Slip Boundary Conditions Research Articles

FEM computations and Taguchi optimization in nonlinear radiative MHD MWCNT-MgO/EG hybrid nanoliquid flow and heat transfer over a 3D wedge surface

The problems concerning to heat transport in hybrid nanofluids on a wedge surfaces are of great interest due to their relevance in applications such as solar panels, drying processes, cooling of electronic equipment, heat exchangers, and air heaters. Therefore, the present study explores the nonlinear thermal radiative heat transport features and three-dimensional rheological characteristics of MWCNT-MgO/EG hybrid nanofluid flowing over a wedge considering the variable magnetic field, and multiple slip boundary conditions. The single-phase model comprising of the experimental data with their dependency on temperature and nanoparticle weight fraction is used for thermal conductivity and viscosity of composite nanomaterial. Rosseland and Boussinesq approximations are accounted. The wedge surface is maintained at thermal jump condition, whereas the ambient state is considered at a constant temperature. The governing conservation laws are transformed into a system of ordinary differential equations via space type similarity transformations, and then are solved using the Galerkin finite element method. The L16 orthogonal array-based Taguchi method is applied to determine the optimal setting of governing parameters are determined for maximum heat transport rate. The contribution of physical parameters in the enhancement of heat transport rate is also estimated. The temperature jump condition has the maximum contribution (51.72%), among the selected four physical parameters whereas the nanoparticle weight fraction has the least (10.02%). The nonlinear thermal radiation has the maximum heat transfer rate compared to the linear one.

Agrawal nanofluid flow towards a stagnation point past a moving disk with smoluchowski temperature and Maxwell velocity slip boundary conditions: The case of Buongiorno's model

AbstractNanofluid is a novel heat transfer fluid with the ability to significantly improve the heat transfer efficiency of regular fluids. Many efforts have been made to study its viscosity and thermal conductivity, both of which are crucial thermophysical properties. This work reports the significance of nanofluid along with thermophoretic and Brownian motion phenomena on the Agrawal flow towards a stagnation point past a permeable moving disk. The impacts of the Maxwell velocity slip and Smoluchowski temperature conditions are also incorporated. The leading equations in form of PDEs (Partial differential equations) are simplified into ODEs (Ordinary differential equations) by employing similarity theory. Then these simplified equations are solved numerically by utilizing a bvp4c solver (fourth‐order boundary value problem).The phenomenal effects of the relevant embedded distinguished parameters on the shear stress, rate of mass, and heat transfer are demonstrated through different graphs and tables. Graphical results indicate that double solutions are detected for stretching/shrinking parameter in a certain range. The heat transport and the wall drag force ascend with the suction aspect, while the mass transfer rate drops with suction in both solutions.

Axisymmetric lattice Boltzmann model for liquid flows with super-hydrophobic cylindrical surfaces

The lattice Boltzmann (LB) method has been extensively applied to the simulation of various fluid flows. Nonetheless, the standard LB model in rectangular coordinates faces some challenges when attempts are made to use it to simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length. Therefore, in this paper, boundary conditions for an axisymmetric LB model are proposed for the simulation of liquid slip at both convex and concave cylindrical surfaces. Based on the Navier slip boundary conditions, an equilibrium–nonequilibrium boundary scheme is developed to obtain the liquid slip in the azimuthal direction, with a combined bounce-back and specular-reflection boundary condition being developed to obtain the liquid slip in the axial direction. These boundary schemes are verified by simulating several established cases, namely, cylindrical Couette flow, harmonic oscillatory cylindrical Couette flow, Hagen–Poiseuille flow, and annular Poiseuille flow. The results are in excellent agreement with analytical results. Furthermore, some more complex flows involving super-hydrophobic cylindrical surfaces, such as stepwise oscillatory cylindrical Couette flow, are also simulated and studied using the proposed LB model. The axisymmetric LB model presented here overcomes the inability of standard LB models to accurately and efficiently simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length.

The Navier–Stokes–Voigt equations with position-dependent slip boundary conditions

The Navier–Stokes–Voigt equations with position-dependent slip boundary conditions

Carbon Nanotubes Flow Induced by Rotating Stretching Disk with Non- Linear Radiations and Slip.

The phenomenon of rotating disks involving flows serves as a crucial element in the field of fluid mechanics. Owing to its massive practical importance in engineering and industry, considerable attention is being paid to the extension of the problems associated with rotating stretching disks. In this regard, Carbon Nanotubes (CNT) are chosen as the best example of true nano technology. CNTs have an incredible range of applications due to their extraordinary characteristics. But single rotating-stretching disk with CNTs fluid flow has not been plowed yet. The objective of this work is to outstretch the study of viscous fluid with Carbon Nanotubes (CNTs) and transfer of heat due to radially stretching and rotating disk contingent to Navier slip, nonlinear radiations and convective boundary conditions. Cylindrical coordinates are utilized in the modeling and the mathematical formulation of the flow equations. These flow equations take the form of ordinary differential equations by means of similarity transformations. The emanated equations are solved by two numerical methods i.e. the shooting method and the Keller box method respectively. Xue model of carbon nanotubes is incorporated to carry out the research. The acquired solutions are tabulated and precise values of the physical parameters with excellent matching results are shown. These results are juxtaposed with CNTs of multi-wall and single-wall carbon nanotubes, while water is taken as a base fluid. Results reveal a significant depletion in skin friction with an increase in the slip parameter. Slip, nonlinear radiation and Biot number proved as liable factors in escalating the rate of heat transfer.

Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis

In this work, we study theoretically and numerically the equations of Stokes and Navier-Stokes under power law slip boundary condition. We establish existence of a unique solution by using the monotone operators theory for the Stokes equations whereas for the Navier-Stokes equations, we construct the solution by means of Galerkin's approximation combined with some compactness results. Next, we formulate and analyze the finite element approximations associated to these problems. We derive optimal and sub-optimal a priori error estimate for both problems depending how the monotonicity is used. Iterative schemes for solving the nonlinear problems are formulated and convergence is studied. Numerical experiments presented confirm the theoretical findings. • New power law slip boundary condition for the Stokes and Navier Stokes system. • Well posedness and optimal convergence rates for standard finite element spaces. • Formulation and analysis of the iterative scheme. • Verification of the convergence properties, simulation of the Lid driven cavity.

Exact multiple solutions of 2-D bidirectional moving plate micropolar hybrid nanofluid flow with heat transfer

Consider a hybrid copper-aluminum oxide/water flow over a permeable deforming surface with constant wall and prescribed wall temperature of non-Newtonian micropolar hybrid nanofluid flow under velocity slip boundary condition. The main purpose is to assess the existence of unique or multiple exact solutions of governing system of nonlinear coupled ordinary differential equations that describe the flow and heat fields. Similarity transformation variables are used to reduce the micropolar hybrid nanofluid flow and heat transfer model into nonlinear differential equations, which are exactly solvable in explicit forms. The classification of solutions into physically meaningful solutions depends entirely on the domains of parameters. Critical values determined for mass transfer are definitive in positioning and bordering the solutions. The profiles of velocity, microrotation and temperatures in the micropolar fluid reveal monotonically decaying behavior. The cases when parameters attain special values, produce special as well as dual exact solutionsIn addition, the visual analysis showing the influences of state parameters on wall moving velocity, angular velocity, constant wall temperature, linearly growing wall temperature and rate of heat transfer is presented. • Multiple solutions for hybrid nanofluid flow of bidirectional deforming plane problem. • Parametric domains determine regions for unique and multiple solutions. • No solutions fall in the region 0 ≤ K ≤ 1 , and only one solution exists for K > 1 . • For large values of velocity slip, the stretching/shrinking velocity diminishes. • Larger temperature jump values abate heat transfer rate.

Electroosmotic slip flow of Eyring fluid under high Zeta potential in a circular microchannel

• Under the combined action of applied electric field force and pressure, the electroosmotic flow of Eyring fluid with Navier slip boundary condition at high Zeta potential. • Apply the Chebyshev spectral method to solve the electric potential distribution, and then apply the numerical method (compound trapezoidal formula) to solve the fluid velocity distribution. • The influences of relevant physical parameters on the velocity are analyzed for the Eyring fluid. In this paper, the electroosmotic flow of Eyring fluid with Navier slip boundary condition under high Zeta potential in a circular micropipe under the combined use of applied electric field force and pressure is studied. The finite difference method is traditionally used to solve the electric potential distribution and fluid velocity distribution under high Zeta potential. In this paper, we try to use the Chebyshev spectral method to solve the electric potential distribution and fluid velocity distribution, and the results are compared with the analytical approximate solution obtained by Debye-Hückel (D-H) linear approximation [1] and the numerical solution obtained by the classical finite difference method. The result not only confirms the validity of the Chebyshev spectral method, but also shows that it has the advantages of high precision and a small amount of calculation; In addition, the effects of various physical parameters on electroosmotic flow are discussed in detail, and it is obtained that the velocity distribution of the Eyring fluid increases with the increase of the electric potential under the high zeta potential.

Statistical Analysis of MHD Flow of an Electrically Conducting Tangent Hyperbolic Fluid over a Stretching Cylinder with Convective Boundary Condition

The dynamics of MHD non-Newtonian fluid flow past a cylinder with slip boundary condition and magnetic field is addressed in this study. The non-Newtonian fluid (tangent hyperbolic) considered in this study are nail polish and whipped cream. This article investigates the statistical analysis of two-dimensional MHD tangent hyperbolic fluid flow over a cylinder with slip condition. The partial differential equations describing the problem are later transformed into the ordinary differential equation by similarity variables. The derived model is solved by the spectral homotopy analysis method (SHAM). The characteristics of the parameters of the flow are demonstrated by the velocity of the flow. The skin friction coefficient is computed and presented with the aid of a tables. The slope of the linear regression is obtained through the data points while bar charts for engineering quantities of interest are presented. The findings indicated that an increase in magnetic parameters builds a resistance to the flow. Also, it was discovered that the radius of curvature decreases when the curvature parameter increases.

FENE-P fluid flow generated by self-propelling bacteria with slip effects

It is hypothesized that gliding bacteria move by producing waves on their own surface and leave an adhesive slime trail. Slime is basically a viscoelastic slippery material. Based on these observations, we use a mathematical model (of undulating sheet) to examine the locomotion of gliding bacteria over a layer of non-Newtonian slime. The constitutive equations of FENE-P model are employed to characterize the rheological behavior of the non-Newtonian slime. Moreover, substratum beneath the slime is approximated by a multi-sinusoidal sheet. A hybrid computational technique to solve the second order DE with a system of algebraic equations is presented. The speed of organism, flow rate and energy loss at larger values of the involved parameters are simulated using bvp5c in conjunction with a modified Newton-Raphson technique (MNRT). The comparison of soft and rigid substrate, slip and no-slip boundary conditions, Newtonian and non-Newtonian slime is displayed in several figures. Streamlines pattern and velocity of the slime are also drawn for the realistic pairs of speed and flow rate and are thoroughly explained.

On the equivalence of nonequilibrium and equilibrium measurements of slip in molecular dynamics simulations

The hydrodynamic wall location at which the slip boundary condition is applied lies inside the fluid. Its distance from the fluid-solid interface is a strong function of the fluid state and system properties and cannot be neglected. Accounting for this distance holds the key to correct calculations of slip as, for example, when reconciling equilibrium and nonequilibrium measurements.

Significance of Free Convection Flow over an Oscillating Inclined Plate Induced by Nanofluid with Porous Medium: The Case of the Prabhakar Fractional Approach.

Given the importance and use of electrically conducted nanofluids, this work aims to examine an engine-oil-based nanofluid including various nanoparticles. In the current study, a fractional model for inspecting the thermal aspect of a Brinkman-type nanofluid, composed of (molybdenum disulfide (MOS2) and graphene oxide (GO) nanoparticles flows on an oscillating infinite inclined plate, which characterizes an asymmetrical fluid flow, heat, and mass transfer. Furthermore, the Newtonian heating effect, magnetic field, and slip boundary conditions were taken into account. The objectives for implementing the Prabhakar-like fractional model are justified because this fractional algorithm has contemporary definitions with no singularity restrictions. Furthermore, the guided fractional model was solved using the Laplace transform and several inverse methods. The obtained symmetrical solutions have been visually analyzed to investigate the physics of several relevant flow parameters on the governed equations. Some exceptional cases for the momentum field are compiled to see the physical analysis of the flowing fluid symmetry. The results show that the thermal enhancement can be progressively improved with the interaction of the molybdenum disulfide-engine oil-based nanofluid suspension, rather than with the graphene oxide mixed nanoparticle fluid. Furthermore, the temperature and momentum profiles enhance due to the factional parameters for molybdenum disulfide and the graphene oxide-engine oil-based nanofluid suspension. This study's graphical and numerical comparison with the existing literature has shown a very close resemblance with the present work, which provides confidence that the unavailable results are accurate. The results show that an increase improved the heat transmission in the solid nanoparticle volume fractions. In addition, the increment in the mass and heat transfer was analyzed in the numerical evaluation, while the shear stress was enhanced with the enhancement in the Prabhakar fractional parameter α.

Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition

Non-Newtonian fluid model was created against the Newton’s Law of viscosity where the viscosity is no more constant and dependent on the shear rate. The existing such fluid can be found in many industrial claims especially in food manufacturing, lubrication, biomedical flows and oil and gas. Besides, the used of non-Newtonian fluid occurs in mining industry where the slurries and muds are often handled. There are many models on non-Newtonian fluid available in literature where some of them capture the specific properties. The Reiner–Philippoff (RP) fluid model is considered in this endeavour due to the capabilities of the model which can be acted in three different family of fluid which are viscous, shear thickening and the shear-thinning. Mathematical model is constructed using continuity, momentum and energy equations where in form of partial differential equations (PDEs). The complexity of the proposed model is abridged by deduced the equations into ordinary differential equations (ODEs) by adopting similarity variables before the computation is done by bvp4c function drive in MATLAB software. To ratify the validity of the proposed model as well as numerical outputs, the comparative study is performed and it found to be in very strong agreement under limiting case where the present model is condensed to be identical with the reported model previously. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form.

Semi-analytical and numerical explorations on entropy optimization of EMHD in Casson hybrid nanofluid with radiation slip and convective boundary conditions

TheTheoretical study of 3D electro magnetohydrodynamic boundary layer steady flow of a Casson fluid across a rotating disk in the presence of velocity slip, porous medium and thermal radiation is indeed the subject of this article. Engine oil with (Copper–Zirconium dioxide) hybrid nanoparticles takes up the fluid in the containment. The nonlinear differential systems are transformed into ordinary differential systems using a suitable self-similarity variable, which are obtained using the Runge–Kutta scheme. When compared to the numerical method, the HPM yields a more precise and dependable conclusion than the Runge–Kutta method. With new parameters, Casson fluid velocity, temperature, entropy production rate, bejan number, skin friction factor and rate of heat transfer are explored and the findings are graphically shown for two different fluid cases that is Newtonian and non-Newtonian. The entropy generation increases for greater values of the electric field parameter, Brinkman number and temperature ratio parameters. Hybrid nanoparticles play a significant role in Power transmission lines, the Automobile industry, fuel cell membranes, and joint implants.

Dynamic behavior of a magnetorheological fluid radial-flow-based energy absorber considering apparent slip boundary condition

Accurate theoretical models play a key role in the development of magnetorheological energy absorbers (MREAs). Traditionally, the apparent slip caused by non-uniformity interface (i.e., the separation of carrier fluid and magnetic particles at the wall) of the working medium is often ignored for simplifying theoretical models. However, the apparent slip influence the cross-sectional flow and decreased the theoretical accuracy of the damping force for MREA applied in the impact absorption area. In this study, a dynamic model with apparent slip boundary condition for radial-flow-based MREA was proposed. The effect of apparent slip layer thickness on the dynamic behavior of an MREA was qualitatively and quantitatively compared in terms of the following three aspects: (1) with the Power-Law constitutive model, theoretical models of the dynamic characteristics of the magnetorheological fluid (MRF) squeeze and MREA are presented based on the apparent slip boundary condition with the MRF behavior of the Navier–Stokes equation; (2) the accuracy of the theoretical model to predict MREA peak force and boundary velocity with different slip-layer thicknesses; and (3) global agreement of the dynamic force and range curves between the modeling and experimental results. The results show that the absolute values of the relative errors in the two models with a 2- and 0-µm thick slip layer were less than 3.73 and 7.41%, respectively, and that a 2-µm thickness can help predict the actual dynamic characteristic more efficiently under accidental collision loading conditions.

The effect of slip on the development of flow separation due to a bump in a channel

A numerical study on the effect of surface slip on the flow in a constricted channel is presented, with the aim of exploring the use of surface slip to control flow separation. Our focus is on two-dimensional flow in a channel over a bump, with a fixed aspect ratio, upon which a Robin-type slip boundary condition is imposed. When the channel walls are fully no-slip, such a flow is known to develop a region of separation behind the bump, at sufficiently large Reynolds numbers. The effect of slip on the separation bubble dynamics occurring behind the bump is investigated, for Reynolds numbers $2000$ and $4000$ . It is shown that surface slip (i) attenuates the intensity of separation as it diminishes the minimum of the streamwise velocity within the recirculation region; (ii) delays the onset of flow separation, shifting it downstream, along the bump, and (iii) reduces the dimensions of the separation bubble behind the bump, allowing the flow to reattach sooner. Ultimately, slip inhibits separation, with both the points of separation and reattachment coalescing, for a slip length $\lambda$ of approximately $0.2$ .

Transportation of thermal and velocity slip factors on three-dimensional dual phase nanomaterials liquid flow towards an exponentially stretchable surface

The fundamental purpose of this research is to elaborate on slip boundary conditions and the flow of three-dimensional, stable, incompressible, rotating movements of nanoparticles lying across a stretchable sheet. The mathematical model for fluid flow is created using the assumptions stated above. The partial differentials are produced after utilizing boundary layer estimates. The partial differential governing equations are reduced into three coupled ordinary differential equations by using similarity transformations. After, applying transformations the system is solved numerically. Numerical results are approved with the help of the MATLAB bvp4c algorithm. The analysis shows that velocity and temperature are strongly dependent on essential parameters like stretching ratio, velocity slip, rotation, thermal slip parameter, and Prandtl number. Numerical values of distinct parameters on heat flux and skin friction factors are shown in a tabulated form. Partial velocity and thermal slip are applied to the temperature surface. The comparison among the nano-sized particles copper oxide and silver with water base nanofluid affecting velocity and temperature fields are used for analysis. Moreover, the Graphical depiction designates that the velocity and temperature spreading of the thermal slip parameter is increasing. It is observed that Ag-water is the best heat carrier as compared to CuO-water nanofluid.

Heat Transfer Problem for the Boltzmann Equation in a Channel with Diffusive Boundary Condition

In this paper, the authors study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures θ0 and θ1. This problem was studied by Esposito-Lebowitz-Marra (1994, 1995) where they showed that the solution tends to a local Maxwellian with parameters satisfying the compressible Navier-Stokes equation with no-slip boundary condition. However, a lot of numerical experiments reveal that the fluid layer does not entirely stick to the boundary. In the regime where the Knudsen number is reasonably small, the slip phenomenon is significant near the boundary. Thus, they revisit this problem by taking into account the slip boundary conditions. Following the lines of [Coron, F., Derivation of slip boundary conditions for the Navier-Stokes system from the Boltzmann equation, J. Stat. Phys., 54(3–4), 1989, 829–857], the authors will first give a formal asymptotic analysis to see that the flow governed by the Boltzmann equation is accurately approximated by a superposition of a steady CNS equation with a temperature jump condition and two Knudsen layers located at end points. Then they will establish a uniform L∞ estimate on the remainder and derive the slip boundary condition for compressible Navier-Stokes equations rigorously.

Validation of inhomogeneous chamber states in rotary positive displacement vacuum pumps

Chamber model simulation is a common approach to simulate rotary positive displacement vacuum pumps. Therefore the pump is abstracted into working chambers and connecting clearances, whereby the clearance leakages can be identified as the major loss mechanism in such machines. The clearance mass flow rates are calculated with respect to the thermodynamic states in the adjacent chambers, which are inhomogeneous for rarefied gases due to the movement of the rotors which causes a pressure gradient within the chamber. This effect increases with higher Knudsen numbers, because of the increasingly dominant friction. These inhomogeneous chamber states are assumed to be quasi-static in case that the chamber volume is constant with time. Therefore the chamber must not have a connection to the suction or discharge port. This can be modelled with a one-dimensional approach for geometrically abstracted chambers. In order to validate the one-dimensional characteristics in circumferential direction three-dimensional steady state simulations of a working chamber are performed using a Computational Fluid Dynamics (CFD) solver. To improve the accuracy for rarefied gases Maxwell velocity slip boundary conditions are applied. It is shown, that the inhomogeneous chamber states can be approximated by a regression analysis of a dimensionless number. Furthermore the housing clearance and the radial clearance mass flow rates for given boundary conditions are geometrically abstracted and calculated using a one-dimensional model. The new clearance models and the inhomogeneous chamber states are implemented in a chamber model simulation software and results of a test machine are compared to measurements and to previous simulations.

Correlation-based algorithms for accurate PIV measurement near the slip boundary

Accurate particle image velocimetry (PIV) measurement near the wall is of great significance in many fields. However, it is challenging for conventional PIV algorithms to deal with the near-wall flow, especially under the slip boundary condition. In general, the conventional window correlation method cannot accurately calculate the flow velocity at any location that is less than half the size of the interrogation window away from the boundary. For steady or periodic flow, the single-pixel ensemble correlation method can estimate the velocity very near the wall, but numerous image pairs are required, which comes at a great computational cost. In this paper, a new method based on window deformation is proposed to estimate the velocity profile of near-wall flows. Furthermore, a multi-pixel ensemble correlation method is proposed based on the single-pixel method, which improves accuracy and significantly reduces the computational cost relative to the single-pixel method. Both methods are validated by synthetic particle images and experiments. The present work extends the PIV methodology for accurately measuring near-wall flows, especially under the slip boundary condition, which will benefit research on the boundary layer, drag reduction, microfluidics, etc.