Partial Slip Conditions Research Articles

MHD Laminar Flows and Heat Transfer Adjacent to Permeable Stretching Sheets with Partial Slip Condition

MHD Laminar Flows and Heat Transfer Adjacent to Permeable Stretching Sheets with Partial Slip Condition

Stabilized approximation of steady flow of third grade fluid in presence of partial slip

This article presents a stable numerical solution to the steady flow of thermodynamic compatible third grade fluid past a porous plate. Problem formulation is completed through partial slip condition. The inability of classical Lagrange-Galerkin methods to provide a stable approximate solution to the envisaged flow problem is demystified. To prevail over the instability issues, a streamline-upwind-Petrov-Galerkin method is invoked. The results thus substantiate an apposite agreement with theory. The stability of the approximate solution is testified and appropriate conclusions on flow profile are delineated.

Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk – A numerical approach

The aim of present exploration is to study the flow of micropolar nanofluid due to a rotating disk in the presence of magnetic field and partial slip condition. The governing coupled partial differential equations are reduced to nonlinear ordinary differential equations using appropriate transformations. The differential equations are solved numerically by using Maple dsolve command with option numeric which utilize Runge-Kutta fourth-fifth order Fehlberg technique. A comparison to previous study is also added to validate the present results. Moreover, behavior of different parameters on velocity, microrotation, temperature and concentration of nanofluid are presented via graphs and tables. It is noted that the slip effect and magnetic field decay the velocity and microrotation or spin component.

Effects of magnetic field and partial slip on unsteady axisymmetric flow of Carreau nanofluid over a radially stretching surface

The unsteady magnetohydrodynamic (MHD) axisymmetric flow of Carreau nanofluid over a radially stretching sheet is investigated numerically in this article. Recently devised model for nanofluid namely Buongiorno’s model incorporating the effects of Brownian motion and thermophoresis is adopted here. Additionally, partial velocity slip and convective boundary condition are considered. Mathematical problem is modeled with the help of momentum, energy and nanoparticles concentration equations using suitable transformation variables. The numerical solutions for the transformed highly nonlinear ordinary differential equations are computed for both shear thinning and shear thickening fluids. For numerical computations, an effective numerical approach namely the Runge-Kutta Felhberg integration scheme is adopted. Effects of involved controlling parameters on the temperature and nanoparticles concentration are examined. Numerical computations for the local Nusselt number and local Sherwood number are also performed. It is interesting to note that the strong magnetic field has the tendency to enhance the thermal and concentration boundary layer thicknesses. Additionally, the local Nusselt and Sherwood numbers depreciate by improving values of unsteadiness parameter, magnetic parameter, velocity slip parameter and thermophoresis parameter in shear thickening and shear thinning fluids.

In situ fretting fatigue crack propagation analysis using synchrotron X-ray radiography

The aim of this work is to study the initiation and propagation of fatigue cracks during fretting tests in partial slip conditions, and to compare the fretting fatigue behaviour to conventional fatigue C(T) crack growth experiments. An experimental device is specially developed in order to perform in situ fretting fatigue tests at a synchrotron facility. 2D radiographs of fretting fatigue cracks are directly observed in situ for the first time for a cylinder/plane contact configuration. FE computations are carried out to calculate stress intensity factor range ΔK at the crack tip for the complex loading configuration, revealing short and long crack propagation behaviours.

Finite element analysis of fretting wear under variable coefficient of friction and different contact regimes

Fretting wear is a material damage in contact surfaces due to micro relative displacement between two bodies. It causes some unexpected results, such as loosening of fasteners or sticking in components supposed to move relative to each other. Since this micro motion of fretting wear is difficult to measure in experiments, finite element method (FEM) is widely used for investigating the evolution of contact variables and wear scars during fretting wear process. In most FEM simulations of fretting wear, coefficient of friction (CoF) is assumed to be constant in order to simplify the models. As measured in experiments, however, the evolution of CoF has a relation with the wear number of cycles, especially during the running-in stage. In this research, the effects of variable CoF are considered in both gross sliding and partial slip conditions of fretting wear. The wear scar and wear volume predicted by FEM models for constant and variable CoF cases are calculated. Results indicate that, in gross sliding condition, whether or not using a variable CoF has little effect on wear volume at the end of the steady state stage of fretting wear cycles. However, when considering partial slip or running-in stage of gross sliding conditions, FE models with variable CoF achieve predictions that are closer to experimental results.

Wear rate impact on Ti-6Al-4V fretting crack risk: Experimental and numerical comparison between cylinder/plane and punch/plane contact geometries

Fretting can lead to surface wear and/or crack nucleation depending on the sliding condition and contact geometry. To formalize this aspect, Ti-6Al-4V cylinder/plane and punch/plane contacts were investigated. The experimental crack nucleation domains in partial and gross slip conditions were established and simulated combining SWT cumulative damage analysis with FEM surface wear simulations. Good correlations were achieved if the experimental boundary conditions including system tangential accommodation and micro-rotations measured using DIC analysis, were considered. Fretting maps were simulated by predicting partial slip and gross slip displacement amplitudes above which cracks were respectively nucleated and removed by surface wear. Finally, it was shown that whatever the contact geometry, the gross slip cracking domain was inversely proportional to the surface wear rate.

Quantitative calorimetric analysis of the fretting damage: Construction of the elastic shakedown boundary

The paper aims to illustrate the relevant use of infrared thermography and energy based approaches to study the plastic behavior and the crack initiation under plain fretting loadings. A well known 35Ni Cr Mo 16 low-alloyed steel was studied under various plain fretting partial slip conditions. The experimental results showed that the proposed 2D image processing method is able to estimate thermoelastic amplitude fields in a good agreement with the theory of linear thermoelasticity, and mean intrinsic dissipation per cycle fields reflecting localized microplastic deformation. The maximal local evolution of the intrinsic dissipation as function of the shear stress amplitude, underlined the presence of a non-dissipative regime, where the specimen mainly undergoes elastic deformation and a dissipative regime where plastic deformation take place. The transition between these two regimes was then coupled with the local elastic shakedown boundary.

A comparison of relative displacement fields between numerical predictions and experimental results in fretting contact

In this paper, a comparison is made between calculated and measured displacements from a complete contact fretting test device. An experimental technique based on digital image correlation was used to measure the local displacement field at the contact interface. The material of the fretting specimen and pads was quenched and tempered steel. The effect of test device compliances and rigid body movement was minimized by measuring displacements very close to the contact interface. The measured displacements were successfully compared to the computed displacements of a corresponding finite element model. The relative slip amplitude in partial slip conditions, slip distribution across the contact, length of the slip region, and accumulated slip distribution, were compared. Relative slip decreases markedly with increasing normal load and friction coefficient. The friction coefficient was calibrated and determined as a function of loading cycles of fretting fatigue tests with two normal loads. The friction coefficient was found to increase at the beginning of tests and stabilize after about 1000 cycles, which is in agreement with general observations.

Radiative and Joule heating effects in the MHD flow of a micropolar fluid with partial slip and convective boundary condition

We have discussed the flow of micropolar fluid past a permeable stretching sheet in attendance of joule heating, thermal radiation, partial slip and magneto hydrodynamic (MHD) with convective boundary conditions. Appropriate transformations are used to convert the boundary layer equations into nonlinear ordinary differential equations. Solution of this system is obtained for velocity, temperature and micro-rotation profiles. Graphical illustrations are added to discuss the effect of evolving parameters against above mentioned distributions. Tabulated values of local Nusselt number are also added and discussed accordingly. It is studied that velocity and micro-rotation profiles decrease with an increase in value of slip parameter. However, increase in temperature distribution is seen with gradual mounting values of thermal radiation parameter.

Stress gradient effects in surface initiated rolling contact fatigue of rails and wheels

The paper investigates gradient effects, which relate to how highly stressed regions should be dealt with in fatigue design analyses. In particular stress gradients in rolling contact are investigated with a focus on differences in response between full and partial slip conditions. To this end the multiaxial state of stress beneath a wheel–rail contact featuring full or partial slip is quantified using a multiaxial equivalent stress criterion. A comparative study shows that the significant differences in peak interfacial shear stress magnitudes between full and partial slip conditions are significantly reduced when translated to equivalent stress magnitudes. An innovative procedure to quantify the gradient effects by comparing the multiaxial contact stress field to uniaxial conditions is developed and employed. For the studied cases stress gradients beneath the frictional contact were found to be similar to stress gradients outside a uniaxially loaded large plate featuring a small hole with a radius in the order of 0.5–0.7mm. The study concludes that the use of local magnitudes of interfacial shear stress in the analysis of surface initiated rolling contact fatigue under partial slip conditions is conservative. The analysis framework established in the current study can be used to estimate the level of conservativeness.

Dual solutions of slip flow past a nonlinearly shrinking permeable sheet

The aim of the paper is to investigate the flow of an incompressible viscous fluid past a nonlinearly shrinking permeable sheet. Partial slip condition is considered instead of no slip condition at the boundary. The self similar equations are obtained and then solved numerically by a shooting technique. Dual solutions are obtained for the flow past a nonlinearly shrinking sheet with slip condition in the presence of suction. It is found that for the first solution the momentum boundary layer thickness decreases with slip and suction parameters; but it increases with the power-law index of the shrinking velocity. The dual solutions for the velocity field are obtained for the positive values of power-law index n and for certain values of the other parameters in the study. Velocity slip controls the boundary layer separation. However, the power-law index acts to accelerate the boundary layer separation.

Response of large-scale coastal basins to wind forcing: influence of topography

Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.

Combined heat and mass transfer of third‐grade nanofluids over a convectively‐heated stretching permeable surface

AbstractThe buoyancy‐induced flows of third‐grade nanofluids are investigated along a vertical permeable stretching sheet, and a numerical solution is obtained for the combined heat and mass transfer during convective cooling of the stretching sheet, subject to partial slip and convective solutal boundary conditions. The Cauchy stress tensor for the fluids of grade three and Buongiorno model for the nanofluids are used in the governing equations. The model is capable of investigating the flow, heat, and mass characteristics of third‐grade nanofluids along the stretching sheet. The partial differential equations are converted into ordinary nonlinear differential equations and are solved using a second‐order numerical technique which includes a finite difference scheme and shooting method. The effects of the buoyancy, third‐grade, viscoelastic, partial slip, convective heat and mass transfer, and nanofluid parameters on the dimensionless velocity, temperature, concentration, skin friction, and heat and mass transfer rates are reported. The present results of skin friction and heat and mass transfer rates are compared with published data, and are found to be in close agreement.

An efficient computational approach to evaluate the ratcheting performance of rail steels under cyclic rolling contact in service

A comprehensive study was carried out to numerically evaluate the ratcheting performance of three high strength pearlitic rail steels under different wheel–rail cyclic rolling contact conditions, i.e. free rolling, partial slip, and full slip conditions, different friction coefficients and different axle loads. The wheel–rail cyclic rolling contact was simulated by repeatedly passing a distributed contact pressure and a distributed tangential traction on the rail surface. This study combined the non-Hertzian contact pressure from finite element analysis with the longitudinal tangential traction from Carter’s theory to simulate the wheel–rail cyclic rolling contact problems. A cyclic plasticity material model considering the non-proportionally loading effect developed recently by the authors was applied to simulate the ratcheting behaviour of rail steels. The ratcheting performance of the rail steels was evaluated by the crack initiation life which was determined from the stabilized ratcheting strain rate and the ductility limit of the rail materials. The numerical results indicate that the crack initiation life decreases with the increase of the normalized tangential traction, the friction coefficient and the axle load for all three rail steels. Among the three rail steels, the hypereutectoid rail steel grade with a lower carbon content provides the best ratcheting performance under higher axle loads such as those used railway transport of mineral products in Australia. Furthermore, the numerical results obtained in this study are in reasonable agreement with the in-service performance of the three rail steels. This indicates that the developed approach has the capacity to evaluate the ratcheting performance of other rail steels under service loading conditions. The outcomes can provide useful information to the development and application of rail steels and the development of effective rail maintenance strategies in order to mitigate rail degradation.

Effects of fatigue damage and wear on fretting fatigue under partial slip condition

The continuum damage mechanics model incorporating wear was developed in the previous paper by the authors [27] to predict the fretting fatigue crack initiation life for both cases of partial slip and gross sliding. In the present study, the effects of external parameters on the fretting fatigue crack initiation behaviour under partial slip condition are investigated systematically. Firstly, a different fatigue damage accumulation rule is used, which can predict a more reasonable damage process. Secondly, the effects of the relative slip amplitude and wear coefficient are evaluated based on the improved approach. It is significant to note that the impact of wear coefficient on the fretting fatigue life is non-monotonic, and the action mechanism of that is analysed in detail in this work. Finally, the combination and competition between fatigue damage and wear are presented. The results indicate that none of the fatigue damage and wear can be neglected in the fretting fatigue life prediction.

Resonances of a submerged fluid-filled spherically isotropic microsphere with partial-slip interface condition

Motivated by the numerous applications of spherical shell models in micro and nano scales (such as microbubbles, bacterial cells, and viral capsids), we have considered the axisymmetric free vibrations of a spherically isotropic fluid-filled thick microspherical shell suspended in another unbounded fluid. A partial-slip condition is considered at the solid-fluid interface(s). Three-dimensional linear elasticity equations for the spherically isotropic shell dynamics and linearized Navier-Stokes equations for the two compressible viscous fluids are used in the analysis. The eigenvalue problem is discretized and solved to find the resonances and quality factors. A perfectly matched layer technique is used to separate the solid driven spectrum from the boundary reflecting spectrum. An example of air filled polymer shell suspended in water is presented. The added mass effect and partial-slip condition from water (air) on the frequencies and quality factors are found to be significant (negligible). Spherical isotropy is found to have major influence on the low frequency and large meridional wave number region of the resonance spectrum. High quality eigenmodes are observed due to very small viscous penetration depth compared to the shell size. In the thin-shell limit, the eigenvalue problem can have only two modes of vibration for any meridional wave number greater than or equal to two. This explains the reason for the second resonance frequency found for the quadrupole shape oscillations of various bacterium cells in the earlier work. The partial-slip condition is found to have very small influence on the first few modes of vibration. Surface tension is found to have significant influence only on the lowest frequency trend of the eigenspectrum. Perfectly matched layer technique used in the present analysis is found to be very effective in handling the boundary truncated problems.

Equivalent configurations for notch and fretting fatigue

Under the typical partial slip conditions under which fretting fatigue takes place, the amount of superficial damage is small. Therefore, the substantial reduction in fatigue life caused by fretting, when compared to plain fatigue, may well be more associated with the stress concentration and the stress gradient phenomena generated by the contact problem than to the superficial loss of material. In this setting, notch stress-based methodologies could, in principle, be applied to fretting in the medium/high cycle fatigue regime. The aim of this work was to investigate whether it is possible to design fretting and notch fatigue configurations, which are nominally identical in terms of damage measured by a multiaxial fatigue model. The methodology adopted to carry out this search considered a cylindrical on flat contact and a V-notch. Load and geometry dimensions of both configurations were adjusted in order to try to obtain the “same” decay of the Multiaxial Fatigue Index from the hot spot up to a critical distance. Positive results of such simulations can lead us to design an experimental program that can bring more firm conclusions on the use of pure stress-based approaches, which do not include the wear damage, in the modeling of fretting fatigue.

Kinematics and shear heat pattern of ductile simple shear zones with ‘slip boundary condition’

Extrusion by Poiseuille flow and simple shear of hot lower crust has been deciphered from large hot orogens, and partial-slip boundary condition has been encountered in analogue models. Shear heat and velocity profiles are deduced from a simplified form of Navier–Stokes equation for simple shear together with extrusive Poiseuille flow and slip boundary condition for Newtonian viscous rheology. A higher velocity at the upper boundary of the shear zone promotes higher slip velocity at the lower boundary. The other parameters that affect the slip are viscosity and thickness of the shear zone and the resultant pressure gradient that drives extrusion. In the partial-slip case, depending on flow parameters (resultant pressure gradient, density and viscosity) and thickness of the shear zone, the velocity profiles can curve and indicate opposite shear senses. The corresponding shear heat profiles can indicate temperature maximum inside shear zones near either boundaries of the shear zone, or equidistant from them.

Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffery fluid in a rectangular duct

The purpose of this paper is to study the closed-form solutions of peristaltic flow of Jeffery fluid under the simultaneous effects of magnetohydrodynamics (MHD) and partial slip conditions in a rectangular duct. The influence of wave train propagation is also taken into account. The analysis of mathematical model consists of continuity and the momentum equations are carried out under long wavelength (0<<→∞) and low Reynolds number (Re→0) assumptions. The governing equations are first reduced to the dimensionless system of partial differential equation using the appropriate variables and afterwards exact solutions are obtained by applying the method of separation of variables. The role of pertinent parameters such as Hartmann number M, slip parameter β1, volumetric flow rate Q, Jeffery parameter λ1 and the aspect ratio β against the velocity profile, pressure gradient and pressure rise is illustrated graphically. The streamlines have also been presented to discuss the trapping bolus discipline. Comparison with the existing studies is made as a limiting case of the considered problem.at the end.