Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Re-adhesion control strategy based on the optimal slip velocity seeking method

In the railway industry, re-adhesion control plays an important role in attenuating the slip occurrence due to the low adhesion condition in the wheel-rail inter- action. Braking and traction forces depend on the normal force and adhesion coefficient at the wheel-rail contact area. Due to the restrictions on controlling normal force, the only way to increase the tractive or braking effect is to maximize the adhesion coefficient. Through efficient uti- lization of adhesion, it is also possible to avoid wheel-rail wear and minimize the energy consumption. The adhesion between wheel and rail is a highly nonlinear function of many parameters like environmental conditions, railway vehicle speed and slip velocity. To estimate these unknown parameters accurately is a very hard and competitive challenge. The robust adaptive control strategy presented in this paper is not only able to suppress the wheel slip in time, but also maximize the adhesion utilization perfor- mance after re-adhesion process even if the wheel-rail contact mechanism exhibits significant adhesion uncer- tainties and/or nonlinearities. Using an optimal slip velocity seeking algorithm, the proposed strategy provides a satisfactory slip velocity tracking ability, which was demonstrated able to realize the desired slip velocity without experiencing any instability problem. The control torque of the traction motor was regulated continuously to drive the railway vehicle in the neighborhood of the opti- mal adhesion point and guarantee the best traction capacity after re-adhesion process by making the railway vehicle operate away from the unstable region. The results obtained from the adaptive approach based on the second- order sliding mode observer have been confirmed through theoretical analysis and numerical simulation conducted in MATLAB and Simulink with a full traction model under various wheel-rail conditions.

Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.

Numerical prediction of particle slip velocity in turbulence by CFD-DEM simulation

Turbulent environment improves the flotation recovery of fine particles by promoting the particle–bubble collision rate,which directly depends on the particle slip velocity.However,the existing slip velocity models are not applicable to fine particles in turbulence.The mechanism of turbulence characteristics and particle properties on the slip velocity of fine particles in turbulence was unclear.In this study,a coupled ANSYS FLUENT and EDEM based on computational fluid dynamics(CFD)and discrete element method(DEM)were used to simulate the slip velocity of fine particles in the approximately homogenous isotropic turbulence,which was excited by the grid.The reliability of the used CFD-DEM simulation method was validated against the slip velocity measured by the particle image velocimetry(PIV)experiments.In particular,the effects of the particle shapes,particle densities,and turbulence intensities on the slip velocity have been investigated with this numerical method.Numerical results show that particle shapes have no significant effect on fine particles between 37 and 225μm.The slip velocity of the spherical particles increases with the turbulence intensity and particle density.Based on the simulated data,a model which has a correlation coefficient of 0.95 is built by using nonlinear fitting.

LOCAL SLIP VELOCITY IN A DOWNER

Based on the EMMS model, the local slip velocity between gas and solid is systematically analyzed and a theoretical correlation of local slip velocity with local voidage for a downer is derived as follows:U_s(r)/U_t=D^(8/7)(1-ε_mt)^(-2/7)[(1-ε(r)/(ε(r))]^(8/7)]ε(r)(47/14)((ε(r)-ε_(mt))/ε(r)) Using this correlation, the local gas-solid slip velocity in a downer is calculated. The calculated results are well consistent with experimental data. In addition, the variation of the local slip velocity with its corresponding solid holdup is also dis-cussed.

Effects of nonlinear velocity slip and temperature jump onpseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cu-water and Cu-kerosene nanofluids

Squeezing flow of nanofluids has been taken into account under the effects of viscous dissipation and velocity slip.Two types of base fluids are used to study the behavior of Copper nanoparticles between parallel plates.Nonlinear ordinary differential equations governing the flow are obtained by imposing similarity transformations on conservation laws.Resulting equations are solved by using an efficient analytical technique the variation of parameters method(VPM).Influences of nanoparticle concentration and different emerging parameters on flow profiles are presented graphically coupled with comprehensive discussions.A numerical solution is also sought for the sake of comparison.Effect of different parameters on skin friction coefficient and Nusselt number is also discussed.

SLIP VELOCITY MODEL OF POROUS WALLS ABSORBED BY HYDROPHOBIC NANOPARTICLES SIO_2

According to new slip effects on nanopatterned interfaces, the mechanism of enhancing water injection into hydrophobic nanomaterial SiO2 was proposed. When Hydrophobic Nanoparticles（HNPs）are adsorbed on surfaces of porous walls, hydrophobic nanoparticles layers are formed instead of hydrated layer, and slip effects appear on the pore wall when a driving pressure is applied to the rock cores sample. It makes fluid to move more quickly and the flow capacity increases greatly. Experiments on changing wettability of porous walls were conducted, and the phenomenon that porous walls surfaces were adsorbed by nanoparticles was validated with the Environment Scan Electron Microscopy（ESEM）. The results of displacement experiments show that flowing resistance is greatly reduced, and water-phase effective permeability is increased by 47 % averagely after being treated by nanofluid. These results indicate that the slip effect may occur on nanoparticle film of porous walls. Based on this new mechanism of enhancing water injection about hydrophobic nanomaterial SiO2, a slip velocity model in uniform porous media was introduced, and some formulas for the ratio of slip length to radius, slip length ,stream slip velocity and flux increment were deduced. and calculated results indicate that the ratio of slip length to radius is about 3.54%-6.97%, and the slip length is about 0.024 μ m -0.063 μ m. The proposed model can give a good interpretation for the mechanisms of enhancing water injection with the HNPs.

Integral Transform Method for a Porous Slider with Magnetic Field and Velocity Slip

Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.

Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating disks.Electrical conducting flow is considered and saturated through Darcy–Forchheimer relation.Both the disks are rotating with different angular frequencies and stretches with different rates.Here graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase liquid.Joule heating,heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy expression.Furthermore,binary chemical reaction with activation energy is considered.The total entropy rate is calculated in the presence of heat transfer irreversibility,fluid friction irreversibility,Joule heating irreversibility,porosity irreversibility and chemical reaction irreversibility through thermodynamics second law.The nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting method.Characteristics of sundry flow variables on the entropy generation rate,velocity,concentration,Bejan number,temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid nanoparticles.The engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through tables.It is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion parameter.Also entropy generation rate is more against the higher Brinkman number.

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.

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid(blood)through a stenosed bifurcated artery are investigated by using ANSYS FLUENT.Blood is regarded as a non-Newtonian power-law fluid,and the magnetization and electrical conductivity are considered in the mathematical model.The no-slip condition is replaced by the first-order slip condition.The slip boundary condition and magnetic force are compiled in the solver by the user-defined function(UDF).Numerical solutions are obtained by the finite volume method based on a nonuniform grid structure.The accuracy and efficiency of the solver are verified through a comparison with the literature.The results are presented graphically for different parameter values,and the effects of the magnetic number,the magnetic source position,the vascular obstruction ratio,the slip parameter,and the power-law index on the flow and temperature fields are illustrated.

Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model

Nanoparticle(drug particle) dispersion is an important phenomenon during nanodrug delivery in the bloodstream by using multifunctional carrier particles. The aim of this study is to understand the dispersion of drug particle(nanoparticle) transport during steady blood flow through a microvessel. A two-phase fluid model is considered to define blood flow through a microvessel. Plug and intermediate regions are defined by a non-Newtonian Herschel-Bulkley fluid model where the plug region appears due to the aggregation of red blood cells at the axis in the vessel. The peripheral(porous in nature)region is defined by the Newtonian fluids. The wall of the microvessel is considered to be permeable and characterized by the Darcy model. Stress-jump and velocity slip conditions are incorporated respectively at the interface of the intermediate and peripheral regions and at the inner surface of the microvessel. The effects of the rheological parameter, the pressure constant, the particle volume fraction, the stress jump constant, the slip constant,and the yield stress on the dispersion are analyzed and discussed. It is observed that the non-dimensional pressure gradient and the yield stress enhance the dispersion rate of the nanoparticle, while the opposite trends are observed for the velocity slip constant, the nanoparticle volume fraction, the rheological parameter, and the stress-jump constant.

Hydrothermal analysis of hybrid nanofluid flow on a vertical plate byconsidering slip condition

Hybrid nanofluids have attracted burgeoning attention owing to their outstanding capacity to improve heat transfer.The influence of velocity and temperature slip parameter and nanoparticls’(NPs’)volume fraction on a vertical plate in the existence of suction has been explored in this work.The investigation’s controlling partial differentiation equations were transformed into a conventional differential equation mechanism using resemblance modifications.Equations were then solved employing the fifth-order Runge-Kutta method.The skin coefficient of friction,temperature,and temperature gradient all rise when the volume percentage of NPs increases from 0 to 2%.Furthermore,a rise in the temperature slip variable was linked to a drop in the Nusselt number(heat transfer).The Nusselt number increased 0.15%and 5.63%respectively when the velocity slip parameter enhanced from 0 to 5 and the NPs volume percentage were increased from 0 to 1.5%.Furthermore,an increase in the temperature slip from 0 to 3 inflated the x-direction skin friction coefficient 8.2%,while inflation in the velocity slip from 0 to 5 was associated with a decline in the x-direction skin friction coefficient 95%.

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier＇s partial slip

In this paper, the effects of viscous and Ohmic heating and heat genera- tion/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similar- ity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4th order Runge-Kutta method is used to solve the transformed equations. Computations are car- ried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which, is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration （VLSI） of electronic chips and film coating.

Unsteady MHD flow over exponentially stretching sheet with slip conditions

The present paper examines the hydromagnetic three-dimensional flow in- duced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.

COMPUTATIONAL FLUID DYNAMICS(CFD) SIMULATIONS OF DRAG REDUCTION WITH PERIODIC MICRO-STRUCTURED WALL

Computational fluid dynamics（CFD） simulations are adopted to investigate rectangular microchannel flows with various periodic micro-structured wall by introducing velocity slip boundary condition at low Reynolds number. The purpose of the current study is to numerically find out the effects of periodic micro-structured wall on the flow resistance in rectangular microchannel with the different spacings between microridges ranging from 15 to 60 pm. The simulative results indicate that pressure drop with different spacing between microridges increases linearly with flow velocity and decreases monotonically with slip velocity; Pressure drop reduction also increases with the spacing between microridges at the same condition of slip velocity and flow velocity. The results of numerical simulation are compared with theoretical predictions and experimental results in the literatures. It is found that there is qualitative agreement between them.