Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lu- brication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

On the Inviscid Limit of the 3D Navier–Stokes Equations with Generalized Navier-Slip Boundary Conditions

In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary conditions u^ε·n=0,n×(ω^ε)=[Bu^ε]τon∂Ω.Some uniform estimates on rates of convergence in C([0,T],L2(Ω))and C([0,T],H^1(Ω))of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.

AParallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions

For the low-order finite element pair P1􀀀P1,based on full domain partition technique,a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed.From the definition of the subdifferential,the variational formulation of this equation is the variational inequality problem of the second kind.Each subproblem is a global problem on the composite grid,which is easy to program and implement.The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen.Finally,some numerical results are given to demonstrate the hight efficiency of the parallel stabilized finite element algorithm.

Effects of viscous dissipation and Joule heating on the Couette and Poiseuille flows of a Jeffrey fluid with slip boundary conditions

In this article,we have presented the exact solutions of the Couette,Poiseuille and generalized Couette flows of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium.The effects of slip boundary conditions and heat transfer are considered.Viscous dissipation,radiation and Joule heating are also considered in the energy equation.The governing equations of the Jeffrey fluid flow are modeled in Cartesian coordinate system.Analytical solutions for the velocity and temperature the velocity and temperature profiles are studied and the results are presented through graphs.It Temperature behaves as a decreasing function due to the impact of Hartmann number,non-Newtonian parameter and slip parameter in all noted problems.

Navier-Stokes equations under slip boundary conditions:Lower bounds to the minimal amplitude of possible time-discontinuities of solutions with two components in L^(∞)(L^(3))

The main purpose of this paper is to extend the result obtained by Beirao da Veiga(2000)from the whole-space case to slip boundary cases.Denote by a two components of the velocity u.To fix ideas setū=(u_(1),u_(2),0)(the half-space)orū=?_(1)ê_(1)+?_(2)ê_(2)(the general boundary case(see(7.1))).We show that there exists a constant K,which enjoys very simple and significant expressions such that if at some timeτ∈(0,T)one has lim sup_(t→^(τ)-0)‖ū(t)‖_(L^(3)(Ω))^(3)<‖ū(τ)‖_(L^(3)(Ω))^(3)+K,then u is continuous atτwith values in L^(3)(Ω).Roughly speaking,the above norm-discontinuity of merely two components of the velocity cannot occur for steps'amplitudes smaller than K.In particular,if the above condition holds at eachτ∈(0,T),the solution is smooth in(0,T)×Ω.Note that here there is no limitation on the width of the norms‖ū(t)‖_(L^(3)(Ω))^(3)·So K is independent of these quantities.Many other related results are discussed and compared among them.

Numerical simulation of cavitating flow around a slender body with slip boundary condition

In this paper, we perform a numerical simulation of the cavitating flow around an underwater hemispherical-head slender body running at a high speed. For the first time, the slip boundary condition is introduced into this problem, and we find that the slip boundary condition has a big influence on the cavitation in the flow-separation zone. By simulating the cavitating flow under different cavitation numbers, we demonstrate that the slip boundary condition can effectively reduce the intensity of cavitation, as represented by the length of cavitation bubbles. The present paper provides a new method for utilization of new surface materials to control the cavitation on the underwater moving objects.

Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.

Comparative Numerical Analysis of Heat and Mass Transfer Characteristics in Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg Fluids on a Stretched Surface

In the current research,a thorough examination unfolds concerning the attributes of magnetohydrodynamic(MHD)boundary layer flow and heat transfer inherent to nanoliquids derived from Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg compositions.Such nanoliquids are subjected to an extending surface.Consideration is duly given to slip boundary conditions,as well as the effects stemming from variable viscosity and variable thermal conductivity.The analytical approach applied involves the application of suitable similarity transformations.These conversions serve to transform the initial set of complex nonlinear partial differential equations into a more manageable assembly of ordinary differential equations.Through the utilization of the FEM,these reformulated equations are solved,considering the specified boundary conditions.The outcomes attained are graphically depicted by means of plots and tables.These visual aids facilitate a comprehensive exploration of how diverse parameters exert influence over the distributions of velocity,temperature,and concentration.Furthermore,detailed scrutiny is directed towards the fluctuations characterizing pivotal parameters,viz.,Nusselt number,skin-friction coefficient,and Sherwood number.It is identified that the Nusselt number showcases a diminishing trend coinciding with increasing values of the volume fraction parameter(φ).This trend remains consistent regardless of whether the nanoliquid under consideration is Al_(2)O_(3)-Eg or TiO_(2)-Eg based.In contrast,both the skin-friction coefficient and Sherwood number assume lower values as the volume fraction parameter(φ)escalates.This pattern remains congruent across both classifications of nanoliquids.The findings of the study impart valuable insights into the complex interplay governing the characteristics of HMT pertaining to Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg nanoliquids along an extending surface.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

Unsteady Mixed Convection Slip Flow around a Stretching Sheet in Porous Medium

The heat and mass transfer of unsteady MHD two-dimensional mixed convection boundary layer flow over an exponentially porous stretching sheet is presented in this paper. Multiple slip conditions, radiation, suction or blowing, heat generation or absorption along with magnetism and porous medium are incorporated. We reduce the leading equations which are partial differential equations into a family of ordinary differential equations that are non-linear using a set of similarity transformations. The resulting equations with coupled boundary conditions are solved numerically with the aid of bvp4c solver with MATLAB package. The impacts of several non-dimensional governing parameters on the flow fields such as velocity, temperature and concentration profiles along with friction coefficient, temperature gradient and concentration gradient are portrayed graphically and discussed in detail. The result indicates that the magnetic parameter decreases the skin friction coefficient. Thermal boundary layer thickness reduces with increasing radiation parameters and enhances with increasing Prandtl number. It is also observed that the thermal slip parameter depreciates the heat transfer rate and the mass slip parameter diminishes the mass transfer rate. A comparison has been made between the current results and the numerical results of previous studies and observed a very close good agreement.

Convective flow of Jeffrey nanofluid along an upright microchannel with Hall current and Buongiorno model:an irreversibility analysis

The thermal properties and irreversibility of the Jeffrey nanofluid through an upright permeable microchannel are analyzed by means of the Buongiorno model.The effects of the Hall current,exponential space coefficient,nonlinear radiation,and convective and slip boundary conditions on the Jeffrey fluid flow are explored by deliberating the buoyant force and viscous dissipation.The non-dimensionalized equations are obtained by employing a non-dimensional system,and are further resolved by utilizing the shooting approach and the 4th-and 5th-order Runge-Kutta-Fehlberg approaches.The obtained upshots conclude that the amplified Hall parameter will enhance the secondary flow profile.The improvement in the temperature parameter directly affects the thermal profile,and hence the thermal field declines.A comparative analysis of the Newtonian fluid and non-Newtonian fluid(Jeffrey fluid)is carried out with the flow across a porous channel.In the Bejan number,thermal field,and entropy generation,the Jeffrey nanofluid is more highly supported than the Newtonian fluid.

Incompressible Limit of the Oldroyd-B Model with Density-Dependent Viscosity

This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

Moving contact line problem: Advances and perspectives

The solid-liquid interface, which is ubiquitous in nature and our daily life, plays fundamental roles in a variety of physical-chemical-biological- mechanical phenomena, for example in lubrication, crystal growth, and many biological reactions that govern the building of human body and the functioning of brain. A surge of interests in the moving contact line （MCL） problem, which is still going on today, can be traced back to 1970s primarily because of the exis- tence of the ＂Huh-Scriven paradox＂. This paper, mainly from a solid mechanics perspective, describes very briefly the multidisciplinary nature of the MCL problem, then summarizes some major advances in this exciting research area, and some future directions are presented.

Study on micronozzle flow and propulsion performance using DSMC and continuum methods

In this paper, both DSMC and Navier-Stokes computational approaches were applied to study micronozzle flow. The effects of inlet condition, wall boundary condition, Reynolds number, micronozzle geometry and Knudsen number on the micronozzle flow field and propulsion performance were studied in detail. It is found that within the Knudsen number range under consideration, both the methods work to predict flow characteristics inside micronozzles. The continuum method with slip boundary conditions has shown good performance in simulating the formation of a boundary layer inside the nozzle. However, in the nozzle exit lip region, the DSMC method is better due to gas rapid expansion. It is found that with decreasing the inlet pressure, the difference between the continuum model and DSMC results increases due to the enhanced rarefaction effect. The coefficient of discharge and the thrust efficiency increase with increasing the Reynolds number. Thrust is almost proportional to the nozzle width. With dimension enlarged, the nozzle performance becomes better while the rarefaction effects would be somewhat weakened.

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

In this paper,the authors study the 1 D steady Boltzmann flow in a channel.The walls of the channel are assumed to have vanishing velocity and given temperaturesθ0andθ1.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.

CONCERNING TIME-PERIODIC SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN CYLINDRICAL DOMAINS UNDER NAVIER BOUNDARY CONDITIONS

The problem of the existence of time-periodic flows in infinite cylindrical pipes in correspondence to any given, time-periodic, total flux, was solved only quite recently in [1]. In this last reference we solved the above problem for flows under the non-slip boundary condition as a corollary of a more general result. Here we want to show that the abstract theorem proved in [1] applies as well to the solutions of the well known slip （or Navier） boundary condition （1.7） or to the mixed boundary condition （1.14）. Actually, the argument applies for solutions of many other boundary value problems. This paper is a continuation of reference [1], to which the reader is referred for some notation and results.