Influence Of Slip Velocity Research Articles

Analytical Modeling of Mass and Heat Transfer on Unsteady Squeezing Viscous Nanofluid Flow under the Influence of Slip Velocity

In this article, two-dimensional unsteady incompressible viscous nanofluids magneto-hydrodynamic (MHD) flow among two parallel plates extended infinitely is investigated. The equations that results from the use of similarity transformations for non-linear partial differential system are solved by the new algorithm. The important key to this construct is the derivatives that appear as coefficients in the power series. The effects of apparent physical parameters on velocity concentration and temperature distributions are described using a schematic diagram and interpreted physically. The effects of apparent physical parameters on concentration, temperature, and velocity distributions are described by graphs. For the flow of nanofluids, the results indicate that it is inversely proportional between the rate of mass and heat transfer with nanoparticle size fraction and magnetic parameter. Over time, squeeze number and schmidt number lead to increase the rate of mass transfer. This problem is dissolved numerically by using the Runge-Kutta scheme of fourth-order (RK4S) .

Temporal evolution of shear-induced dilatancy of rock fractures: controls from surface roughness and normal stress

SUMMARY Understanding the shear-induced dilatancy of rock fractures is important for assessing the permeability evolution and seismic hazard in shale and geothermal reservoirs. The displacement dependence of fracture dilation has been well studied, while the influence of slip velocity is poorly constrained. In this study, we combined displacement- and velocity-dependent aperture models to reproduce the transient shear-induced dilatancy of fractures in sandstone in 16 normal stress unloading tests. Our results show that the combined aperture model can describe the transient fracture aperture evolution during accelerating slip induced by normal stress unloading better than the model dependent only on slip displacement. Slip velocity could enhance the aperture increase on smoother fractures at lower normal stresses and higher slip velocities. Both the dilation factor and characteristic slip distance decrease with increasing normal stress and surface roughness, signifying reduced contribution of slip velocity to transient shear-induced dilatancy at higher normal stresses and surface roughness. The dilation angle increases with the increase of surface roughness, and this increase diminishes at higher normal stresses primarily attributable to more severe asperity wear. These findings highlight the importance of slip velocity in controlling the transient evolution of aperture and permeability of a rock fracture. Our study also provides constraints on the constitutive parameters in the combined aperture model for describing transient shear-induced fracture dilatancy. We suggest that it is crucial to incorporate the velocity-dependent aperture model to simulate the nonlinear evolution of fracture aperture in future analytical and numerical models involving coupled hydromechanical processes in geoenergy systems.

The Role of Slip Velocity in Fractional MHD Casson Fluid Flow within Porous Cylinder

Numerous academics are intrigued by exploring the fractional Casson fluid model due to its enhanced precision compared to the traditional fluid model. However, many researchers have successfully tackled the analytical solution for the fractional fluid model while overlooking the impact of boundary slip. Hence, this study aims to tackle the challenge of describing the Casson fluid behaviour with fractional properties in a cylindrical domain, considering the influence of slip velocity at the boundaries. Furthermore, magnetohydrodynamics (MHD) had been introduced into the analysis and considered a porous medium resembling a blood clot or fatty plaque. The Caputo-Fabrizio fractional derivative is employed to establish the dimensionless governing equation. Subsequently, we solve it analytically using the Laplace transform in conjunction with finite Hankel transform techniques. A thorough examination follows the graphical presentation of the analytical solution in the context of relevant parameters. The findings illustrate those higher values of the Casson parameter, slip velocity parameter, Darcy number, and fractional parameter lead to an augmentation in fluid velocity. Conversely, an escalation in magnetic parameters causes a reduction in fluid velocity. These findings can be utilized to validate the accuracy of numerical results. The findings of this study hold considerable importance in enhancing our understanding of human blood flow, especially in scenarios where a velocity gradient occurs between blood particles and the stretching motion of arteries.

Consequences of mass transpiration and thermal radiation on Jeffery fluid with nanofluid

The present work is focused on the stagnation point flow over a Jeffery fluid flow through a stretching/shrinking sheet. The nanoparticles namely Cu are considered by exploiting water-based fluid. The governing nonlinear system of partial differential equations is converted into a system of highly nonlinear ordinary differential equations via a similarity transformation. Therefore, it is quite significant to assimilate the analytical extension of heat transfer and mass transfer fluid in the presence of porous under the influence of slip velocity. The analytical solution available for nondimensional momentum, heat transfer, and concentration profiles across the boundary layer is examination is done by checking the various values of physical parameters viz., Prandtl number, Radiation parameter, stretching/shrinking parameter, and mass transpiration for the flow and heat transfer which are obtainable through graphs. The present work on nanofluids flowing through stretching/shrinking surfaces has numerous applications in biomedicine, solar energy, cooling, nuclear system cooling, etc.

Chemical reaction impacts the unsteady MHD convective flow of an incompressible viscous fluid past an infinite vertical porous plate

AbstractWe studied the radiation magnetohydrodynamic flow of an incompressible viscous electrically conducting fluid past an exponentially accelerated perpendicular surface under the influence of slip velocity in the revolving structure. A steady homogeneous magnetic strength is applied under the assumption of low magnetic Reynolds quantity. The ramped heat and time‐altering concentration near the plate are taken into consideration. First‐order consistent chemical reactions and thermal absorption were also studied. The Laplace transformation technique is used for the non‐dimensional governing equations to get the closed‐form solutions. Supporting these results, the phases for nondimensional shear stress, rate of thermal as well as accumulation transport are also found. Graphical profiles are represented to examine the impact of physical parameters on the important physical flow features. The computational quantities of shear stress and rate of thermal and mass transportation near the surface are tabulated with a variety of implanted parameters. The resulting velocity is growing with an increase in heat and solutal buoyancy forces, while revolution and slip parameters have reverse effects on this. The resulting velocity is falling due to an increase in the Hartmann quantity, while the penetrability parameters have the opposite impacts on this. The species concentration of fluid is reduced by an increase in Schmidt number and chemical reacting parameter.

Heat and mass transfer on unsteady MHD flow of Casson fluid over an infinite perpendicular absorbent plate with slip effects

AbstractWe study the radiative magnetohydrodynamic flow of an incompressible viscous electrically performing non‐Newtonian Casson fluid past an exponentially accelerated perpendicular surface under the influence of slip velocity in the revolving frame. A steady homogeneous magnetic strength is applied under the assumption of a less magnetic Reynolds number. The ramped temperature and time‐altering concentration near the plate are taken into consideration. Primary order consistent chemically reacting and thermal absorptions are also considered. Laplace transformation technique is engaged in the nondimensional leading equations for the closed‐form solutions. Supporting these results, the phases for nondimensional shear stresses, rate of heat as well as mass transport are also found. The graphical profiles are represented to examine the impacts of physical parameters on the important physical flow features. The computational quantities of the shears stress, rates of heat as well as mass transportation near the surface are tabulated with a variety of implanted parameters. It is observed that the resultant velocity is growing by an increase in heat and solutal buoyancy forces, while revolution, as well as slip parameters, has reverse outcomes on this. The resulting velocity is falling by an increase in the Hartmann number while the permeability parameters have overturned the impacts on this. Species concentration of Casson fluid is reduced by an increase in Schmidt quantity as well as a chemically reacting parameter.

Influence of slip velocity in a two-phase bubbly jet

The effect of the slip velocity in a bubbly jet ( $Re = 3000$ , initial void $\textrm {fraction} = 1.1\,\%$ ) is studied with various bubble slip ratios (0.07–2.1 times the inlet velocity, 0.01–0.31 m s $^{-1}$ in dimension). The governing equations, which are the conservation of mass, momentum and volume fraction, are solved by direct numerical simulations. A set of ordinary differential equations was derived by using a conventional one-dimensional integral framework on jets and by expressing the slip velocity using an exponential function. The one-dimensional analysis of bubbly jets successfully predicted the jet velocity radius, centreline velocity and the gas spread rate downstream of the bubbly jet. Second- and third-order statistics were also analysed to better understand the turbulent characteristics of the bubbly jet. A high slip ratio results in a rigid, narrower bubbly jet core region, where the turbulent kinetic energy is conserved along the centreline but does not diffuse towards the ambient region. The narrow, circular region around the core at high slip ratios decreased the turbulent kinetic energy. In the rigid bubbly jet core, turbulent diffusion of the gas phase is suppressed and has low correlations with the velocity fluctuations. Turbulence characteristics such as turbulence stress were compared with single-phase jet and plume results from existing literature. The magnitude of the turbulence characteristics at the lowest slip ratio is comparable with what is found in the literature, but there is a rapid transition from slip ratios of $0.14$ to $0.7$ . Furthermore, the turbulent kinetic energy budget was analysed for each case. The production term had the largest contribution, and its magnitude was almost five times the buoyancy production downstream. High slip ratio cases show a positive peak of pressure strain and turbulent diffusion along the centreline.

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Computational of unsteady flow with slip condition is essential since physically the heat transfer process is time-dependent and there may exist slip between fluid and surface. Therefore, this study aims to investigate the unsteady stagnation-point flow and heat transfer over a stretching/shrinking sheet immersed in nanofluid in the presence of slip velocity. By applying boundary layer theory and Tiwari-Das model, the governing equations are developed and transformed into a system of ordinary differential equations using similarity transformation, which are then solved numerically using bvp4c solver in MATLAB. The influence of slip velocity, stretching/shrinking parameters, nanoparticle volume fraction and unsteadiness parameter on the local skin friction coefficient, local Nusselt number, as well as velocity and temperature profiles are analysed. There are three types of nanoparticles considered, namely Copper (Cu), Alumina (Al203), Titania (TiO2) and water (H20) is the base fluid. It is found that dual solutions occur for certain parameters and the stability analysis is performed. The analysis shows that the first solutions are found to be stable than the second solution. The local skin friction coefficient and local Nusselt number are increasing with slip velocity, nanoparticle volume fraction for shrinking case; however, the opposite trend is observed for stretching case. By raising 20% of nanoparticle volume fraction for the shrinking sheet ( the friction at the surface increases 24% and 15.5% for heat transfer rate for the first solution. Moreover, for 10% of nanoparticle volume fraction for the shrinking sheet (and the first solution, varying slip parameters from 0 to 0.2, give rise to approximately 21% of the friction at the surface and 68% of the heat transfer rate.

Hall and ion slip effects on the MHD flow of Casson hybrid nanofluid past an infinite exponentially accelerated vertical porous surface

In the present investigation, the radiative MHD flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol combination should be formed by a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations to ensure closed-form analytical solutions. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters. For uniform and ramped wall temperatures, the resultant velocity grows by an increase in Hall and ion slip parameters. The resultant velocity increases by an increase in volume fractions of nanoparticles with uniform wall temperature, and a reverse effect is observed with ramped wall temperature. The temperature of Casson hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Casson Ag-WEG nanofluid. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid decreases with an increase in Schmidt number and chemical reaction parameters. The heat absorption increases the Nusselt number near the surface, while Ag and TiO2 nanoparticle volume fractions tend to lessen it.

Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface

The radiative unsteady magnetohydrodynamic (MHD) flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluid over an infinite exponentially accelerated vertical moving porous surface under the influence of slip velocity in a rotating frame has been explored in this paper. Water and ethylene glycol mixture have been considered as a base Casson fluid. A steady homogeneous magnetic field is applied under the assumption of low magnetic Reynolds number. The ramped temperature and time varying concentration at the surface is made into consideration. First order consistent chemical reaction and thermal absorption are also considered. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol mixture to be formed as hybrid nanofluid. Laplace transformation technique is employed on the non-dimensional governing equations for the closed form solutions. Based on those outcomes, the expressions for non-dimensional shear stress, rates of heat and mass transfer are also evaluated. The graphical representations are presented to scrutinize the effects of physical parameters on the significant flow characteristics. The computational values of the shear stresses, rate of heat transfer and rate of mass transfer at the surface are tabulated by the different implanted parameters. The resultant velocity is increasing with an increasing in thermal and concentration buoyancy forces, whereas rotation and slip parameters have overturn result on it for both cases of uniform wall temperature and ramped wall temperature. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid is decreased with an increase in Schmidt number and chemical reaction parameter. The Nusselt number is increased with an increase in heat absorption at the surface.

Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility.

Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility.

Fluid Flow and Solute Transfer in a Permeable Tube with Influence of Slip Velocity

In this paper, the influence of slip velocity on the fluid flow and solute transfer in a tube with permeable boundary is studied as a mathematical model for blood flow in glomerular capillaries. The viscous incompressible fluid flow across the permeable tube wall, as a result of differences in both hydrostatic and osmotic pressure, is considered. The solutions of differential equations governing the fluid flow and solute transfer are obtained using analytical and Crank-Nicolson type numerical methods. It is observed that the effect of slip on the hydrostatic and osmotic pressures, velocity profiles, concentration profile, solute mass flux and total solute clearance is significant and the results are presented graphically.

Numerical simulation of hydrodynamic and heat transfer characteristics of slug flow in serpentine microchannel with various curvature ratio

A numerical investigation is carried out to study hydrodynamic behavior and thermal performance of slug flow in serpentine microchannel with different curvature ratio and wall properties. By using coupled Level Set and Volume of Fluid (CLSVOF) method implemented in Fluent, gas-liquid interface shows good consistency with experimental results especially for slug flow. Distribution of sectional velocity profile in curved microchannel with various curvature ratios was investigated. On the basis of fluid flow in microchannel with non-slip boundary condition, by means of user defined function (UDF), influence of slip velocity on hydrodynamic characteristics was performed numerically. For a better prediction on thermal performance, further analysis of combined effect of wall properties and curvature ratio on fluid flow characteristics was also conducted. As a consequence, the increasing slip velocity on channel wall can reduce hydraulic resistance. Both the contact angle and the curvature ratio have an appreciable influence on thermal performance of gas-liquid two-phase flow in serpentine microchannel.

The mechanism of long-wave instability in a shear-thinning film flow on a porous substrate

A linear stability analysis of a thin shear-thinning film with a deformable top surface flowing down an inclined porous substrate modelled as a smooth substrate with velocity slip at the wall is examined, and the physical mechanism for the long-wave instability is analysed. Through a phenomenological model, the influence of slip velocity and the shear-thinning rheology on the wave speed of long surface waves on a non-Newtonian shear-thinning film down a substrate with velocity slip is predicted. The viscosity disturbance plays a significant role in the destabilization of the flow system. Indeed, slip at the bottom that accounts for the characteristics of the porous/rough substrate does not affect the physical mechanism of the instability. However, it is shown that slip at the bottom enhances the inertia effects which in turn destabilizes the flow system at smaller Reynolds numbers.

Influence of slip velocity on the flow of viscous fluid through a porous medium in a permeable tube with a variable bulk flow rate

Abstract A mathematical model is presented for an axisymmetric flow of a Newtonian fluid through a permeable tube filled with porous medium and slip at the wall. The bulk flow rate is prescribed as a decreasing function of axial distance. The governing coupled partial differential equations are solved analytically using Adomian decomposition method and numerically using a second order finite difference scheme. Numerical method is validated by already published work and a good agreement is observed between the two solutions. Trusting this validity, effects of pertinent parameters on the flow variables such as velocity components, wall shear stress and pressure drop are discussed graphically. This study reveals that the slip parameter (ϕ), reabsorption parameter (α) and permeability parameter (k) have significant influences on flow variables involved in the problem. Creeping flow (Re = 0), flow without porous medium ( k → ∞ ) and flow with no slip ( ϕ = 0 ) at the wall are the limiting cases of this study.

CFD study of the effect of unsteady slip velocity waveform on shear stress in membrane systems

An unsteady forced slip velocity has an important effect on the flow conditions adjacent to a membrane interface, which can help control concentration polarisation (CP) and fouling. This study explores the effect of non-sinusoidal slip velocity waveforms on mass transfer and shear stress in membrane channels. The hydrodynamics and mass transfer of unobstructed and obstructed membrane channels under the influence of slip velocity are simulated using two-dimensional computational fluid dynamics (CFD). At a Reynolds number where vortex shedding occurs, the results show that both sinusoidal and non-sinusoidal slip velocity profiles cause a similar increase in mass transfer and shear stress. However, for systems without vortex shedding, a non-sinusoidal waveform with a sudden decrease in slip velocity can significantly increase maximum shear stress (by over 20%). This effect shows a clear advantage of non-sinusoidal slip velocity profiles over sinusoidal slip velocity profiles.

Temperature Resistance of the Boundary Lubrication Layers Under Rolling with Slippage Condition

The influence of slip velocity at rolling with slippage on the intensity of heat release in the local contact at different modes of lubricating action was examined. Efficiency of using different procedures for calculating a temperature increase in the friction contact under conditions of dominating elastohydrodynamic and boundary modes of lubricating action was shown. The interrelation between the processes of heat release intensity in tribotechnical contact and wear of friction pairs was established. It was analyzed that the locality of the increased wear in the central section of the contact line is determined by a change in the stress–strained surface condition at friction and by the occurrence of stress concentrator center.

Influence of slip velocity in Herschel-Bulkley fluid flow between parallel plates - A mathematical study

This theoretical study investigates three types of basic flows of viscous incompressible Herschel-Bulkley fluid such as (i) plane Couette flow, (ii) Poiseuille flow and (iii) generalized Couette flow with slip velocity at the boundary. The analytic solutions to the nonlinear boundary value problems have been obtained. The effects of various physical parameters on the velocity, flow rate, wall shear stress and frictional resistance to flow are analyzed through appropriate graphs. It is observed that in plane Poiseuille flow and generalized Couette flow, the velocity and flow rate of the fluid increase considerably with the increase of the slip parameter, power law index, pressure gradient. The fluid velocity is significantly higher in plane Poiseuille flow than in plane Couette flow. The wall shear stress and frictional resistance to flow decrease considerably with the increase of the power law index and increase significantly with the increase of the yield stress of the fluid. The wall shear stress and frictional resistance to flow are considerably higher in plane Poiseuille flow than in generalized Couette flow.

INFLUENCE OF SLIP VELOCITY ON BLOOD FLOW THROUGH AN ARTERY WITH PERMEABLE WALL: A THEORETICAL STUDY

A theoretical investigation concerning the influence of slip velocity on the flow of blood through an artery having its wall permeable has been carried out. Here blood is treated as a homogeneous Newtonian fluid. The flow is characterized by three parameters: β the ratio of radius to length of the arterial segment, Re the characteristic Reynolds number associated with the pressure outside the arterial segment and ϵ the filtration coefficient. The problem has been solved by the use of a perturbation technique. ϵ is considered to be very small, ensuring the validity of the perturbation method. The computed numerical results are presented graphically to depict the variations in velocity, volumetric flow rate, wall shear stress and flow resistance.

FLOW THROUGH NONUNIFORM CHANNEL WITH PERMEABLE WALL AND SLIP EFFECT

An investigation of viscous incompressible fluid flow in a nonuniform rigid channel with permeable walls is presented by taking into consideration the influence of slip velocity at the walls. The effect of fluid absorption through permeable walls is accounted for by prescribing flux as a function of axial distance. The nonlinear governing equations of motion are linearized by the perturbation method by assuming ‐ (the ratio of inlet width to the length of the channel) as a small parameter to get an approximate analytical solution. The effects of reabsorption coefficient (a), slope parameter (k), and slip parameter (fl) on the velocity profiles, mean pressure drop, and wall shear stress are studied and presented graphically. The results indicate that the slip parameter influences the flow field considerably.