No-slip Cases Research Articles

Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition

In this paper, we solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution are investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. Thus our method is also valid for the total-slip and no-slip cases. The main novelty is that the total flux of the velocity can be relatively large (proportional to the slip length) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case.

Numerical exploration of slip effects on second-grade fluid motion over a porous revolving disk with heat and mass transfer

Revolving-disk systems are employed in various industrial settings including turbine engineering, chemical and food processing industries and others. The current article scrutinizes a second-grade fluid motion generated by an infinite porous disk having partial slip character. Heat transfer induced by heating of the disk surface and by viscous and ohmic heating effects is modeled and analyzed under thermal slip condition. Accompanying mass transfer process with thermophoretic diffusion is also formulated. A self-similar system is obtained akin to the case of no-slip case discussed in a previously published study. The adoption of velocity slip assumption induces non-linearity in the boundary conditions in velocity components. Computational procedure embedded in MATLAB bvp4c platform is opted to simulate the system for full range of slip parameters. In contrast to a previously published work pertaining to the no-slip case, present numerical methodology gives accurate results for wide ranges of Prandtl number and elasticity parameter. Boundary layer formations above the disk are examined under various controlling parameters. A comparative assessment of slip and no-slip cases is presented through both graphical illustrations and tabulated results for the resisting torque, the Nusselt number and the Sherwood number. Current numerical findings match very well with the existing homotopy solutions for the no-slip case. The presence of a wall slip mechanism leads to a clear suppression of all the velocity components. Furthermore, an augmentation in the thermal/concentration slip coefficient significantly reduces the thermal/solutal penetration depth. Additionally, we observe a noticeable increase in the driving torque as the elasticity parameter enhances. The slip action of the surface is also predicted to raise the torque required by the disk.

Impact of Joule heating on magnetohydrodynamic dissipative flow above a slendering surface with thermophoresis and Brownian movement with slip/no-slip conditions

ABSTRACT Purpose Hybrid nanofluids meet the necessities of several technological and production industries. Owing to these ample applications, a numerical investigation is accomplished to examine the thermal transmission feature of magneto-hybrid nanofluid flow due to an extending surface of varied thickness with multiple slip effects. Design/methodology The arising system of Partial Differential equations (PDEs) are exercised by adopting suitable similarities to attain the non-dimensional Ordinary Differential equations (ODEs) and the solutions are obtained by implementing bvp5c built in MATLAB package. The energy equation is loaded with Brownian motion, thermophoresis and Joule heating effects. The implication of pertinent constraints upon the flow features is discussed graphically. Findings The outcomes imply that the energy transmission rate is considerably high in no-slip case as equated with the slip case. Further, the power-law index parameter effectively uplifts the thermal and concentration gradients in both the situations. Originality The prime motive of this research is to present the relative analysis of heat transmission of hybrid nanoliquid in two different situations, namely slip and no-slip cases.

Lubricated surface oblique stagnation point flow of second-grade fluid with heat and mass transfer phenomenon: applications to hydraulic systems

The lubrication phenomenon with heat and mass transfer phenomenon justified applications in ploy engineering, polymer processes, compressor oils, piston oils, hydraulic systems, and paint industries. This contribution attributes the significance of heat and mass transfer due to the lubricated surface. The enhancement in the lubricated phenomenon is further suggested by incorporating the nonlinear radiative impact and chemical reaction. The viscoelastic fluid flow is confined in the zone of stagnation point of the lubricated surface. The axial and tangential velocities are presented for no-slip and full-slip cases. Moreover, a comparative analysis is carried out for temperature distribution over lubricated and non-lubricated surfaces for linear and nonlinear radiations. The problem is modeled in view of fundamental conservation laws, and the similarity variables are used to transfer them to the system of coupled nonlinear boundary value problem which is approximated by the Keller box method. The obtained results are validated with the existing literature as a particular case of the present study. It is noted that the local Nusselt number and Sherwood number are reduced by decreasing the efficiency of the lubricant also the nonlinear thermal radiation assists the heat transfer rate. The increase in chemical reaction declined the concentration phenomenon.

Analysis of pulsatile combined electroosmotic and shear-driven flow of generalized Maxwell fluids in a microchannel with slip-dependent zeta potential

The present study investigates the flow characteristics for a pulsatile, combined electroosmotic and shear-driven flow of generalized Maxwell fluid through a straight planar microchannel including the effect of hydrodynamic slippage on asymmetric zeta potential. Mathematical expressions have been obtained in dimensionless form for the electrical potential distribution of the electrical double layer (EDL), velocity distribution and the volumetric flow rate after analytically solving the Poisson-Boltzmann and momentum equations. Critical values and critical ranges of time period of oscillating electric field have been obtained for no-slip and slip cases respectively where anomalous behaviour of dimensionless volumetric flow rate is observed. Flow rate magnitude sensitivity on hydrodynamic slippage is also analyzed. Moreover, critical values of the time period of oscillating electric field are obtained where the sensitivity of flow rate magnitude on the relaxation time of Maxwell fluid vanishes. Similarly, pivotal values of the time period of oscillating electric field are obtained at which the sensitivity of flow rate magnitude on the relaxation time of Maxwell fluid becomes invariant with the lower wall velocity.

Heat transport in Rayleigh-Bénard convection with linear marginality.

Recent direct numerical simulations (DNS) and computations of exact steady solutions suggest that the heat transport in Rayleigh-Bénard convection (RBC) exhibits the classical [Formula: see text] scaling as the Rayleigh number [Formula: see text] with Prandtl number unity, consistent with Malkus-Howard's marginally stable boundary layer theory. Here, we construct conditional upper and lower bounds for heat transport in two-dimensional RBC subject to a physically motivated marginal linear-stability constraint. The upper estimate is derived using the Constantin-Doering-Hopf (CDH) variational framework for RBC with stress-free boundary conditions, while the lower estimate is developed for both stress-free and no-slip boundary conditions. The resulting optimization problems are solved numerically using a time-stepping algorithm. Our results indicate that the upper heat-flux estimate follows the same [Formula: see text] scaling as the rigorous CDH upper bound for the two-dimensional stress-free case, indicating that the linear-stability constraint fails to modify the boundary-layer thickness of the mean temperature profile. By contrast, the lower estimate successfully captures the [Formula: see text] scaling for both the stress-free and no-slip cases. These estimates are tested using marginally-stable equilibrium solutions obtained under the quasi-linear approximation, steady roll solutions and DNS data. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Magnetohydrodynamic Hybrid Nanofluid Flow Past an Exponentially Stretching Sheet with Slip Conditions

This study presents the magnetized hybrid nanofluid flow with heat source/sink over an exponentially stretching/shrinking sheet. Slip conditions are implemented to analyze the hybrid nanofluid flow for both slip and no-slip conditions. Additionally, the hybrid nanofluid of alumina and copper (hybrid nanoparticles) with blood (base fluid) has been considered and discussed with both suction and injection parameters. The appropriate similarity variables are used to convert partial differential equations (PDEs) into ordinary differential equations (ODEs) and solved analytically with the help of the homotopy analysis method (HAM). The impact of different embedded parameters has been shown in the form of graphs and tables. The numerical values of skin friction and Nusselt number are presented in the form of Tables for both slip and no-slip cases. It is summarized that the upsurge of the velocity slip parameter and magnetic parameter increases the skin friction, while the rising of the thermal slip parameter and heat generation parameter decreases the Nusselt number.

Exploration of Unsteady Squeezing Flow through Least Squares Homotopy Perturbation Method

Squeezing flow has many applications in different fields including chemical, mechanical, and electrical engineering as these flows can be observed in many hydrodynamical tools and machines. Due to importance of squeezing flow, in this paper, an unsteady squeezing flow of a viscous magnetohydrodynamic (MHD) fluid which is passing through porous medium has been modeled and analyzed with and without slip effects at the boundaries. The least squares homotopy perturbation method (LSHPM) has been proposed to determine the solutions of nonlinear boundary value problems. To check the validity and convergence of the proposed scheme (LSHPM), the modeled problems are also solved with the Fehlberg–Runge–Kutta method (RKF45) and homotopy perturbation method (HPM) and residual errors are compared with LSHPM. To the best of the authors’ knowledge, the current problems have not been attempted before with LSHPM. Moreover, the impact of different fluid parameters on the velocity profile has been examined graphically in slip and no-slip cases. Analysis shows that the Reynolds number, MHD parameter, and porosity parameter have opposite effects in case of slip and no slip at the boundaries. It is also observed that nonzero slip parameter accelerates the velocity profile near the boundaries. Analysis also reveals that LSHPM provides better results in terms of accuracy as compared to HPM and RKF45 and can be effectively used for the fluid flow problems.

Thermophoresis effect on peristaltic flow of viscous nanofluid in rotating frame

In this paper simultaneous effects of Coriolis forces, Brownian motion and thermophoresis on the peristaltic motion of Newtonian fluid are incorporated. The governing nonlinear flow equations with appropriate conditions are converted into non-dimensional form, afterward, they were solved numerically by the Keller box procedure. Also, another numerical method is used to solve these transformed equations and by tabular data, we made a comparison of the numerical values of velocities, temperature and concentration profiles. A parametric investigation was conducted and the influence of various parameters on primary and secondary velocities is conducted for both slip and no-slip flow cases. The obtained results are compared with the existing literature as a particular case and found with an excellent agreement. Furthermore graphical results for temperature and nanoparticle concentration profiles are reported for both rotating and non-rotating frames. It is worth mentioning that the effects of Nt and Nb are the dominant in rotating frame as compared to the non-rotating frame of reference and the magnitude of temperature distribution is small for slip flow.

The analytical solution of the Brinkman model for non-Brownian suspensions with Navier slip on the particles

The analytical solution of the Stokes-Darcy equations is derived for a Newtonian, statistically homogenous, suspension with non-Brownian (non-colloidal) rigid spherical particles. Navier-type linear slip over the surface of the particles is applied. The mathematical model is based on Brinkman's (1949) original idea for the viscous force exerted by a flowing fluid on a dense swarm of spherical particles. First, the equations are solved analytically for the pressure-driven and uniform flow of the suspension. Self-consistency of the model allows for the evaluation of the resistance parameter as function of the volume fraction of the solid phase and the dimensionless slip coefficient. The results show that for fixed solid concentration, the drag force on each particle decreases due to the slippage of the fluid over its surface. Consequently, the resistance parameter decreases compared to the classic no-slip case. However, in all cases, divergence of the resistance parameter occurs as the solid volume fraction approaches the value 2/3 which is very close to the maximum volume fraction 0.637( ≈ 2/π)for random close packing of spherical particles. The analysis is also performed for steady shear and steady uniaxial elongational flows and exact analytical solutions for the velocity and the pressure are derived. Then, a volume average of the total stress tensor in the suspension allows for the analytical evaluation of the shear and elongational viscosities of the complex flow system. Limiting expressions for the no-slip and perfect slip cases are also found and discussed.

Blasius and Sakiadis slip flow of H2O–C2H6O2 (50:50) based nanoliquid with different geometry of boehmite alumina nanoparticles

The geometry of the nanoparticles in nanoliquids has significant influence in many engineering and bio medical applications and also the classical flow problems such as Blasius and Sakiadis problems are important in industrial applications. In view of this, an investigation on the flow of H2O–C2H6O2 (50:50) mixture based nanoliquid with different geometry of boehmite alumina nanoparticles is carried out in the presence of viscous dissipation effects. Spherical, blades, bricks, platelets and cylindrical geometries of the nanoparticels are considered. Both Blasius and Sakiadis flow types are analysed for slip and no-slip cases. The thermal and velocity slip boundary conditions are included as a function of nanoparticle volume fraction. Mathematical model is solved numerically by the Iterative Power Series (IPS) method and shooting strategy with the thermo-physical properties of different geometries nanoparticles. It is observed that the thermal boundary layer thickness is increased for cylindrical nanoparticles and decreased for spherical nanoparticles in both slip and no-slip cases of Blasius and Sakiadis flows. The reduced Nusselt number is increased with nanoparticle volume fraction for all shapes of boehmite alumina nanoparticles except spherical nanoparticles.

Slip flow of hydromagnetic micropolar nanofluid between two disks with characterization of porous medium

An analysis is performed for axisymmetric, incompressible, hydromagnetic micropolar nanofluid flow through infinite porous parallel disks subjected to porous medium. The flow is imposed via uniform injection through surface of disks. The utilization of similarity transformations converts the system of partial differential equations with combined boundary conditions into highly nonlinear ordinary ones. Boundary conditions of velocity, temperature and concentration slips are executed. Both slip and no-slip cases are discussed. Runge–Kutta–Fehlberg (RKF45) numerical method is effectuated to obtain the results in pictorial representations and tabular forms.

Numerical simulation of electroosmosis regulated peristaltic transport of Bingham nanofluid

The effects of slip condition and Joule heating on the peristaltic flow of Bingham nanofluid are investigated. The flow is taken in a porous channel with elastic walls. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. The transformed equations for the flow are solved to seek values for the nanoparticles velocity, concentration and temperature along the channel length. Graphs are plotted to evaluate the behavior of various physical parameters on flow quantities in both slip and no-slip cases. The main features of the physical parameters are highlighted on the inclined non uniform channel. The results show an increment in velocity with rise in inclination and porosity while it reduces with magnetic field. Moreover, nanofluid favors the heat transfer and decline the concentration.

Peristaltic slip flow of a Bingham fluid in an inclined porous conduit with Joule heating

Abstract The present study deals with simultaneous effects of Joule heating and slip on peristaltic flow of a Bingham fluid in an inclined tapered porous channel with elastic walls. The closed form solutions for the stream function, the velocity and the temperature fields are obtained. The effects of the physical parameters on the flow characteristics are presented through graphs for both slip and no-slip cases. In addition, the performance of the temperature is studied with and without Joule heating effects. Moreover, the trapping phenomenon is analysed. The size of the trapped bolus increases with increasing values of the slip parameter and decreasing values of the magnetic, the permeability and the yield stress parameters. The present results are compared with the available results in the literature and our results agree well with the available results for some special cases.

Slip effects on MHD boundary layer flow of Oldroyd-B fluid past a stretching sheet: An analytic solution

Present analysis is made for the laminar flow of Oldroyd-B fluid induced by a deforming sheet in the existence of transverse magnetic field. Flow model is constructed in the presence of slip boundary condition. The governing problem even after utilizing boundary layer approximations comprises of non-linear differential equation with the non-linear boundary condition. Such boundary condition for the no slip case is linear. Highly accurate analytic solutions for velocity distribution are derived by powerful homotopy analysis approach. Permissible values of the convergence control parameter are obtained by the so-called h-curves. The behavior of parameters on the solutions is shown graphically. In the light of numerical results, we predict that slip effect gives opposition to the momentum transport phenomenon. Moreover, the behaviors of relaxation and retardation time are qualitatively opposite. A comparative study of slip and no-slip cases is also discussed.

Vertically Bounded Double Diffusive Convection in the Finger Regime: Comparing No-Slip versus Free-Slip Boundary Conditions.

Vertically bounded fingering double diffusive convection is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e., the no-slip condition, which is inevitable in the lab-scale experimental researches, and the free-slip condition, which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case, although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of horizontally focused fingers and sheet structures near the free-slip boundaries. This counterintuitive result might be relevant for properly estimating and modeling the mixing and entrainment phenomena at free surfaces and interfaces widespread in oceans and geophysical flows.

Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells

We study rotating thermal convection in spherical shells. We base our analysis on a set of about 450 direct numerical simulations of the (magneto)hydrodynamic equations under the Boussinesq approximation. The Ekman number ranges from $10^{-3}$ to $10^{-5}$. The supercriticality of the convection reaches about 1000 in some models. Four sets of simulations are considered: non-magnetic simulations and dynamo simulations with either free-slip or no-slip flow boundary conditions. The non-magnetic setup with free-slip boundaries generates the strongest zonal flows. Both non-magnetic simulations with no-slip flow boundary conditions and self-consistent dynamos with free-slip boundaries have drastically reduced zonal-flows. Suppression of shear leads to a substantial gain in heat-transfer efficiency, increasing by a factor of 3 in some cases. Such efficiency enhancement occurs as long as the convection is significantly influenced by rotation. At higher convective driving the heat-transfer efficiency tends towards that of the classical non-rotating Rayleigh-B\'enard system. Analysis of the latitudinal distribution of heat flow at the outer boundary reveals that the shear is most effective at suppressing heat-transfer in the equatorial regions. Furthermore, we explore the influence of the magnetic field on the {\em non-zonal} flow components of the convection. For this we compare the heat-transfer efficiency of no-slip non-magnetic cases with that of the no-slip dynamo simulations. We find that at $E=10^{-5}$ magnetic field significantly affects the convection and a maximum gain of about 30\% (as compared to the non-magnetic case) in heat-transfer efficiency is obtained for an Elsasser number of about 3. Our analysis motivates us to speculate that convection in the polar regions in dynamos at $E=10^{-5}$ is probably in a `magnetostrophic' regime.

The effect of slip length on vortex rebound from a rigid boundary

The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett. 106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the no-slip case in this limit. We study the same problem, for both no-slip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the no-slip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.

Peristaltic motion of Phan–Thien–Tanner fluid in the presence of slip condition

This investigation considers the peristaltic flow of a Phan–Thien–Tanner fluid in the presence of slip condition and induced magnetic field. By use of the long wavelength and low Reynolds number approximations, closed form series solutions for stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density were obtained. The pressure gradient and frictional forces per wavelength were computed by numerical integration. The velocity slip condition in terms of shear stress is taken into account. Graphical results show the comparison between no-slip and viscous fluid cases. Pumping and trapping phenomena are discussed.

Mobile Robot Vision Tracking System Using Dead Reckoning & Active Beacons

AbstractThis paper presents a new vision tracking system for mobile robot by integrating information received from encoders, inertial sensors, and active beacons. The proposed system accurately determines mobile robot position and orientation using relative and absolute position estimates, and rotates the camera towards the target during locomotion. Among the implemented sensors, the encoder data give relatively accurate robot motion information except when wheels slip. On the other hand inertial sensors have the problem of integration of noisy data, while active beacons are slow when compared to other sensors. The designed system compensates the sensors limitations and slip error by switching between two Kalman filters, built for slip and no-slip cases. Each Kalman filter uses different sensors combination and estimates robot motion respectively. The slip detector is used to detect the slip condition by comparing the data from the accelerometer and encoder to select the either Kalman filter as the output of the system. Based on the proposed sensor fusion method, a vision tracking system is implemented on a two-wheeled robot. The experimental results depict that proposed system is able to locate robot position with significantly reduced position errors and successful tracking of the target for various environments and robot motion scenarios.