Slip Boundary Conditions Research Articles

Global Well-Posedness of Classical Solutions to the Compressible Navier–Stokes–Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains

Global Well-Posedness of Classical Solutions to the Compressible Navier–Stokes–Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains

Exploration of Stokes hydrodynamic law at molecular length scales

Exploration of Stokes hydrodynamic law at molecular length scales

Thermal and viscous slip effects on electroosmotic Casson nanofluid flow with microorganisms in peristaltic porous media

Current work focuses on increasing heat transmission in thermal systems with the incorporation of gyrotactic motile microbes, promoting the creation of structured fluids useful for bio-cooling and nanotechnology. This study explores the effects of electroosmosis and slip boundary conditions in a non-Newtonian Casson nanofluid with mass transfer. Specifically, it looks at bio-convection peristaltic events and conducts a thermodynamic analysis. The Arrhenius activation energy in an asymmetric channel is considered in this study. In addition, the authors evaluate viscous resistance, thermophoresis diffusion, porous surface properties, coupled convection, Brownian diffusion, and thermal viscosity behavior. The results obtained from mathematical expressions together with surface conditions are handled by means of a numerical algorithm implemented by means of the shooting technique through traditional program Mathematica, with the aid of its built-in tool, NDSolve. Many physical parameters, such as entropy generation, the Bejan number, velocity profiles, the density of gyrotactic motile microbes, and the accumulation profile of nanoparticles, are depicted graphically. The graphical study shows that entropy generation increases with a greater Helmholtz-Smoluchowski factor by 10%, but declines as the heat generation/absorption factor increases with same percentage. The Bejan number tends to increase with stronger heat sources by 5%. Application possibilities include improved control and effectiveness in mechanisms that include microfluidic equipment, systems for delivering medications, and biotechnological operations.

Dynamics of methanol conveying mono and hybrid nanoparticles to optimization of heat transfer across stretching cylinder

This manuscript investigates the comparative analysis of SiC and SiC − Ag with methanol-base fluid. The nano species are more important in many fields such as medicine, catalysis, energy-based research, imaging, and environmental sciences. The present study includes theoretical and numerical studies of the Prandtl hybrid nanofluid flow model, which takes into account the effects of heat radiation across a stretched cylinder, inclined magnetohydrodynamics (MHD), and Darcy-Forchheimer. The cylinder’s surface is subjected to the convective slip boundary condition as part of the study. The main aim of this study is to enhance heat transformation. The flow problem is formulated in a system of nonlinear partial differential equations. By employing a similarity transformation, a nonlinear system of partial differential equations can be converted into a linear system of ODEs. A feasible numerical technique Bvp4c is used to solve the reduced system of ODEs through MATLAB software. The results of temperature, concentration, and velocity profiles are discussed graphically. In section and injection scenarios, the velocity profile of both fluids decreased with increasing inputs of magnetic and Darcy-Forchheimer parameters. The heat transmission improved for higher inputs of Prandtl and thermal radiation parameters for both section and injection cases. Furthermore, our findings align with the body of current literature. The conclusions are supported by a careful comparison with pertinent research that has been published in earlier publications.

Cut-PFEM: a Particle Finite Element Method using unfitted boundary meshes

AbstractIn this work, we present a novel unfitted mesh boundary strategy in the context of the Particle Finite Flement Method (PFEM) aiming to improve endemic limitations of the PFEM relative to boundary conditions treatment and mass conservation. In this new methodology, which we called Cut-PFEM, the fluid–wall interaction is not performed by adding interface elements, as is done in the standard PFEM boundaries. Instead, we use an implicit representation of (all or some of) the boundaries by introducing the use of a level set function. Such distance function detects the elements trespassing the (virtual) contours of the domain to equip them with opportunely boundary conditions, which are variationally enforced using Nitsche’s method. The proposed Cut-PFEM circumvents important issues associated with the standard PFEM contact detection algorithm, such as the artificial addition of mass to the computational domain and the anticipation of contact time. Furthermore, the Cut-PFEM represents a natural ground for the imposition of alternative wall boundary conditions (e.g., pure slip) which pose significant difficulties in a standard PFEM framework. Several numerical examples, featuring both no-slip and slip boundary conditions, are presented to prove the accuracy and robustness of the method in two-dimensional and three-dimensional scenarios.

3D concrete printing using computational fluid dynamics: Modeling of material extrusion with slip boundaries

This paper investigates the role of slip boundary conditions in computational fluid dynamics modeling of material extrusion and layer deposition during 3D concrete printing. The mortar flow governed by the Navier-Stokes equations was simulated for two different slip boundary conditions at the extrusion nozzle wall: no-slip and free-slip. The simulations were conducted with two constitutive models: a generalized Newtonian fluid model and an elasto-viscoplastic fluid model. The cross-sectional shapes of up to three printed layers were compared to the experimental results from literature for different geometrical- and speed-ratios. The results reveal that employing free-slip boundary conditions at the extrusion nozzle wall improves layer-mimicking quality for both constitutive models, indicating the presence and importance of a lubricating layer of fine particles at the concrete-solid wall interface. This enhanced performance is primarily due to the observed decrease in extrusion pressure that minimizes layer height- and width-deviations compared to the experimental prints. Furthermore, the free-slip boundary conditions play an important role in predicting the multilayer prints, its deformation and groove shapes.

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection–diffusion–reaction equation

Full discretization of the time dependent Navier–Stokes equations with anisotropic slip boundary condition coupled with the convection–diffusion–reaction equation

Hypersonic boundary layer over a flat plate with slip and shear nonequilibrium effects

Near-space hypersonic vehicles could encounter significant rarefied nonequilibrium effects during the flight through atmosphere, which largely influence the gas-surface momentum and heat transfer. In this paper, hypersonic boundary layer over a flat plate with velocity slip, temperature jump, and shear nonequilibrium effects is theoretically considered. The slip boundary conditions and nonlinear transport relations are embedded into the boundary-layer equations to describe the flow. Local similar solutions are derived, and key parameters for characterizing slip and shear nonequilibrium effects are determined. The velocity-slip and temperature-jump effects are determined by [(2−σu)/σu]Mae/Rex and [(2−σT)/σT]Mae/Rex respectively, and the shear nonequilibrium effect is characterized by Mae2/Rex. The obtained boundary-layer solutions are compared with the Navier–Stokes solutions for a Mach 4.5 slip flow, and the results of Direct Simulation Monte Carlo for a Mach 10 rarefied flow, good agreements are achieved. The separate and combined effects of velocity slip, temperature jump, and shear nonequilibrium on boundary-layer solutions and momentum/heat transfer are clarified. The results show that both the slip and shear nonequilibrium effects cause the boundary layer to become thinner and decrease the skin friction and Fourier heat conduction. However, with including sliding friction, the total heat flux might even increase as the slip degree increases. These results provide valuable insight into the boundary-layer characteristics of hypersonic near-continuum flows.

Impact of porous material and slip condition on the MHD flow of immiscible Couple stress-Newtonian fluids through an inclined channel: Head loss and pressure difference

Nowadays, non-Newtonian and Newtonian non-miscible fluid flow problems are much more effective in real-life physical problems. The understanding of flow behavior of magneto-hydrodynamic non-miscible fluids through a porous region playing an important role in the areas of biochemical sciences, crude oil extraction, transport issues and biomedicine. The aim of the present study is to know the impact of inclination angle of the channel, porous material used in the channel, slip boundary condition and applied magnetic field on the flow variables such as velocity profile, wall shear stress, pressure differences, head loss and volumetric flow rate of the two electrically conducting non-miscible couple stress and Newtonian fluids flowing through an inclined channel occupied with porous material of different porosity and permeability. An inclined channel is divided into two sub-regions of equal width through which the Newtonian and Couple stress fluids flow, respectively. Here, Brinkman’s model has been used to study the flow of immiscible fluid in their respective porous region. The equations that govern the flow of non-miscible fluids are solved using a well-defined analytical method and Mathematica 10.3 software. The present study concludes that the porous materials can be used to control the velocity of immiscible fluids in an inclined channel. It is also concluded from the present study that the use of slip condition promotes the values of velocity, volumetric flow rate, pressure differences and head loss. This work is validated with the previously published research work. Such models can be helpful in industries for filtering or refining immiscible oils.

Analysis of Magnetohydrodynamic Free Convection in Micropolar Fluids over a Permeable Shrinking Sheet with Slip Boundary Conditions

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases.

The existence of R$$ \mathcal{R} $$‐bounded solution operator for Navier–Stokes–Korteweg model with slip boundary conditions in half space

This paper proves the existence of ‐bounded solution operator families of the resolvent problem of Navier–Stokes–Korteweg model in half‐space with slip boundary condition. Especially we investigate the model for arbitrary constant viscosity and capillarity. We employ the ‐bounded solution operators of the model obtained from the whole space cases and partial Fourier transform techniques to analyze the model.

An extended model to assess Jeffery–Hamel blood flow through arteries with iron-oxide (Fe2O3) nanoparticles and melting effects: Entropy optimization analysis

Abstract Nanofluids are utilized in cancer therapy to boost therapeutic effectiveness and prevent adverse reactions. These nanoparticles are delivered to the cancerous tissues under the influence of radiation through the blood vessels. In the current study, the propagation of nanoparticles within the blood in a divergent/convergent vertical channel with flexible boundaries is elaborated computationally. The base fluid (Carreau fluid model) is speculated to be blood, whereas nanofluid is believed to be an iron oxide–blood mixture. Because of its shear thinning or shear thickening features, the Carreau fluid model more precisely depicts the rheological characteristics of blood. The arterial section is considered a convergent or divergent channel based on its topological configuration (non-uniform cross section). An iron oxide ( F e 2 O 3 {\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3} ) nanoparticle is injected into the blood (base fluid). To eliminate the viscous effect in the region of the artery wall, a slip boundary condition is applied. An analysis of the transport phenomena is preferred using the melting heat transfer phenomena, which can work in melting plaques or fats at the vessel walls. The effects of thermal radiation, which is advantageous in cancer therapy, biomedical imaging, hyperthermia, and tumor therapy, are incorporated in heat transport mechanisms. The governing equation for the flow model with realistic boundary conditions is numerically tickled using the RK45 mechanism. The findings reveal that the flow dynamism and thermal behavior are significantly influenced by melting effects. Higher Re \mathrm{Re} can produce spots in which the track of the wall shear stress fluctuates. The melting effects can produce agitation and increase the flow through viscous head losses, causing melting of the blockage. The maximum heat transfer of 5 % 5 \% is achieved with We {\rm{We}} when the volume friction is kept at 1 % 1 \% . With higher estimation of inertial forces Re \mathrm{Re}\hspace{1em} and same volume friction, the skin drag coefficient augmented to 34 % 34 \% . The overall temperature is greater for the divergent flow scenario.

Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

AbstractWe consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

Finite speed axially symmetric Navier-Stokes flows passing a cone

Let D be the exterior of a cone inside a ball, with its altitude angle at most π/6 in R3, which touches the x3 axis at the origin. For any initial value v0=v0,rer+v0,θeθ+v0,3e3 in a C2(D‾) class, which has the usual even-odd-odd symmetry in the x3 variable and has the partial smallness only in the swirl direction: |rv0,θ|≤1100, the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition have a finite-energy solution that stays bounded for all time. In particular, no finite-time blowup of the fluid velocity occurs. Compared with standard smallness assumptions on the initial velocity, no size restriction is made on the components v0,r and v0,3. In a broad sense, this result appears to solve 2/3 of the regularity problem of ASNS in such domains in the class of solutions with the above symmetry. Equivalently, this result is connected to the general open question which asks that if an absolute smallness of one component of the initial velocity implies the global smoothness, see e.g. page 873 in Chemin et al. (2017) [6]. Our result seems to give a positive answer in a special setting.As a byproduct, we also construct an unbounded solution of the forced Navier Stokes equation in a special cusp domain that has finite energy. The forcing term, with the scaling factor of −1, is in the standard regularity class, and it can be generated by an electric current in a long and straight wire (i.e. Ampère force). This result confirms the intuition that if the channel of a fluid is very thin, arbitrarily high speed in the classical sense can be attained under a mildly singular, physically reasonable force.

Slip boundary conditions effect on bidispersive convection with local thermal non-equilibrium: Significant findings

We examine a theory concerning heat convection within a porous material characterized by a skeletal structure comprising macropores and, additionally, cracks or fissures leading to a network of micro pores. Brinkman theory and slip conditions were considered applicable within the macropores, while exclusively Darcy theory was applied within the micropores. This represents a scenario of thermal convection within a double-porosity porous medium. The theory accommodates non-equilibrium thermal conditions, allowing for the possibility that the temperature of the solid skeleton differs from that of the fluid present in either the macro or micro pores. Importantly, the model permits independent fluid velocities and pressures within both the macro and micro pores. We conducted both linear and nonlinear stability assessments, with a specific focus on assessing how slip boundary conditions affect the stability of the system. Once we pinpointed the onset of instability, we calculated the critical Rayleigh number as a variable dependent on the slip coefficient. Additionally, we provided numerical results that outline the thresholds for stability and instability.

Vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg equations with slip boundary condition

In this paper, we investigate the vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg (NSK) equations in a three-dimensional horizontally periodic strip domain, in which the velocity of the fluid is supplemented with slip boundary condition and the gradient of density with Dirichlet boundary condition on the boundary. We prove that there exists an positive constant T0 independent on the capillarity and viscosity coefficients, such that the incompressible NSK equations have a unique strong solution on [0,T0] and the solution is uniformly bounded in H3. Based on the uniform estimates, we further give the convergence rate in H1 from the solutions of the incompressible NSK equations to the solution of the inhomogeneous incompressible Euler equations as the capillarity and viscosity coefficients go to zero simultaneously.

Squeeze film derivation of the porous curved annular plates with variable magnetic field, Rosensweig’s viscosity and slip velocity in the Shliomis model

PurposeThe present article aims to investigate the squeeze effects on hematite suspension-based curved annular plates with Rosensweig’s viscosity and Kozeny–Carman’s porous structure under the variable strong magnetic field and slip in the Shliomis model. The variable magnetic field is utilised to retain all magnetic elements within the model. The aforementioned mechanism would have the benefit of generating a maximal field at the system’s required active contact zone.Design/methodology/approachThe Kozeny–Carman globular sphere model is used for porous facing. Rosensweig’s extension of Einstein’s viscosity is taken into consideration to enhance the fluid’s viscosity, and Beavers and Joseph’s slip boundary conditions are employed to assess the slip effect.FindingsThe pressure and lifting force under squeezing are computed through modification of the Reynolds equation with the addition of Kozeny–Carman’s model-based porosity, Rosensweig’s viscosity, slip and varying magnetic field. The obtained results for the lifting force are very encouraging and have been compared with Einstein’s viscosity-based model.Originality/valueResearchers so far have carried out problems on lubrication of various sliders considering Einstein’s viscosity only, whereas in our problem, Rosensweig’s viscosity has been taken along with Kozeny–Carman’s porous structure model.

Investigation of the slip boundary conditions effect on the flow regimes, mixing efficiency and heat transfer in a T-type micromixer

This paper presents the research of effect of the slip coefficient on the mixing efficiency, flow regimes and heat exchange of two fluids in a T-shaped micromixer. The slip coefficient ranged from 0 to 10−4 m, and the Reynolds number varied from 1 to 300. Two cases with the same (41 °C) and different (27 °C and 55 °C, average – 41 °C) initial temperatures of fluids were considered. It was found that for the case of identical initial temperatures with an increase in the slip coefficient, the mixing efficiency practically does not change in the region before the onset of the engulfment mode, while in the region after the onset of such mode it increases. For the case of different initial temperatures, with an increase in the slip coefficient, the mixing efficiency increases in the area before the onset of the engulfment mode, while, on the contrary, decreasing in the area after the engulfment mode onset. The pressure drop decreased with an increase in the slip coefficient every time. At that, the change in the slip coefficient affected only the amplitude of pulsations in the quasi-periodic flow regime (250 < Re < 300), and the frequency of these pulsations remained unchanged.

Hydrodynamic stability of Poiseuille flow in a bidisperse porous medium with slip effect

Hydrodynamic stability of Poiseuille flow in a bidisperse porous medium with slip effect