disk

Summary The thermal effects on the dynamics of an axisymmetric flow of a non-volatile incompressible viscous thin liquid film on a rotating disk due to viscosity variation depending exponentially on temperature are considered. The nonlinear evolution equation is solved numerically. The numerical results reveal that heating the film from below enhances the rate of thinning. The increase in Biot number increases the film thickness, when the film is heated from below. Further, the relative amount of fluid retained on the substrate decreases as the film is heated from below. The results are reversed for the case of a film which is cooled from below. The rate of thinning of the film is more (less) for the case of temperature dependent viscosity when the film is heated (cooled) from below than for the case of constant viscosity of the fluid.     

Development of a generalized model for analyzing phase characteristics of SAW devices under mass and fluid loading

vA generalized model that integrates the Navier-Stokes equation and coupling-of-modes (COM) model for biosensing SAW devices is developed in this paper. The SAW device is separated into three regions: interdigital transducer (IDT), substrate (delay line), and sensing regions. To evaluate the effects of metal thickness, mass loading caused by bioreaction, and different viscous fluid loading, the sensing region is further divided into three layers: piezoelectric substrate, metal layer, and fluid layer. In contrast to the conventional study, which is focused on the change of phase velocity, this model can evaluate the insertion loss and phase shifts under different sensing conditions. It can be shown that the integration of the COM model can provide guidelines for designing the bio-sensing device such as choosing the proper number of IDT, the width of the overlap, and the thickness of the metal layer. Furthermore, the generalized model can be utilized to evaluate the optimal thickness of the metal layer to achieve the maximum sensitivity.     

静水中反应堆吊篮结构的振动特性研究

将吊篮与压力容器视为包含粘性流体的有限长同心圆柱壳体结构。从圆柱壳的运动控制微分方程和流体的 N- S方程出发 ,在流体不可压缩粘性假设下 ,导出吊篮结构自由振动时 ,流体作用于壳体结构上的附加质量、附加阻尼矩阵。再结合固体有限元技术 ,建立吊篮结构的流固耦合振动的有限元模型。用此模型对吊篮结构在静水中的固有振动特性进行分析 ,计算结果与试验实测结果的比较表明 ,本文方法能较好地满足工程分析要求     

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

Summary The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.     

Optimizing the operation of a direct-flow filtration device

A mathematical model of an oscillating wave surge converter is developed to study the effect that viscous dissipation has on the behaviour of the device. Recent theoretical and experimental testing have suggested that the standard treatment of viscous drag (e.g. Morison’s equation) may not be suitable when the effects of diffraction dominate the wave torque on the device. In this paper, a new model of viscous dissipation is presented and explored within the framework of linear potential flow theory, and application of Green’s theorem yields a hypersingular integral equation for the velocity potential in the fluid domain. The hydrodynamic coefficients in the device’s equation of motion are then calculated, and used to examine the effect of dissipation on the device’s performance. A Haskind relationship, expressing the link between the scattering- and radiation-potential problems is derived, and its connection to existing Haskind relations is explored. A sensitivity study of the device’s power capture to the magnitude of the dissipation present in the system is carried out for a selection of device widths. The results of the sensitivity study are explained with reference to existing experimental and numerical data. A special focus is given to the effects of dissipation on the performance of a device whose pitching motion is tuned to resonate with the incoming waves.     

Propagation of thickness-twist waves in a piezoelectric ceramic plate in contact with viscous fluids

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.     

信道阻尼边界对井下钻杆声传输的影响

为改善低频声波沿钻杆管肇的传输性能，分析了影响声遥测的阻尼机制。考虑钻杆内外沿轴向流动的钻井液的阻尼影响，引入流体的粘性阻尼力，建立了一维纵波波动方程。基于圆柱源辐射理论，研究纵波的径向耦合损耗，并将地层等效为Kelvin粘弹性介质，应用有限单元法求解时域波动方程，讨论了钻井液粘性阻尼和粘弹性地层边界对行波传播特性的影响。理论分析表明，径向辐射和由此产生的波型耦合是声阻尼损耗的主要形式，地层粘弹性系数的变化列低频特性影响很大，但并不改变信道通阻带交替的梳状滤波器频谱。     

Integral formulation to simulate the viscous sintering of a two-dimensional lattice of periodic unit cells

In this paper a mathematical formulation is presented which is used to calculate the flow field of a two-dimensional Stokes fluid that is represented by a lattice of unit cells with pores inside. The formulation is described in terms of an integral equation based on Lorentz's formulation, whereby the fundamental solution is used that represents the flow due to a periodic lattice of point forces. The derived integral equation is applied to model the viscous sintering phenomenon, viz. the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical simulation is carried out by solving the governing Stokes flow equations for a fixed domain through a Boundary Element Method (BEM). The resulting velocity field then determines an approximate geometry at a next time point which is obtained by an implicit integration method. From this formulation quite a few theoretical insights can be obtained of the viscous sintering process with respect to both pore size and pore distribution of the porous glass. In particular, this model is able to examine the consequences of microstructure on the evolution of pore-size distribution, as will be demonstrated for several example problems.     

两黏性颗粒间切向阻力的渐近解析解

从分析两黏性颗粒的相对切向运动着手,化二阶变系数非齐次液桥流体压力微分方程为欧拉方程,解得具有相对运动的不等径颗粒间液桥流体压力和切向黏性阻力的渐近解析解,并与Goldman意义上的近似解和其他文献中的数值解进行对比。结果表明:利用这些解析解可直接定义黏性颗粒力学模型,也可分析不同参数条件下液桥流体压力与颗粒间切向阻力的变化规律。     

Theoretical magnetohydrodynamic analysis of mixed convection boundary-layer flow over a wedge with uniform suction or injection

Summary The purpose of this work is to study the effects of an applied magnetic field on the mixed convection boundary-layer flow over a wedge with suction or injection. The fluid is assumed to be viscous, incompressible and electrically conducting, and the magnetic field is applied transversally to the direction of the flow. Such a flow model has great significance not only of its own theoretical interest, but also for applications to aerodynamics and engineering. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary-layer analysis. Numerical calculations are carried out for different values of the dimensionless parameters of the problem, and the analysis of the obtained results showed that the flow field is appreciably influenced by the applied magnetic field.     

The structure and modes of a compressible superfluid film

A formal apparatus is constructed for study of the structure and modes of a single-component film system. The essential ingredients of this apparatus are an equation of motion for the two-dimensional complex order parameter and an energy functional that is the driving force in this equation. The film profile, energy, chemical potential, third sound velocity, etc., are studied for four model films: model 1, a free-standing self-bound fluid; models 2:0 and 2:1, a self-bound fluid in a substrate potential; and model 3, a non-self-bound fluid in a substrate potential. Model 1 can be studied analytically; models 2:0, 2:1, and 3 are studied numerically. Liquid⁴He is a self-bound fluid; spin-polarized hydrogen is a non-self-bound fluid.     

A new finite element technique for the analysis of steady viscous flow problems

A new finite element technique for two-dimensional viscous incompressible fluid flow problems is presented in this paper. The vorticity transport equation is integrated in a small control volume, which results in the conservation law of vorticity. The finite element technique is applied to this equation together with the continuity equation, where simple linear triangular elements with three nodes are used for the formulation. Resulting sets of algebraic equations are solved by the use of a kind of relaxation method. Numerical results for viscous flow past a cavity show good agreement with experimental results.     

The movement law and orientation control of rectangular particles in the viscous fluid domain based on IS-FEM

Understanding the movement law and orientation control mechanism of non-spherical particles are significant for industrial applications. In this work, the flow characteristics of rectangular particles, in the uniform and wedge viscous fluid domain, are simulated by the immersed smoothed finite element method (IS-FEM). The influences of mesh resolution and time-step on particle velocity are analyzed, and the numerical procedure is validated by the published model and sedimentation experiments. The operating parameters that affect the particle flow are systematically studied, including Reynolds number, initial angle, channel offset distance, and aspect ratio. Moreover, the particle angles are adjusted by the velocity gradient of fluid domains. The result indicates that the velocities, angle, and drag of rectangular particles are closely related to the working conditions. The long axis of rectangular particles is consistent with the flow direction in shrinking fluid domains and is perpendicular to the flow direction in expanding fluid domains. The angle distribution law of rectangular particles in moving wedge fluid domains is determined. These findings provide a theoretical foundation for particle sedimentation and suspension flow, which is helpful for the further separation and orientation control of mixed particles.     

Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space

In this paper we analyze the problem of a penny-shaped hydraulic fracture propagating parallel to the free-surface of an elastic half-space. The fracture is driven by an incompressible Newtonian fluid injected at a constant rate at the center of the fracture. The flow of viscous fluid in the fracture is governed by the lubrication equation, while the crack opening and the fluid pressure are related by singular integral equations. We construct two asymptotic solutions based on the assumption that either the solid has no toughness or that the fluid has no viscosity. These asymptotic solutions must be understood as corresponding to limiting cases when the energy expended in the creation of new fracture surfaces is either small or large compared to the energy dissipated in viscous flow. It is shown that the asymptotic solutions, when properly scaled, depend only on the dimensionless parameter cal R cal, the ratio of the fracture radius over the distance from the fracture to the free-surface. The scaled solutions can thus be tabulated once and for all and the dependence of the solution on time can be retrieved for specific parameters, through simple scaling and by solving an implicit equation.     

Exact Analysis of Non-Linear Fractionalized Jeffrey Fluid. A Novel Approach of Atangana-Baleanu Fractional Model

It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence of relative parameters on fluid flow and temperature distribution is shown graphically. As special cases, and for the sake of correctness, the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained. It is interesting to note that fractional parameter α provides more than one line as compared to the classical model. This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model. It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.     

The torque on a rotating disk in the surface of a liquid with an adsorbed film

Summary In this paper we consider the problem of calculating the resistive torque on a disk rotating slowly with constant angular speed in the surface of a liquid with an adsorbed surface film. Using the method of complementary representations for generalised axially symmetric potential functions, the boundary-value problem for the azimuthal velocity component is reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved numerically and asymptotically for all values of the ratio of the surface shear viscosity of the film to the viscosity of the substrate fluid, and values calculated for the substrate and film torques on the disk. The results are compared with previous work of Goodrich and his co-workers.     

Nonlinear waves in a prestressed elastic tube filled with a layered fluid

In this work, we studied the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an incompressible layered fluid, where the outer layer is assumed to be inviscid whereas the cylindrical core is considered to be viscous. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is studied. The governing equation is shown to be the Korteweg-de Vries-Burgers' (KdV-B) equation. A travelling wave type of solution to this evolution equation is sought and it is observed that the formation of shock wave becomes evident with increasing core radius parameter.     

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.     

On the motion of a micropolar fluid drop in a viscous fluid

Summary The problems of the flow of a viscous fluid past a micropolar fluid sphere and the flow of a micropolar fluid past a viscous fluid drop are discussed. The expressions for the stream functions, velocities, spins and the drag are obtained in each case and are compared with the classical (viscous fluid past a viscous fluid sphere) results. It is found that the viscosity ratios and the parameters, which arises in connection with the boundary condition, have significant effect upon the drag on the sphere in each case.