Effect of the temperature dependence of the viscosity of pseudoplastic lubricants on the boundary friction regime

The boundary friction regime appearing between two atomically smooth solid surfaces with an ultrathin lubricating layer between them is considered. The interrupted (stick-slip) regime of motion typical of the boundary lubrication is represented as a first-order phase transition between the structural states of the lubricant. The thermodynamic and shear melting is described. The universal dependence of the viscosity of high-molecular alkanes (lubricants) on the temperature and velocity gradient is taken into account. The dependence of the friction force on the lubricant temperature and the relative shear velocity of the interacting surfaces are analyzed. It is shown that the temperature dependence of the viscosity makes it possible to describe some experimentally observed effects. The possibility of prolonged damped oscillations after lubricant melting prior to the stabilization of the steady-state sliding mode is predicted. In the stick-slip regime in a wide range of parameters, a reversive motion is observed when the upper block moves in both directions after melting.     

Multimode Active Control of Friction,Dynamic Ratchets and Actuators

Active control of friction by ultrasonic vibration is a well-known effect with numerous technical applications ranging from press forming to micromechanical actuators. Reduction of friction is observed with vibration applied in any of the three possible directions (normal to the contact plane, in the direction of motion and in-plane transverse). In this work, we consider the multi-mode active control of sliding friction, where phase-shifted oscillations in two or more directions act at the same time. Our analysis is based on a macroscopic contact-mechanical model that was recently shown to be well-suited for describing dynamic frictional processes. For simplicity, we limit our analysis to a constant, load-independent normal and tangential stiffness and two superimposed phase-shifted harmonic oscillations, one of them being normal to the plane and the other in the direction of motion. As in previous works utilizing the present model, we assume a constant local coefficient of friction, with reduction of the observed force of friction arising entirely from the macroscopic dynamics of the system. Our numerical simulations show that the resulting law of friction is determined by just three dimensionless parameters. Depending on the values of these parameters, three qualitatively different types of behavior are observed: (a) symmetric velocity-dependence of the coefficient of friction (same for positive and negative velocities), (b) asymmetric dependence with respect to the sign of the velocity, but with zero force at zero velocity, and (c) asymmetric dependence with nonzero force at zero velocity. The latter two cases can be interpreted as a "dynamic ratchet" (b) and an actuator (c).     

Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.     

Mixed convection of a conducting third-grade fluid past an oscillating porous plate

We study heat transfer in the incompressible flow of a conducting third-grade fluid subject to a uniform magnetic field past an oscillating porous vertical plate.We obtain the analytical form of the boundary-layer velocity profile, the temperature profile, and the skin friction coefficient for small deviations from the Newtonian rheology. We examine the dependence of these quantities on the Prandtl number, the mixed convection parameter, the Hartmann number, and the suction parameter.     

Dynamics of the coefficient of friction between a rigid conical indenter and a viscoelastic foundation under step-wise change of sliding velocity

We numerically calculated the coefficient of friction between a rigid cone and a viscoelastic Kelvin body under step-wise change of the velocity of sliding. The time dependence of the coefficient of friction has been empirically approximated. We show that the transition process has different character for the cases of increasing and decreasing of the sliding velocity.     

Rheology of polymer suspensions: II. Translation,rotation and viscosity

The theory of average local velocity fields developed in the preceding article is applied to a suspension of spherically symmetric polymers. Three transport properties of the suspension are analyzed, namely the concentration dependence of the translational and rotational friction coefficient of a polymer, and the concentration dependence of the viscosity of the solution.     

An Analytical Study of Hydrodynamic Instability in the Flame. 1. Viscous Gas in the Flame Zone

The problem of the hydrodynamic stability of slow combustion is analytically solved with consideration given to the viscosity of the gas in the flame zone, the temperature dependence of the viscosity, and the dependences of the flame speed on the front curvature according to the Markstein model and on the pressure. The viscous forces in the flame zone alone cannot ensure the stability of the flame at any values of the Reynolds number. These forces act only as amplifiers of the stabilizing factor according to the Markstein model or in the case of a negative dependence of the flame velocity on the pressure. This property of internal friction forces is the more pronounced, the stronger the viscosity increases with the temperature. Thermal expansion is not only a destabilizing factor, leading to an increase in viscosity and other transport coefficients, but also produces a stabilizing effect.     

不同亚格子模型在亚声速槽道流大涡模拟中的应用对比

湍流边界层流动是一种广泛存在于飞行器内部和外部的流动现象，是基础理论和模型验证的重要研究对象.能够捕捉大部分流动细节且计算量适中的大涡模拟（large-eddy simulation，LES）方法在湍流数值模拟中得到了越来越广泛的应用.文章基于格心有限差分方法，使用4阶紧致中心格式离散N-S方程无黏项，分别应用5种不同的亚格子（subgrid-scale，SGS）模型，即隐式，SM（Smagorinsky model），DSM（dynamic Smagorinsky model），WALE（wall-adapting local eddy-viscosity model）和CSM（coherent structures model），对Re = 3 000，Ma = 0.5的等温壁面槽道流动进行了大涡模拟研究.与实验值和直接数值模拟（direct numerical simulation，DNS）结果对比后发现，流场平均温度、平均密度等热力学量以及平均流向速度对亚格子模型不敏感，不适宜作为判断模型优劣的判据.亚格子模型在壁面附近的耗散越大，壁面摩擦速度以及阻力系数就越小.对于与速度相关的脉动量来说，不同模型得到的结果在壁面和脉动峰值附近误差比较大，中心线附近较小；显式模型结果在流向速度峰值处均高于参考值，而在展向和壁面法向速度脉动峰值处则均偏低.考虑显式的4种模型在壁面附近的涡黏系数分布，DSM和CSM曲线满足涡黏系数与无量纲壁面距离3次方成正比的分布规律，SM曲线斜率偏小而WALE曲线斜率偏大.      

Experimental investigation of the adhesive contact of an elastomer

The present work is an experimental study of adhesion between an elastomer and a rigid cylindrical indented The experimental characterization was carried out using a specially developed apparatus. Adhesive force was measured as function of contact geometry, pull-off velocity, normal force, temperature, waiting time, and material properties. Experimental results are compared with existing theoretical models for adhesion of elastic and viscoelastic bodies. Our study shows that the adhesive force between the studied elastomer and a steel cylinder is determined by completely different mechanisms than assumed in the Kendall’s theory. In particular, it does not depend on the surface energy and is almost entirely dominated by the viscosity of the elastomer.     

Effects of nonlocal hydromechanics in a flow in thin channels

An approach to viscous friction is described as nonlocal momentum exchange between different layers of a fluid. The Navier?Stokes equations are replaced by pseudo-differential equations hyperbolic in time. In this case, instead of zero velocity on the boundary, a nonlocal nonlinear boundary condition is set in the form of the velocity dependence of the coefficient before the intensity of the momentum exchange with the boundary. The non-newtonian character of the viscosity of water is shown in experiments with thin insulin needles and explained by the nonlinear character of the momentum exchange of water with the boundary. The calculations agree very well both with our experiments and with the experiments of other authors. Calculations show that the flow decreases more than one-and-a-half times in comparison with the Poiseuille flow for channels with a diameter of 360?390 μm, which is confirmed in experiments.     

Scaling theory of polymer thermodiffusion

The motion of a linear polymer chain in a good solvent under a temperature gradient is examined theoretically by breaking up the flexible chain into Brownian rigid rods, and writing down an equation of motion for each rod. The motion is driven by two forces. The first one is Waldmann’s thermophoretic force (stemming from the departure of the solvent’s molecular-velocity distribution from Maxwell’s equilibrium distribution) which here is extrapolated to a dense medium. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings an important correction to the Stokes law of friction. We use scaling considerations relying upon disparate length scales and omitting non-universal numerical prefactors. The present scaling theory is compared with recent experiments on the thermodiffusion of polymers and is shown to account for (i) the existence of both signs of the thermodiffusion coefficient of long chains, (ii) the order of magnitude of the coefficient, (iii) its independence of the chain length in the high-polymer limit and (iv) its dependence on the solvent viscosity.     

Multiscale simulation of friction with normal oscillations in the method of reduction of dimensionality

In the framework of the method of reduction of dimensionality, the dependence of the kinetic coefficient of friction of elastomers with linear rheology on normal loads with a static and an oscillatory part has been examined. It is shown that the sinusoidal excitation leads to a reduction of the coefficient of friction by up to 20 % for a sliding velocity range of two orders of magnitude. The largest reduction of the coefficient of friction occurs at a velocity, which is proportional to the characteristic wave length of the surface and the frequency of the acting normal force.     

A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity

The steady flow and heat transfer of an electrically conducting fluid with variable viscosity and electrical conductivity between two parallel plates in the presence of a transverse magnetic field is investigated. It is assumed that the flow is driven by combined action of axial pressure gradient and uniform motion of the upper plate. The governing nonlinear equations of momentum and energy transport are solved numerically using a shooting iteration technique together with a sixth-order Runge-Kutta integration algorithm. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that the combined effect of magnetic field, viscosity, exponents of variable properties, various fluid and heat transfer dimensionless quantities and the electrical conductivity variation, have significant impact on the hydromagnetic and electrical properties of the fluid.     

Thermo-physical characteristics during the flow and heat transfer analysis of GO-nanoparticles adjacent to a continuously moving thin needle

Nanofluids have shown significant promise in thermal enhancement of many industrial systems and they have been used extensively in energy applications during recent years. Keeping such applications in mind, the present work exhibits a two-dimensional numerical simulation for the boundary layer flow of Graphene oxide (GO)-nanofluids adjacent to a thin needle along with heat transfer. Influence of heat generation/absorption and viscous dissipation have been included to explore the heat transport analysis. The nanofluid flow is generated due to a continuously moving horizontal thin needle. The non-linear expressions governing the flow and heat transfer analysis are changed into dimensionless form by introducing new dimensionless variables. The novelty of current study is to predict the multiple numerical solutions for dimensionless velocity and temperature fields. Numerical computations and graphical delineations were done with the assistance of MATLAB software. This study explores the impacts of several dimensionless key parameters, like, magnetic parameter, Prandtl number, nanoparticles volume fraction and ratio of needle's velocities on the flow and thermal distributions. The computational results have proved that the fluid temperature enhances for higher values of nanoparticles volume fraction while an opposite is true for velocity distributions. In addition, the computed outcomes revealed that for the case of upper branch solution, significant reduction in skin-friction coefficient is seen for higher magnetic parameter.     

Theoretical and numerical study of a thermal convection problem with temperature-dependent viscosity in an infinite layer

A convection problem with temperature-dependent viscosity in an infinite layer is presented. This problem has important applications in mantle convection. The existence of a stationary bifurcation is proven together with a condition to obtain the critical parameters at which the bifurcation takes place. A numerical strategy has been developed to calculate the critical bifurcation curves and the most unstable modes for a general dependence of viscosity on temperature. An exponential dependence of viscosity on temperature has been considered in the numerical calculations. Comparisons with the classic Rayleigh-Bénard problem with constant viscosity indicate that the critical temperature difference threshold decreases as the exponential rate parameter increases. The vertical velocity of the marginal mode exhibits motion concentrated in the region where viscosity is smaller.     

MHD Double-Diffusive Carreau Fluid Flow through a Porous Medium with Variable Thermal Conductivity and Suction/Injection

In this article, we consider the effects of double diffusion on magnetohydrodynamics (MHD) Carreau fluid flow through a porous medium along a stretching sheet. Variable thermal conductivity and suction/injection parameter effects are also taken into the consideration. Similarity transformations are utilized to transform the equations governing the Carreau fluid flow model to dimensionless non-linear ordinary differential equations. Maple software is utilized for the numerical solution. These solutions are then presented through graphs. The velocity, concentration, temperature profile, skin friction coefficient, and the Nusselt and Sherwood numbers under the impact of different parameters are studied. The fluid flow is analyzed for both suction and injection cases. From the analysis carried out, it is observed that the velocity profile reduces by increasing the porosity parameter while it enhances both the temperature and concentration profile. The temperature field enhances with increasing the variable thermal conductivity and the Nusselt number exhibits opposite behavior.     

Fluid-like transport variables in a kinetic collisionless plasmanear a surface with ion and electron reflection

Transport variables of the positive ions and electrons in the presheath and sheath of a plasma near a wall that partially reflects ions and electrons are determined from a kinetic analysis. Because velocity distributions of the ions and electrons near the wall are highly non-Maxwell-Boltzmann distributions, accurate predictions of transport variables, such as density, fluid velocity, mean pressure, fluid-like viscous stress, and conduction, require kinetic analysis. The results find that dimensionless transport variables of ions and electrons in the presheath and sheath can be exactly expressed in terms of transcendental functions determined by dimensionless independent parameters of ion and electron reflectivities of the wall, ion-to-electron mass ratio, charge number, and electron-to-ion temperature ratio at the presheath edge. The effects of the parameters on transport variables at the wall are also obtained. The computed transport variables in the presheath and sheath show agreement with available theoretical data for a completely absorbing wall     

Mathematical simulation of melting inside a square cavity with a local heat source

Numerical simulation of transient melting regimes inside an enclosure in the presence of a local heat source has been carried out. Mathematical model formulated in terms of dimensionless variables such as stream function, vorticity, and temperature has been numerically solved by finite difference method. Effects of the Rayleigh number 4·10⁵ ≤ Ra ≤ 5·10⁷, Stefan number 2.21 ≤ Ste ≤ 5.53, and dimensionless time on velocity and temperature fields as well as on the local Nusselt number along the heat source surface have been analyzed in detail. The transient effects of the considered process at high values of the Rayleigh number have been identified.