Effect of slip boundary condition on flow and heat transfer of a double fractional Maxwell fluid

The purpose of the present paper is to investigate the flow and heat transfer of a double fractional Maxwell fluid with a second order slip model. The fractional governing equations are solved numerically by using the finite difference method. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. The effects of the two slip parameters and the fractional parameters on the velocity and temperature distribution are presented graphically and discussed. The results reveal that the fractional Maxwell fluid exhibits a stronger viscosity or elasticity for different fractional parameters, and the oscillation phenomenon will gradually decrease as expected with an increase in slip parameters.     

Analytical Solution for Peristaltic Transport of Viscous Nanofluid in an Asymmetric Channel with Full Slip and Convective Conditions

The peristaltic flow of nanofluids is a relatively new area of research. Scientists are of the opinion that the no-slip conditions at the boundaries are no longer valid and consequently, the first and the second order slip conditions should be addressed. In this paper, the effects of slip conditions and the convective boundary conditions at the boundary walls on the peristaltic flow of a viscous nanofluid are investigated for. Also, the exact analytical solutions are obtained for the model. The obtained results are presented through graphs and discussed. The results reveal that the two slip parameters have strong effects on the temperature and the nanoparticles volume fraction profiles. Moreover, it has been seen that the temperature and nanoparticles volume fraction profiles attain certain values when the first slip condition exceeds a specified value. However, no limit value for the second slip parameter has been detected. Further, the effects of the various emerging parameters on the flow and heat transfer characteristics have been presented.     

微通道内气体流动的格子Boltzmann方法研究

采用格子Boltzmann方法模拟了微通道在滑移区内不同Knudsen数下的微气体Poiseuille流,分析了微气体流动的速度分布以及流量与压降的关系,并给出了相对滑移长度和Poiseuille数随Knudsen数的变化特性。研究结果表明,微气体Poiseuille流的速度轮廓呈抛物线分布,但是边界速度大于0,出现速...     

微平行管道内Eyring流体的电渗滑移流动

研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.     

Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity

The magnetohydrodynamic(MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.     

Series solutions of stagnation slip flow and heat transfer by the homotopy analysis method

An analytical approximation for the similarity solutions of the two- and three-dimensional stagnation slip flow and heat transfer is obtained by using the homotopy analysis method. This method is a series expansion method, but it is different from the perturbation technique, because it is independent of small physical parameters at all. Instead, it is based on a continuous mapping in topology so that it is applicable for not only weakly but also strongly nonlinear flow phenomena. Convergent [m,m] homotopy Padé approximants are obtained and compared with the numerical results and the asymptotic approximations. It is found that the homotopy Padé approximants agree well with the numerical results. The effects of the slip length ℓ and the thermal slip constant β on the heat transfer characteristics are investigated and discussed. Supported by the National Natural Science Foundation of China (Grant No. 10872129)     

Influence of partial slip on the peristaltic flow in a porous medium

In this paper, the slip effects are discussed on the peristaltic flow of a viscous fluid in a porous medium. A long wavelength approximation is used in the flow modelling. The solutions for stream function and axial velocity are constructed by employing the Adomian decomposition method. Numerical integration has been used for the pumping and trapping phenomena. Graphs illustrate the physical behavior. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the slip parameter. Further, the peristaltic pumping rate decreases by increasing the slip parameter.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Surface effects in plastic deformation of metals

It is now accepted that the appearance of slip bands on the surface of a plastically deformed metal is evidence that the deformation is not homogeneous but is concentrated on relatively few atomic planes. Recent microscopical experiments have suggested that this conclusion is only valid in the later stages of deformation and that the first fractional per cent of strain is much more nearly homogeneous. Theories to account for both these stages of deformation are examined in the light of microscopical evidence.

The validity of conclusions about internal processes based on experiments on the surface is discussed; it is shown that the surface finish affects not only the appearance of internal processes but also the processes themselves.

In cases where the deformation is not homogeneous the balance of evidence is that it is also not continuous in time: instead, slip on an active slip plane tends to a limit which is reached either gradually or suddenly depending on the nature of the metal and the conditions of stress. The same processes which stop slip on the active planes produce general hardening of the metal. However, slip can restart on or near to former slip planes as a result of mechanisms activated by temperature and stress, and can, in favourable cases, continue until fracture. Therefore slip bands, the sources of hardening, are also places of weakness.     

Provide a suitable range to include the thermal creeping effect on slip velocity and temperature jump of an air flow in a nanochannel by lattice Boltzmann method

The thermal creeping effect on slip velocity of air forced convection through a nanochannel is studied for the first time by using a lattice Boltzmann method. The nanochannel side walls are kept hot while the cold inlet air streams along them. The computations are presented for the wide range of Reynolds number, Knudsen number and Eckert number while slip velocity and temperature jump effects are involved. Moreover appropriate validations are performed versus previous works concerned the micro–nanoflows.The achieved results are shown as the velocity and temperature profiles at different cross sections, streamlines and isotherms and also the values of slip velocity and temperature jump along the nanochannel walls. The ability of the lattice Boltzmann method to simulate the thermal creeping effects on hydrodynamic and thermal domains of flow is shown at this study; so that its effects should be involved at lower values of Eckert number and higher values of Reynolds number especially at entrance region where the most temperature gradient exists.     

Numerical study of rotating electroosmotic flow of Oldroyd-B fluid in a microchannel with slip boundary condition

In the present study, the effect of slip boundary condition on the rotating electroosmotic flow (EOF) of Oldroyd-B fluid in a microchannel under high zeta potential is considered numerically. The potential distribution of the electric double layer (EDL) is acquired by solving the nonlinear Poisson-Boltzmann equation. The numerical solution of velocity profile is obtained by using a finite difference method. The effects of rotating Reynolds number, electric width, viscous parameter, slip parameter etc on velocity and boundary stress for Oldroyd-B fluid EOF are discussed, which show that the slip boundary effect can reduce the boundary stress and promote the development of flow.     

On slip in AgCl crystals at room temperature

At moderately wavy and branched slip bands on the surfaces of sheets of AgCl crystals the distribution of slip lines has been observed by means of the electron microscope. From the results it can be deduced that the cross slip of screw dislocations takes place. The divergence of the ends of slip bands has also been observed, which can be as well explained by the cross slip. From the active slip direction and the directions of straight slip lines in the cross-slip regions the microscopic slip planes have been determined. They lie in the region roughly limited by the {113} and {331} planes and the problem is discussed whether these planes are low-index crystallographic planes.     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels

Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). In this Letter, similarity transformation for the Navier-Stokes equation for 2-dimensional steady slip flow in microchannels is given. We provide an analytical solution for the slip flow using a powerful, easy-to-use analytic technique for non-linear problems, that is, the homotopy analysis method (HAM). The analytical solution is presented in the form of an infinite series. The effects of the Knudsen number (Kn) is discussed on the velocity profiles. It is found that the results are in excellent agreement with the existing results in the literature for the case of laminar developed flow.     

A note on the geometry of slip controlled by the Peierls mechanism

The macroscopic slip plane in solids with undissociated dislocations is determined as the average plane of motion of screw dislocations. It is assumed that their motion is controlled by thermally activated overcoming of the Peierls potential into different crystallographic planes. The screw dislocations have a unit motion or jump of one atomic distance and they are free to jump into a number of different positions. Under these circumstances cross slip jumps are frequent and the macroscopic slip plane for a given applied stress is determined by the Peierls potential in the different planes of cross slip. The geometry of slip in b.c.c. metals is discussed in some detail and it is shown that experimental results can be described formally using this approach.     

Study of Friction between Liquid Crystals and Crystalline Surfaces by Molecular Dynamic Simulations

The lubrication characteristics of liquid crystal (LC) molecules sheared between two crystalline surfaces obtained from molecular dynamics (MD) simulations are reported in this article. We consider a coarse-grained rigid bead-necklace model of the LC molecules confined between two atomic surfaces subject to different shearing velocities. A systematic study shows that the slip length of LC lubrication changes significantly as a function of the LC-surface interaction energy, which can be well described though a theoretical curve. The slip length increases as shear rate increases at high LC-surface interaction energy. However, this trend can not be observed for low interaction energy. The orientation of the LC molecules near the surface is found to be guided by the atomics surfaces. The influence of temperature on the lubrication characteristics is also discussed in this article.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

Features of slip-band formation during the plastic straining of layered crystals

The effects of the narrowing and branching of screw slip bands during the plastic straining of nonuniformly doped or nonuniformly irradiated (layered) crystals are discussed theoretically on the basis of the equations of dislocation kinetics. Band formation is treated as a process involving the self-organization of dislocations in a dislocation ensemble at the mesoscopic level. The distributions of the densities of mobile and immobile dislocations, as well as of the local plastic strain rate, in a slip band propagating in a layered crystal are obtained. It is found that the narrowing of bands is due to the lower rate of broadening of the bands in stiff layers than in soft layers, which have not been hardened by doping or irradiation, and that branching is due the low local strain rate in stiff layers compared with the strain rate per slip band assigned by the straining machine. In the latter case the nucleation of new bands or the branching of existing bands is required to restore the balance between these rates. Fiz. Tverd. Tela (St. Petersburg) 41, 252–258 (February 1999)     

Simultaneous features of Wu's slip,nonlinear thermal radiation and activation energy in unsteady bio-convective flow of Maxwell nanofluid configured by a stretching cylinder

This continuation deals with the bioconvection flow of magnetized Maxwell nanofluid over a stretched cylinder in presence of slip effects. The novel features of activation energy and thermal radiation are also encountered to analyze the flow. The higher order slip relations are introduced to inspect the thermal flow problem. The flow model is developed in terms of dimensionless equations via appropriate variables. The numerical simulations are presented with shooting scheme by using MATLAB software. The physical outcomes of interesting parameters are visualized. The observations show that velocity profile reduces with unsteady parameter, curvature constant and second order slip factor. The temperature profile enhanced with first order velocity slip parameter and curvature constant. Moreover, nanofluid concentration reduces with Lewis number and Brownian constant.