Slip Boundary Conditions Research Articles

Mathematical analysis of MHD hybrid nanofluid flow with variable viscosity and slip conditions over a stretching surface

There are number of real-world uses for hybrid nanofluids. Studies have shown that hybrid nanofluid is better at transferring heat than nanofluid with only one type of nanoparticle. It can be used in new ways, like in microfluidics, dynamic sealing, heat dissipation, and so on. The use of hybrid nanofluids in MHD flow over a stretching surface with varying viscosity can enhance heat transfer rates. This has various applications in industries such as, cooling systems in electronics, thermal management in aerospace, and energy system. But the properties of boundary layer flow and rate of heat transfer for hybrid nanofluids could be studied more in a space with more dimensions and with other physical assumptions around the flow of fluids. The current study's major purpose is to investigate the flow of a three-dimensional hybrid nanofluid over a stretched sheet as its viscosity changes. Furthermore, the effects of the Smoluchowski temperature and Maxwell velocity slip boundary conditions are considered. Hybrid nanofluid was created by dispersing copper (Cu) and alumina (Al2O3) nanoparticles in a base fluid (H2O). Similarity variables are employed to transform a set of nonlinear partial differential equations (PDEs) that govern fluid flow and heat transfer into a system of higher-order ordinary differential equations (ODEs). The RKF method in Mathematica solves the higher-order nonlinear ODEs. Graphical analyses and in-depth discussions examine how leading variables affect velocity and temperature profiles. The expressions for skin friction and local Nusselt number are explicitly formulated, and graphs illustrate the variations of these two quantities across different parameter values. When velocity slip parameter goes up, velocity profile f′ηgoes down, and the temperature profile θ(η) also goes down when the temperature slip parameter goes up. As the velocity slip parameter goes up, skin friction goes down, while the Nusselt number goes up as the temperature slip parameter goes up. When results of this study are compared to some of results that have already been published, they are found to be very interesting as heat transfer increases due to the impacts of physical parameters.

Hybrid Nanofluid Flow with Multiple Slips Over a Permeable Stretching/Shrinking Sheet Embedded in a Porous Medium

Including slip boundary conditions in the study involving the flow of foams, emulsions, polymer solutions, and suspensions over moving surfaces are crucial for real-life applications. The current study analysed the multiple slips effects on the magnetohydrodynamics (MHD) flow of Ag-CuO/water hybrid nanofluid past a permeable stretching/shrinking sheet embedded in a porous medium. Appropriate similarity variables are introduced for transforming the governing equations and boundary conditions into ordinary differential equations before being solved using the bvp4c solver. Dual solutions are yielded from the numerical computation of flow over a shrinking sheet, and the first solution is identified as stable through a stability analysis. It is found that the imposition of velocity, thermal, and mass slips promotes the reduction of momentum, thermal, and concentration boundary layer thickness, respectively. The hybrid nanofluid around the sheet is observed to flow at a different velocity from the sheet due to the imposition of velocity slip. Thermal and mass slips, meanwhile, obstruct the flow's ability to transport heat and mass. An increased suction parameter, however, can aid in enhancing the rates of heat and mass transfers.

The Effect of Slip Boundary Conditions on The Newtonian Die-Swell Flow

The Effect of Slip Boundary Conditions on The Newtonian Die-Swell Flow

Numerical analysis of heat transfer in Ellis hybrid nanofluid flow subject to a stretching cylinder

This work covers the theoretical and computational examination of the Ellis hybrid nanofluid flow model with magnetic, Darcy-Forchheimer, and non-linear thermal radiation effects across the stretching cylinder. The convective slip boundary condition is imposed on the surface of the cylinder. Hybrid nanoparticles (AA7072 and AA7075) are scattered in base fluid (water) to create a hybrid nanofluid. The phenomenon of fluid flow has been analytically developed for energy and fluid velocity as a non-linear partial differential equation (PDE)-based system. Through appropriate similarity replacements, the design of PDEs is further streamlined to the set of ordinary differential equations (ODEs). Utilizing a built-in MATLAB (R2020b) algorithm called bvp4c, numerical solutions are found for the obtained dimensionless equations. Graphical discussions are used to illustrate the outcomes of velocity and temperature profiles. The velocity profile of mono and hybrid nanofluids declined for higher inputs of Darcy–Forchheimer and magnetic parameters. Additionally, it has been observed that the energy contour is improved caused of thermal radiation and thermal Biot number. Moreover, our results are consistent with the existing literature.

Exploring the influence of span-wise boundary conditions on the wake of a thin flat plate using Fourier-Averaged Navier–Stokes equations

The wake of a thin normal flat plate with different end conditions is numerically analyzed at a Reynolds number of 250. Periodic, slip, and no-slip boundary conditions are considered for the spanwise boundaries in order to analyze the effect of spanwise flow constraints using a new technique: Fourier-Averaged Navier–Stokes equations (FANS). The results of cases with periodic and slip end conditions were similar in both mean and unsteady fields. However, no-slip boundary conditions, which could represent the case of experimental setups with end plates, significantly reduce the velocity, drag and lift fluctuations in the flow. FANS analysis confirmed that loss of the nominal two-dimensional behavior due to the no-slip end condition relates to the presence of a spanwise flow coherence at the vortex shedding frequency (mode). Interactions between the rollers and boundary layer induces large-scale spanwise fluctuations that are absent without the end plates. In this way, the boundary layer due to the end plate serves as a flow control mechanism that suppresses fluctuations in the flow and reduces stresses in the center-plane, alongside increasing coherence in the spanwise flow.

Comparative analysis of the flow of the hybrid nanofluid stagnation point on the slippery surface by the CVFEM approach

In the present analysis,the stagnation point flow model is employedto evaluate the energy transient across the nanofluid using the comparative analysis. The consequences of slip surface are engaged to the momentum equation, to assess the lubrication. Hybride nanofluid has been synthesized by the dispersion of silver (Ag) and Titanium oxide (TiO2), in two different solvents (H2O and C2H6O2), having a great deal of interest in the field of advancement and innovation. The flow mechanismis formulated in the form of a nonlinear set of PDEs with an additional impact of a magnetic field, thermal radiation, and natural convection.As a principal contribution, a specific type of thermophysical model based on thermal conductivity and viscosity is used in the present study with slip boundary conditions. The modeled system of equations is processed by the Numerical Runge Kutta (RK-4) procedure. The accuracy of the observation is checked using the control volume finite element method (CVFEM). The influence of Cf and Nu is estimated according to the characteristics of the flow rate. Drag force and heat transmission velocity are displayed for optimization with the modeled parameters. The results are authenticated by prior studies and a decent level of coherence is demonstrated.

Slip and non-slip flows of MHD nanofluid through microchannel to cool discrete heat sources in presence and absence of viscous dissipation

This paper investigates heat transfer (HTR) and fluid flows of a magnetohydrodynamic (MHD) nanofluid (NFD) in a two-parallel-plate microchannel with three isothermal heat sources and under temperature jump and slip (0 < B* < 0.1) and non-slip regimes. The flow is subjected to a magnetic field (0 < Ha < 60) in three zones in the presence and absence of viscous dissipation (VDS) (0 < Br < 0.1). Using SIMPLE algorithm, it is found that a rise in the Re (0 < Re < 100) increases HTR under both slip and non-slip conditions. VDS decreases HTR from the isothermal heat source to the NFD flow. An increase in the slip coefficient raises the Nu, particularly at higher Ha. A rise in the Ha leads to greater HTR under the slip boundary condition. An increase in the slip coefficient raises the Nu by 52.52% in the presence of VDS and by 1.16% in the absence of VDS.

Scale and shear investigation of the viability and consequences of controlling viscous heating for Argon flows in nano-channels

Molecular dynamics (MD) is used to investigate the combined effects of channel size and wall shear stress on force-driven Argon flows in nanochannels. The adaptive wall thermostat (AWT) is used to automatically adjust wall temperature refraining the viscous heating upsurge with the increased body force from increasing mean fluid temperature. AWT is functional up to “wall shear stress limit” (WSSL), classifying wall shear stress range into controllable and uncontrollable viscous heating ranges (CVH and UVH) before and beyond WSSL, respectively. With increasing wall shear stress in CVH, liquid Argon at ∼119.9 K exhibits more non-uniform temperature profile in larger channels. Consequently, further shear dependence of density profile and fluid molecular layering which leads to controversial size-dependent slip length. Within UVH, supercritical Argon emerges from the significant increase of temperature and pressure exceeding critical state; consequently, density profile and molecular layering decrease noticeably drifting toward walls which results in minor and proximate values of slip length in all channels approaching no-slip condition. The apparent viscosity is higher in larger channels with decreasing and increasing trends within CVH and UVH, respectively, associated with changing fluid state and phase. Finally, the continuum solution suggests the possibility of estimating the mass flow rate with reasonable accuracy relative to MD if implemented with appropriate properties and slip boundary condition.

Jeffery’s paradox for the rotation of a single ‘stick–slip’ cylinder

We consider the problem of determining the two-dimensional fluid velocity due to the rotation of an infinitely-long ‘stick–slip’ cylinder in an otherwise quiescent Stokes flow. Stick–slip boundary conditions are introduced as a model of a rough superhydrophobic surface, via a distribution of alternating solid–liquid (stick) and gas–liquid (slip) interfaces. This leads to a mixed boundary-value problem for Stokes flow. Complex variable techniques are employed to transform the flow problem into a Hilbert problem, which involves finding a function analytic in a plane region assuming that on some portions of the boundary its real part is known, while on others its imaginary part is given. We solve the Hilbert problem to obtain semi-analytic expressions for all the pertinent fluid-dynamic quantities. We find that in the general aperiodic case there is no solution in which the velocity of the fluid vanishes at infinity. This is a form of Jeffery’s paradox, typically associated with viscous flow due to the counter-rotation of two equal rigid cylinders. Our work provides the first example of Jeffery’s paradox due to the rotation of a single cylinder.

Case study of thermal and solutal aspects on non-Newtonian Prandtl hybrid nanofluid flowing via stretchable sheet: Multiple slip solution

The effect of multiple slip boundary conditions is one more important physical parameter on the flow investigation and have been studied in this analysis. Further, the effect of Ohmic heating and varying chemical reaction on non-Newtonian Prandtl hybrid nanofluid with water based nanofluids to an extending of leading edge was also investigated to this current analysis. An inclined magnetic field is introduced to fluid flow to regulate the fluid stream. Hybrid nanomaterial is synthesized by the dispersion of Cu and Cofe2O4 nanoparticles in Prandtl fluid. All chemical science specifications of nanofluid are measured as constant. Due to the nanofluid particles motion, the fluid concentration is inspected underneath chemical implications. A mathematical model is developed by assuming the flow as incompressible and purely cartesian coordinate system and appropriate non-dimensional variables are introduced for problem simplifications and dimensional analysis. The scheme for semi analytical study named Homotopy Analysis Method (HAM) is implied to get solutions to the equations. The procedure is then displayed pictorially where fluid velocity, temperature and concertation against various pertinent parameters are examined. It was found that, the Concentration field profiles have been shown to deteriorate because molecule diffusivity reduces as the chemical reaction parameter rises in both cases. In order to maintain thermal balance management in tiny heat density equipment and gadgets, current research may also be helpful in enhancing the thermal efficiency of heat exchangers.

Statistical and numerical analysis of unsteady hybrid nanoliquid flows over an elongating surface with oblique Lorentz force: A comparison of Cu–Al2O3/H2O, Cu–Al2O3/CH3OH and Cu–Al2O3/H2O–EG

The current work investigates the effects of oblique Lorentz force and Navier’s slip boundary condition on unsteady hybrid nanoliquid flow with three different base liquids (H2O, CH3OH and H2O–EG) across a nonlinearly elongating surface set in a porous medium. This research considers the effects of viscous–Ohmic dissipation, nonlinearly variable thermal radiation, internal heat source, the Soret effect, first-order chemical reaction and thermal and solutal jump conditions at the boundary. Proper thermo-physical relationships for the hybrid nanoliquid have been established. Rosseland’s estimate for an optically thick regime is used when calculating the heat flow owing to radiation. The dimensional governing equations are translated into nondimensional forms using appropriate similarity transformations. The velocity, energy and concentration fields are numerically solved using a shooting strategy based on the secant iteration and the Runge–Kutta–Fehlberg method. The physical implications of several essential parameters on the hybrid nanoliquid velocity, temperature and concentration are investigated using graphical and tabular representations of numerical data. Furthermore, the multiple (quadratic) regression analysis reveals that physical parameters strongly influence the local skin friction coefficient, Sherwood and Nusselt numbers. For continuously growing values of the unsteadiness parameter, the velocity, thermal and concentration scattering declined everywhere within the boundary layer region.

Validity of steady Prandtl layer expansions

AbstractLet the viscosity for the 2D steady Navier‐Stokes equations in the region and with no slip boundary conditions at . For , we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer. Our uniform estimates in ε are achieved through a fixed‐point scheme: for solving the Navier‐Stokes equations, where are the tangential and normal velocities at , DNS stands for of the vorticity equation for the normal velocity v, and the compatibility ODE for at .

THE FLOW OF LUBRICANT IN A NARROW WEDGE-SHAPED SLOT WITH A MOVABLE WALL IS CONSIDERED

The article presents the results of a study of the lubricant flow in a narrow wedge-shaped slot with a movable wall. A solution to the problem with slip boundary conditions on the channel walls is obtained. The effect of slippage on the change in hydrostatic lift and hydraulic resistance in the slotted channel is shown.&#x0D; It was determined in the work that with an increase in the slip intensity (an increase in the value of the Knudsen number), the pressure variation weakens. This is due to the weakening of the interaction of the flow with the wall. As a result, the hydraulic resistance is reduced.&#x0D; The dependence of the relative hydrostatic lifting force on the Knudsen number and the opening angle of the channel is obtained. It is determined that with an increase in the Knudsen number, the magnitude of the hydrostatic lifting force decreases, since the influence of the flow on the wall weakens. The influence of slippage weakens with an increase in the opening angle of the channel.

Time-periodic electromagnetohydrodynamic flow in a circular microtube with surface charge dependent slip

The time-periodic electromagnetohydrodynamic (EMHD) flow in circular microtubes is studied by considering slip boundary conditions. An oscillating electric field and a constant magnetic field orthogonal to each other are applied externally to drive the fluid flow. The slip length considered here depends on the surface charge of the channel, which is generally a more realistic situation as demonstrated by recent experimental work. The velocity is obtained by using the characteristics of the Bessel equation. The influences of surface charge density σs and electrical oscillating Reynolds number Re on velocity and flow rate are discussed in detail. Our results demonstrate the EMHD slip flow rate can be reduced by up to 8.5% at low Reynolds number (Re=1) by considering the surface charge effect on slip, but enhanced by up to 8% at high Reynolds number (Re=50). These theoretical results can provide some theoretical basis for experimental studies.

Suppression of Wave Instability in a Liquid Film Flow Down a Non-Uniformly Heated Slippery Inclined Plane Using Odd Viscosity

Abstract We study the effects of odd viscosity on the stability of a thin Newtonian liquid film flowing down a nonuniformly heated plane under a slip boundary condition. The effect of odd viscosity arises in classical fluids when the time-reversal symmetry breaks down. Due to the odd viscosity, the odd part of the Cauchy stress tensor consists of symmetric and antisymmetric parts and shows several striking effects. We apply the Navier slip boundary condition for the slippery inclined plane at the solid–liquid interface. For our problem, we first derive an evolution equation whose solution describes the film thickness. The equation contains parameters considering the effect of inertia, thermocapillarity, slip length, and odd viscosity. We then perform the linear stability analysis and find that odd viscosity can significantly suppress the combined destabilizing effects of the thermocapillarity and slip length. Next, we analyze the dynamics using the weakly nonlinear approach, which provides details of different subregions of the instability zone. We observe that as the influence of the odd viscosity increases, the supercritical stable and explosive zones shrink while the unconditional stable and subcritical unstable zones expand. We also perform numerical investigation and observe that linear analysis, weakly nonlinear theory, and numerical results are consistent.

Slip and convective flow of Williamson nanofluid influenced by Brownian motion and thermophoresis mechanism in a horizontal microchannel

The current work is an attempt to explicate the repercussions caused by the transmission of heat as well as mass along with the enhancement of heat transmission for a steady MHD Williamson nano-substance flowing through the microchannel with slip and convective boundary conditions. The consequence of magnetic field and viscous dissipation on the flow is recorded. The simultaneous impact of the two well-known slip-mechanisms Brownian movement and thermophoresis is elaborated explicitly. The governed non-linear systems obtained were illustrated numerically via Runge-Kutta Fehlberg 4–5th order method based on shooting scheme. The pertinent features of assorted parameters have been scrutinized with the aid of graphs. Results reveal that magnetic parameter along with buoyancy ratio parameter was observed to decline the velocity whereas Weissenberg number displays both rising and depleting conduct on velocity. Temperature was reported to boost with Brownian motion and thermophoresis parameter whereas concentration profile declines with the same. Also drag across the enclosures of the microchannel with wall heat flux are computed and studied through graphs.

Effect of sliding speed on the thermohydrodynamic performance of partially slip‐textured slider bearings

AbstractThe present study evaluates the combined use of micro‐textures and ‘wettability gradient’ on the thermohydrodynamic performance of inclined slider bearings. Mass conserving Elrod cavitation model with slip boundary condition has been used to investigate the dimensionless static performance parameters at different convergence ratios and sliding speeds. The most effective location of the wettability gradient and textures has been considered in the present work. It has been observed that with the increase in sliding speed, the load carrying capacity, friction force and volumetric inflow rate of the slip‐textured bearings were improved. The improvements were more pronounced at smaller convergence ratios. Moreover, the slip‐textured bearings exhibited significant improvement in the average pressure and temperature of the lubricant. However, at higher sliding speeds, a substantial increase in friction force and average lubricant temperature was noticed. The square textured slip bearing exhibited maximum improvements towards various performance parameters of the three considered texture shapes.

On variational–hemivariational inequalities in Banach spaces

This paper is devoted to a well-posedness analysis of elliptic variational–hemivariational inequalities in Banach spaces. The differential operator associated with the variational–hemivariational inequality is assumed to be strongly monotone of a general order, in contrast to that in the majority of existing references on this subject where the differential operator is assumed to be strongly monotone of order 2. Moreover, the solution existence is proved with an approach more accessible to applied mathematicians and engineers, instead of through an abstract surjectivity result for pseudomonotone operators in existing references. Equivalent minimization principles are established for certain variational–hemivariational inequalities, which are valuable for developing efficient numerical algorithms. The theoretical results are applied to the analysis of a mixed hemivariational inequality in the study of a generalized Newtonian fluid flow problem involving a nonsmooth slip boundary condition of friction type. Existence and uniqueness of both the velocity and pressure unknowns are shown for the mixed hemivariational inequalities.

Dual Solutions of Boundary Layer Flow and Heat Transfer in Hybrid Nanofluid over a Stretching/Shrinking Cylinder

The boundary layer flow over a stretching/shrinking cylinder in hybrid nanofluid with the effects of suction, partial slip and convective boundary condition is studied. Hybrid nanoparticles Al2O3 and TiO2 with water as based fluid are considered in the study. The partial differential equations are transformed to ordinary differential equations by employing the similarity variables. The numerical results are obtained using the bvp4c solver in MATLAB software. The influence of nanoparticles volume fraction (Al2O3-TiO2 in water-based fluid), curvature parameter, suction parameter, partial slip parameter and Biot number on the velocity profile, temperature profile, skin friction coefficient and heat transfer rate are discussed. The numerical results indicate that for shrinking surface case, the dual solutions exist for a certain range of curvature parameter and suction parameter.

Significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation

For its applications in nuclear reactors, food processing, chemical engineering, water emulsions and thermal power generating systems, the significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation have been investigated. The flow problem has been modeled utilizing the modified Buongiorno model and the thermophysical characteristics of water-based Cu − F e 3 O 4 hybrid nanoliquid. Effects like passive control of nanoparticles, hydrodynamic slip and convective boundary conditions are also heeded to boost the realistic nature of this work. Further, engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated which boosts the novelty of this research work. The modeled governing equations are transmuted into a system of first-order ODEs, with the help of apposite similarity transformations, which are then numerically resolved using the finite-difference based bvp5c algorithm. It is noticed that per unit increase in the electric parameter decreases the skin friction coefficient by 41.75% and increases the heat transfer rate by 15.31%. It is also observed that the entrainment velocity is directly proportional to the changes in electric field parameter and is inversely proportional to the changes in volume fraction of copper and magnetite nanoparticles.