Slip Boundary Conditions Research Articles

The effects of the Soret and slip boundary conditions on thermosolutal convection with a Navier–Stokes–Voigt fluid

In this paper, we study the problem of thermosolutal convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from above or below. This problem is studied under the effects of Soret and slip boundary conditions. Both linear and nonlinear stability analyses are employed. When the layer is heated from below and salted from above, the boundaries exhibit great concordance, resulting in a very narrow region of probable subcritical instabilities. This proves that linear analysis is reliable enough to forecast the beginning of convective motion. The Chebyshev collocation technique and QZ algorithm have been used to solve systems of linear and nonlinear theories. For thermal convection in a dissolved salt field with a complex viscoelastic fluid of the Navier–Stokes–Voigt type, instability boundaries are computed. When the convection is of the oscillatory type, the Kelvin–Voigt parameter is observed to play a crucial role in functioning as a stabilizing agent. This effect's quantitative size is shown.

Rheological study of Hall current and slip boundary conditions on fluid-nanoparticle phases in a convergent channel.

Purpose: the purpose of this theoretical study was to analyze the heat transfer in the fluid-particle suspension model under the effects of a porous medium, magnetic field, Hall effects, and slip boundary conditions in a convergent channel with the addition of electrokinetic phenomena. The Darcy-Brinkman (non-Darcy porous medium) model was used to assess the effects of the porous medium. Methodology: the rheological equations of both models were transformed into a dimensionless form to obtain the exact solutions of the fluid and particle phase velocities, pressure gradient, volumetric flow rate, stream function, temperature distribution, and heat-transfer rate. To obtain an exact solution to the models, the physical aspects of the parameters are discussed, analyzed, and reported through graphs, contour plots, and in tabular form. Findings: mixing in hafnium particles in a viscous fluid provide 1.2% more cooling compared to with a regular fluid. A reduction of the streamlines was observed with the contribution of the slip condition. The utilization of the Darcy parameters upgraded both the fluid flow and temperature profiles, while the heat-transfer rate decreased by up to 3.3% and 1.7% with the addition of a magnetic field and porous medium, respectively. Originality: the current study is an original work of the authors and has not been submitted nor published elsewhere.

Existence and exponential growth of global classical solutions to the compressible Navier-Stokes equations with slip boundary conditions in 3D bounded domains

Existence and exponential growth of global classical solutions to the compressible Navier-Stokes equations with slip boundary conditions in 3D bounded domains

Pressure boundary conditions for viscous flows in thin tube structures: Stokes equations with locally distributed Brinkman term

The steady state Stokes-Brinkman equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure at the inflow and outflow of the tube structure and the no slip boundary condition on the lateral boundary. The complete asymptotic expansion of the problem is constructed. The error estimates are proved. The method of partial asymptotic dimension reduction is introduced for the Stokes-Brinkman equations and justified by an error estimate. This method approximates the main problem by a hybrid dimension problem for the Stokes-Brinkman equations in a reduced domain.

Thermocapillary migration of thin droplet on wettability-confined track

The thermocapillary migration of droplets on a solid surface is widely used in daily life and industrial fields. Regulating droplet thermocapillary migration by changing surface wettability has received extensive attention. According to the lubrication theory and slip boundary conditions, we establish a mathematical model of the thermocapillary migration dynamics of a droplet on wettability-confined tracks subjected to a uniform temperature gradient. Combined with the contact line dynamics, a method of determining the velocity of the contact line in a different direction of the three-dimensional droplet is proposed, the simulation is carried out with FreeFEM++. The evolution of droplet migration is examined, and the effects of track width and wettability on the droplet migration dynamics are emphatically investigated. The results show that the main part of the droplet moves from the high-temperature region to the low-temperature region, the trailing edge of the droplet forms a small bulge during the movement, and a thin liquid film is formed between the bulge and the main part of the droplet. The droplet spreading perpendicular to the track direction is inhibited and remains pinned after shrinking to the track edge. Negative correlation between the velocity of the advancing contact line and the track width is observed. The velocity of the advancing line first rapidly and then slowly decrease to a steady state. The squeezing effect caused by the wettability confined perpendicular to the track direction accelerates the thermocapillary migration of the droplet on the track in the initial short time. The enhanced track wettability increases the initial velocity of the receding contact line but has little effect on its stable value. The velocity of the advancing contact line is positively correlated with track wettability. Changing the track width is possibly easier to regulate the thermocapillary migration of a droplet than varying the track wettability.

Viscoelastic fluid flow over a horizontal flat plate with various boundary slip conditions and suction effects

This study examines the numerical representation of fluid flow on the Maxwell model in a double-diffusive boundary layer over a horizontal plate.

Dynamics of prolate spheroids in the vicinity of an air-water interface.

In this article, we present the mobilities of prolate ellipsoidal micrometric particles close to an air-water interface measured by dual wave reflection interference microscopy. Particle's position and orientation with respect to the interface are simultaneously measured as a function of time. From the measured mean square displacement, five particle mobilities (3 translational and 2 rotational) and two translational-rotational cross-correlations are extracted. The fluid dynamics governing equations are solved by the finite element method to numerically evaluate the same mobilities, imposing either slip and no-slip boundary conditions to the flow at the air-water interface. The comparison between experiments and simulations reveals an agreement with no-slip boundary conditions prediction for the translation normal to the interface and the out-of-plane rotation, and with slip ones for parallel translations and in-plane rotation. We rationalize these evidences in the framework of surface incompressibility at the interface.

Significance of heat transfer for second-grade fuzzy hybrid nanofluid flow over a stretching/shrinking Riga wedge

<abstract> <p>This investigation presents the fuzzy nanoparticle volume fraction on heat transfer of second-grade hybrid $ {\text{A}}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{ + Cu/EO}} $ nanofluid over a stretching/shrinking Riga wedge under the contribution of heat source, stagnation point, and nonlinear thermal radiation. Also, this inquiry includes flow simulations using modified Hartmann number, boundary wall slip and heat convective boundary condition. Engine oil is used as the host fluid and two distinct nanomaterials ($ {\text{Cu}} $ and $ {\text{A}}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}} $) are used as nanoparticles. The associated nonlinear governing PDEs are intended to be reduced into ODEs using suitable transformations. After that 'bvp4c, ' a MATLAB technique is used to compute the solution of said problem. For validation, the current findings are consistent with those previously published. The temperature of the hybrid nanofluid rises significantly more quickly than the temperature of the second-grade fluid, for larger values of the wedge angle parameter, the volume percentage of nanomaterials. For improvements to the wedge angle and Hartmann parameter, the skin friction factor improves. Also, for the comparison of nanofluids and hybrid nanofluids through membership function (MF), the nanoparticle volume fraction is taken as a triangular fuzzy number (TFN) in this work. Membership function and $ \sigma {\text{ - cut}} $ are controlled TFN which ranges from 0 to 1. According to the fuzzy analysis, the hybrid nanofluid gives a more heat transfer rate as compared to nanofluids. Heat transfer and boundary layer flow at wedges have recently received a lot of attention due to several metallurgical and engineering physical applications such as continuous casting, metal extrusion, wire drawing, plastic, hot rolling, crystal growing, fibreglass and paper manufacturing.</p> </abstract>

Stability Scrutinization of Agrawal Axisymmetric Flow of Nanofluid through a Permeable Moving Disk Due to Renewable Solar Radiation with Smoluchowski Temperature and Maxwell Velocity Slip Boundary Conditions

The utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy. Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly. The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy. Moreover, the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer. The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically. The current numerical approach can produce double solutions by providing suitable initial guesses. In addition, the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction. The suction parameter delays the boundary layer separation. Moreover, stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.

A parallel subgrid stabilized algorithm for incompressible flows with nonlinear slip boundary conditions

We present and study a parallel subgrid stabilized algorithm for simulating the incompressible Navier-Stokes equations with nonlinear slip boundary conditions. The algorithm uses finite element discretizations and an approach of completely overlapping region division for the parallelization, where an elliptic projection operator is applied to define the stabilization term. It has the following appealing features: 1) each subproblem used to calculate a local solution in a subdomain is actually a global problem defined on a global mesh that is locally refined around the subdomain; 2) it can re-use existing sequential software in coding, where both parallelization and stabilization are easy to implement based on existing sequential codes without extensive effort; 3) it inherits the advantages of the subgrid stabilization method and the completely overlapping region division approach; 4) with suitable algorithmic parameters, it is able to yield an optimal convergence rate for the approximate solutions with a comparable accuracy to that of the solutions from the global subgrid stabilized method, with considerable reduction in computational time. With the help of a local a priori estimate, we estimate error bounds of the obtained solutions from the algorithm, and perform some numerical tests to validate the theoretical prediction and illustrate the applicability of the proposed algorithm.

On linearization principle for Navier-Stokes system with dynamic slip boundary condition

We consider incompressible Navier-Stokes equations in a bounded 3D regular domain, coupled with the so-called dynamic boundary condition. We rigorously establish the principle of linearized stability. Namely, given a smooth stationary state, we prove that the linearized equation has a complete basis of generalized eigenfunctions, and that the non-linear stability depends on the supremum of the real part of spectrum in the usual way. We work in the class of weak solutions satisfying the energy inequality, for which the global existence (but not uniqueness) is known.

Hydromagnetic Flow of Two Immiscible Couple Stress Fluids in an Inclined Porous Channel: Effects of Slip Boundary

In this study, we investigated the effects of slip boundary and magnetic field on the flow of two immiscible couple stress fluids in an inclined porous media channel. The Stokes model was used to define the two couple stress fluids. The fluids in both the regions are assumed to be incompressible and immiscible and the transport properties in the two regions are assumed to be constant. The governing coupled linear ordinary differential equations are made dimensionless by using appropriate fundamental quantities. The expressions for the velocity components in both the regions are obtained in closed form using the undetermined coefficient method; by applying slip boundary condition at the boundary of the channel and at fluid‐fluid interface, the continuity of velocities, vorticities, shear stresses, and couple stresses are applied. The effects of the nondimensional parameters including the couple stress parameters, slip parameter, Hartmann number, Darcy number, and the ratio of basic fluid properties on the velocity components are presented graphically; the flow rate and shear stress are presented in table and discussed briefly. It is reported that the presence of couple stresses and magnetic field have a declining impact while slip boundary has an enhancement impact on the fluid velocity and the volumetric flow rate. In the absence of couple stress, the results for the liming case as s⟶∞(η⟶0) for Newtonian flow are achieved and further limiting cases are established and briefly addressed.

THERMOSOLUTAL CONVECTION IN A BIDISPERSE POROUS MEDIUM WITH CHEMICAL REACTION EFFECT AND RELATIVELY LARGE MACROPORES

The model of double diffusive convection in a bidisperse porous medium was examined. Brinkman effects and slip were allowed to be used in macropores. In the micropores, only the Darcy effects are held. In equilibrium, the concentration of solutes is thought to be a linear function of temperature. We performed both a linear and a nonlinear stability analysis, with a particular emphasis on the impact of slip boundary conditions on the system's instability and stability. After deciding when the instability started, we determined the critical Rayleigh number as a function of the slip coefficient. Numerical findings for stability/instability thresholds were also presented.

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.

Chemical Reaction Effects on of Nanofluid Past a Permeable Stretching Sheet with Slip Boundary Conditions and MHD Boundary Layer Flow

The overall exploration is excited to investigate the MHD limit layer float of a nanofluid with the results of attractive field, slip limit situation, warm radiation and synthetic reaction has been researched. Closeness change is utilized to change over the administering non-straight limit layer conditions into coupled better request non-direct normal differential conditions. those conditions are mathematically addressed utilizing fourth request R-k technique alongside shooting strategy. An assessment has been accomplished to explain the outcomes of overseeing boundaries like assorted materially conditions. Mathematical results are gotten for the speed, temperature and mindfulness, as well as, for the pores and skin rubbing, close by Nusselt reach and neighborhood Sherwood range for a few benefits of overseeing boundaries. The mathematical results are talked about through graphically and referenced subjectively.

Global strong solutions to the viscous liquid–gas two-phase flow model with slip boundary conditions in 3D exterior domains

This paper is concerned with the viscous liquid–gas two-phase flow model in a three-dimensional exterior domain with the slip boundary conditions. We are able to prove the existence of a global strong solution when the initial total energy is suitably small. The initial masses of liquid and gas are allowed to contain a vacuum, with no extra restriction between the initial masses of liquid and gas. It should be noted here that we consider the slip boundary condition in a three dimensional (3D) exterior domain which is in sharp contrast to result of Yu (2021) where they consider the Cauchy problem.

Entropy analysis of magneto-radiative SWCNT-MWCNT/H2O hybrid nanofluid flow with slip boundary conditions

In the presence of nonlinear thermal radiation, viscous dissipation, and heat source/sink, this paper investigates the impact of entropy generation and heat transfer on the flow of single-walled carbon nanotube (SWCNT)/water (H 2 O) and SWCNT-multiwalled carbon nanotube (SWCNT-MWCNT)/water (H 2 O) hybrid nanofluids under the influence of a permeable stretching sheet. We also take into account the velocity slip and thermal slip boundary conditions. By using the correct similarity transformations, the nonlinear partial differential equations are transformed into ordinary differential equations. The Runge–Kutta-Fehlberg method (RKF45) with the shot approach is then used to numerically solve the generated dimensionless model. It is also noticed that the frictional coefficient, local Nusselt number, temperature distribution, and fluid velocity are all significantly affected by the presence of SWCNT-MWCNT based hybrid nanofluid. Using the second law of thermodynamics, we can determine the total entropy production using Bejan number, which is very sensitive to the values of the nanoparticle volume fraction, magnetic parameter, and radiation parameter. The results show that the skin friction coefficient decreases with increasing nanoparticle volume fraction and magnetic field, whereas the local Nusselt number increases due to heat radiation and increasing nanoparticle volume fraction. Furthermore, it is shown that the rate of heating/cooling of hybrid nanofluid is greater than that of mono nanofluid. Researchers have not made any efforts to optimise entropy using a SWCNT-MWCNT/H2O hybrid nanofluidmodel, taking into account the impacts of nonlinear thermal radiation and an external magnetic field, as well as the effects of velocity and thermal slip. After comparing the cooling and heating capabilities of mono and hybrid nanofluids, we can say that hybrid nanofluids are superior, and that their usage in the construction of efficient electromagnetic appliances is of the utmost importance.

Anisotropic slip impact on nanofluid flow over a biaxial exponentially stretching sheet with Hall current: Corcione's correlation

This study introduces the Corcione correlation that accentuates the role of fluid temperature, particle volume fraction, and sizes in the increment of the nanofluid heat transfer rate and thermal conductivity. Here, the flow of nanofluid comprising Al2O3/H2O over a biaxial exponentially stretching sheet is considered. The analysis is performed for nanoparticles’ sizes 28, 30, and 45 nm and volume concentrations up to 7%. The mathematical model is strengthened by the anisotropic slip and convective boundary conditions. The momentum and heat equations are enriched with the inclusion of the Hall current and the non-uniform heat generation/absorption terms respectively. The nonlinear, coupled momentum and heat nondimensionalized ordinary differential equations (ODEs) are formulated with appropriate transformations and are solved numerically. The effects of many relevant factors are depicted using graphs. It is scrutinized that by enhancing the diameter of nanoparticles (Al2O3), the skin friction coefficient enhances and the heat transfer rate in the case of different nanoparticle sizes boosts for gradually growing estimations of the volume fraction. It is also deduced that surface slip increases pumping power and the insertion of the nanoparticles into the working fluid enhances heat transmission. To support the thesis, the presented model's validation is also provided.

On the two-step BDF finite element methods for the incompressible Navier–Stokes problem under boundary conditions of friction type

This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with slip boundary conditions of friction type. It studies the well-posedness and error analysis properties of the numerical scheme in L2-norm for all positive time using the two-step backward differentiation formula (BDF) in time and the finite element approximation in space. Error estimates are proved under feasible assumptions on the regularity of the solution and with the aid of different versions of discrete Grownwall lemmas. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

Unsteady radiative–convective flow of a compressible fluid: a numerical approach

This article is designed to inspect the thermal effects of an unsteady compressible flow of a viscous fluid through a symmetric channel. Combined effects of convective heat transfer, magnetic field, and radiation are also given special attention in this article. Basic laws of mass, momentum, and energy for compressible flow are employed in the modeling of the current problem. In addition, slip boundary conditions are also implemented in the analysis of the above thermal flow problem. Coupled nonlinear differential equations are solved numerically using explicit finite difference technique. Finally, the influence of different sundry parameters on the axial velocity, flow rate, and heat transfer are visualized through graphs. Time variant behavior of flow rate is calculated. Outcomes of the results reveal that the increment of the flow rate is related to the increase of compressibility parameters. Enhancement in the temperature profiles in the presence of radiation number is also reported. This model is the most general version of peristalsis of compressible flow in view of natural convection and radiation impact with extensive applications in aircraft industry, geophysics, and other industrial situations (cooling of electronic equipment, heat exchangers, and so forth).