Slip Boundary Conditions Research Articles

Inclined MHD Effects in Tapered Asymmetric Porous Channel with Peristalsis: Applications in Biomedicine

This paper emphasized an inclined magnetohydrodynamics (MHD) effects in tapered asymmetric porous channel with peristalsis in the presence of slip boundary conditions. Here we considered the two-dimensional channel with a porous medium. The fundamental assumptions of long wavelength and low Reynolds number are applied in the relevant nonlinear equations for momentum, heat, and mass transfer as part of mathematical modeling. The equations subjected to slip boundary conditions have been solved numerically by the Mathematica software. Various essential physical characteristics of velocity, temperature, concentration, and heat transfer rate are captured graphically in the end. The velocity profile is found parabolic for various involved parameters. It is observed that the embedded parameters behave in the exact opposite manner when compared with temperature and concentration distributions. The sinusoidal behavior of the heat transfer rate is also displayed. The unique aspect of this effort is specifically to relate the Joule heating, Darcy resistance, and inclined magnetic field effects in peristaltic flow for a non-Newtonian Jeffrey fluid in an asymmetric tapered channel under the influence of slip boundary conditions. Such preferences have a wide range of applications in engineering, biology, and industry. The outcomes of the presented work are also proficient in the medical field for the treatment of cancer using MHD. The MHD also aids in controlling blood pressure during systolic and diastolic pressure conditions by regulating the blood flow stream.

Non-equilibrium flow of van der Waals fluids in nano-channels

The Enskog–Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on the kinetic and mean-field theories. The fluid flows in nano-channels are investigated by the Bhatnagar–Gross–Krook (BGK) type Enskog–Vlasov model, which simplifies the complicated Enskog–Vlasov collision operator and enables large-scale engineering design simulations. The density distributions of real fluids are found to exhibit inhomogeneities across the nano-channel, particularly at large densities, as a direct consequence of the inhomogeneous force distributions caused by the real fluid effects including the fluid molecules' volume exclusion and the long-range molecular attraction. In contrast to the Navier–Stokes equation with the slip boundary condition, which fails to describe nano-scale flows due to the coexistence of confinement, non-equilibrium, and real fluid effects, the Enskog–Vlasov–BGK model is found to capture these effects accurately as confirmed by the corresponding molecular dynamics simulations for low and moderate fluid densities.

Entropy Generation Analysis in Magnetohydrodynamic Couple Stress Nanofluid Flow Through an Oblique Microchannel in a Permeable Medium with Thermal Radiation

The present work examines the flow and thermal energy process in conducting couple stress nanofluid flows through an oblique microchannel. The microchannel is embedded with permeable medium and thermal radiation is implemented. The microchannel boundaries retain the slip boundary conditions. The impact of buoyancy force and magnetic field are incorporated. The temperature dependent heat source effect was also taken into account. The momentum equation has been made by the permeability of the porous medium. The equations are modeled and non-dimensionalized using non-dimensional entities and further solved with the aid of the Runge-Kutta Fehlberg method and the shooting procedure. The detailed discussions about the importance of the effective parameters on entropy generation, the Bejan number have been observed through graphs. The findings of the examination depict that rise in radiation parameter augments the entropy generation and the Bejan number in the channel. The entropy generation and Bejan number diminishes with inflation of the permeability parameter.

Global strong solutions to the compressible magnetohydrodynamic equations with slip boundary conditions in 3D bounded domains

We deal with the barotropic compressible magnetohydrodynamic equations in three-dimensional (3D) bounded domain with slip boundary condition and vacuum. By a series of a priori estimates, especially the boundary estimates, we prove the global well-posedness of classical solution and the exponential decay rate to the initial-boundary-value problem of this system for the regular initial data with small energy but possibly large oscillations. The initial density of such a classical solution is allowed to contain vacuum states. Moreover, it is also shown that the oscillation of the density will grow unboundedly with an exponential rate when the initial state contains vacuum.

Numerical investigation for entropy‐based magneto nanofluid flow over non‐linear stretching surface with slip and convective boundary conditions

AbstractThe nanoliquid flows place a significant role in modern research due to the vast number of applications in the Food industry, manufacturing, thermal management, enhanced oil recovery, biomedical applications, and so on. This article presents the analysis of entropy generation on convective nanofluid flow in a three‐dimensional nonlinear stretching sheet with slip effects. Brownian motion and thermophoresis impacts are adopted by the nanoparticle concentration and temperature profiles. The PDEs are remodeled into ODEs by employing the appropriative simulated alternations, and the ODEs are solved by utilizing the R–K–F scheme along with the shooting technique. The main contributions of physical stream factors on the nanofluid concentration, heat, and speed profiles are displayed and explored via plots. Moreover, the rate of heat transfer and surface drag force are examined through tabular structures. In view of this, the nanofluids have more heat transfer capability and improve thermal properties. The slip factors are used in the boundary conditions of the velocity, and the limit conditions are utilized for the hotness and speed of the nanoparticles. The rate of heat transfer in a non‐linear stretching sheet is 1%–2% more than linear stretching sheet for varying values of Prandtl number Pr and Magnetic field M.

Global classical solutions to the viscous two-phase flow model with slip boundary conditions in 3D exterior domains

We consider the two-phase flow model in 3D exterior domains with slip boundary conditions. We establish the global existence of classical solutions of this system, provided that the initial energy is suitably small. Furthermore, we prove that the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.

Weak solutions to the full MHD system with non-homogeneous boundary conditions

ABSTRACT This paper is devoted to the study of weak solutions for full compressible magnetohydrodynamic flows in a 3D bounded domain, with non-homogeneous boundary condition for the velocity, absolute temperature and density on the inflow part, with Navier-type slip boundary condition for magnetic field. We show the weak–strong uniqueness principle as well as the global existence under a new notion of weak solution.

Weak solutions to the generalized Navier–Stokes equations with mixed boundary conditions and implicit obstacle constraints

This paper is concerned with the investigation of a generalized Navier–Stokes equation for non-Newtonian fluids of Bingham-type (GNSE, for short) involving a multivalued and nonmonotone slip boundary condition formulated by the generalized Clarke subdifferential of a locally Lipschitz superpotential, a no leak boundary condition, and an implicit obstacle inequality. We obtain the weak formulation of (GNSE) which is a generalized quasi-variational–hemivariational inequality. By introducing an Oseen model as an auxiliary (intermediated) problem and employing Kakutani-Ky Fan theorem for multivalued operators as well as the theory of nonsmooth analysis, an existence theorem to (GNSE) is established.

Entropy generation in magnetohydrodynamic radiative non-Darcy slip flow of a Casson nanofluid with Hall effects and activation energy

The present research work examines the entropy generation in the magnetohydrodynamic second-order slip flow of Casson nanofluid surpassing a horizontal stretching sheet inside a non-Darcy porous medium under the dominance of Hall current and nonlinear thermal radiation. The present model is made more realistic by taking second-order velocity slip flow. The energy field is pursued by incorporating the consequences of distinctive viscous dissipation and Joule heating. The chemical reaction incited by activation energy is comprised in the current exploration. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with second-order velocity slip and convective boundary conditions. A compatible similarity transformation comprised is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via the spectral quasi-linearization method. The present article deals with an in-depth exploration of the characteristics of diagnostic flow parameters against the-flow field and other efficient physical quantities with the help of distinctive graphs and tables. As per the regression analysis, the maximum relative error for the reduced Nusselt number ranging from .000090231% to .00015936% is less than that of the other physical quantities. Magnetic force, thermophoresis, and Brownian motion assist in lessening the heat transport rate, but it gets enriched under the Hall current effects. For the increasing Casson parameter, fluid movement tends to rise near the sheet’s surface and gets decelerated afterwards. The intense Hall current accelerates the Casson fluid’s motion. But the velocity components in xandz-directions become abated across the flow region due to increasing the first-order velocity slip parameter. Besides, the enhancement in the magnitude of the second-order velocity slip parameter undermines the velocity components in xandz-directions.

Buoyancy driven flow and slippage constraints influences on Casson hybridity nanofluid of Yamada-Ota and Xue type via rotating cone

Analysis of the extended two-hybrid nanofluid models: The Casson fluid with the combination of the base fluid (Ethylene Glycol) and two different nanoparticles is described in detail by Yamada-Ota and Xue (CoFe 2 O 4 and Mn-Zn Fe 2 O 4 ). This fluid is considered to flow in a rotating cone system, where the tangential vector (x-axis), azimuthal vector (y-axis) and normal vector are all part of the coordinate system (z-axis). The flow and thermal properties of the Casson hybrid nanofluid are controlled by the slipping boundary conditions (velocity and temperature components), the porous media, and buoyancy. To create a collection of ordinary differential equations (ODEs) from the initial mathematical specification, similarity transformations are used. Then, using a specialized method, namely the Galerkin finite element method (GFEM), these ODEs are solved numerically. Finally, this research has produced the graphical results of the velocity in the tangential and azimuthal directions, as well as thermal dispersal. Additionally, under the effect of relevant regulating parameters, the values of the tangential and azimuthal skin friction coefficients, along with the dimensionless Nusselt number, are tabulated. The results showed that radiation raises the thermal field while the Darcy-Forchheimer parameter escalates the flow for the two-dimensional axes (x and y). The buoyancy ratio parameter also upsurges the frictional coefficient for both the x- and y-components. Additionally, the dimensionless Nusselt number is decreased by managing variables like radiation, porosity, and slipping boundary conditions (velocity and temperature).

Lie-group method solutions for a viscous flow in a dilating-squeezing permeable channel with velocity slip

The investigation focuses on the effects of wall velocity slip on the solution of a viscous, laminar, incompressible channel flow subjected to small-scaled contraction and expansion of the weakly permeable walls. The study of such flow systems is often contextual for fluid transport in biological organisms. In the considered flow configuration, the vertically moving porous walls enable the fluid to enter or exit with a constant rate. The tangential slip velocity of the flow at the porous walls is modeled with the Navier slip boundary condition. The flow dynamics inside the channel is governed by the full Navier–Stokes equations. The Lie symmetry analysis and the invariant method are adopted to reduce the number of independent variables in the system of governing equations. Consequently, a single fourth-order ordinary differential equation is obtained, which is solved analytically by the double perturbation method and the variation of iteration method. The solutions are compared for different arrangements. Furthermore, the approximated analytical solutions are likened to the numerical solutions obtained from a fourth-order Runge–Kutta solver embedding the Shooting method to check the accuracy. It is observed that the boundary layers are formed, and the flow rapidly turns near the walls, when suction and wall contraction coexist. Alternatively, if injection and wall expansion are paired, the flow adjacent to the walls is delayed. The existence of wall velocity slip advances the near-wall velocity and cuts down the speed of centerline velocity. It results in a change in the volumetric flow rate and shear rate. The overall pressure is also varied by higher wall velocity slip. The results are explored for different values of the permeation Reynold number and the dimensionless wall dilation rate to capture all possible impacts of the flow parameters. The current analysis rectifies the existing errors in the work of Boutros et al. [“Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability,”Appl. Math. Model. 31(6), 1092–1108 (2007)] with the no-slip boundary condition and discusses the overall influences of slip boundary condition on the Lie symmetry solution of the flow system.

Significance of Weissenberg Number, Soret Effect and Multiple Slips on the Dynamic of Biconvective Magnetohydrodynamic Carreau Nanofuid Flow

This study focused on the analysis of two-dimensional incompressible magnetohydrodynamic Carreau nanofluid flow across a stretching cylinder containing microorganisms with the impacts of chemical reactions and multiple slip boundary conditions. Moreover, the main objective is concerned with the enhancement of thermal transportation with the effect of heat source and bioconvection. By assigning pertinent similarity transitions to the governing partial differential equations, a series of equations (ODES) is generated. An optimum computational solver, namely the bvp5c software package, is utilized for numerical estimations. The impact of distinct parameters on thermal expansion, thermophoresis, and the Nusselt number has been emphasized, employing tables, diagrams, and surface maps for both shear thinning (n < 1) and shear thickening (n > 1) instances. Motile concentration profiles decrease with Lb and the motile microorganism density slip parameter. It is observed that with increasing values of Pr, both the boundary layer thickness and temperature declined in both cases. The Weissenberg number demonstrates a different nature depending on the type of fluid; skin friction, the velocity profile and Nusselt number drop when n < 1 and increase when n > 1. The two- and three-dimensional graphs show the simultaneous effect of involving parameters with physical quantities. The accuracy of the existing observations is evidenced by the impressive resemblance between the contemporary and preceding remedies.

Flow-field in a lid driven cavity with slip boundaries: An investigation using lattice Boltzmann modelling

Investigation of the flow behaviour in a lid driven square enclosure has been performed imposing slip boundary conditions at all sidewalls. The slip on the walls is described by prescribing a tangential momentum accommodation coefficient (σ). While the range of Reynolds number (Re) is varied between 20 and 300, the value of σ is taken in the range of 0.01 to 1. Simulations have been carried out using single relaxation time based lattice Boltzmann method (SRT- LBM). To account for the slip, two different methods are used for treatment of boundary conditions, namely tangential momentum accommodation coefficient (TMAC) and modified bounce-back specular reflection (MBSR). While both schemes are comparable in terms of computing requirements, it is observed that the MSBR scheme predicts higher slip velocity on the wall as compared to that of TMAC scheme in lid driven cavity. Results show that the appearance of secondary vortex is affected by the accommodation coefficient. The size of the secondary vortex in the cavity reduces and eventually vanishes as the slip on the wall increases. The threshold accommodation coefficient for disappearance of corner vortex decreases with increasing Reynolds number. With reducing value of σ i.e., as the effect of slip increases, the location of the primary vortex centre shifts towards the centre of the cavity.

Global existence and decay of strong solutions to the compressible Navier-Stokes-Poisson equations in bounded domains

This paper concerns the global existence and decay rate of strong solutions to initial-boundary-value problem of the 3D compressible Navier-Stokes-Poisson equations. When the velocity admits slip boundary condition, it shows that strong solutions exist globally in time for small initial energy. The difficulties caused by Poisson term are overcome through uniform estimate of ‖ρ−1‖L2(0,T;L2) and time-weighted a priori estimates. In particular, the initial density has large oscillations and allows vacuum states. As a byproduct, we do not need any initial compatibility conditions.

Apparent permeability in tight gas reservoirs combining rarefied gas flow in a microtube

In tight gas reservoirs, the major flow channels are composed of micro/nanopores in which the rarefaction effect is prominent and the traditional Darcy law is not appropriate for gas flow. By combining the Maxwell first-order slip boundary condition and Navier–Stokes equations, a three-dimensional (3D) analysis of compressible gas slip flow in a microtube was presented, and the flux rate and pressure variation in the flow direction were discussed. Subsequently, by superimposing the Knudsen diffusion, a gas flux formula applicable to a larger Knudsen number was further proposed and satisfactorily verified by two groups of published experimental data in microtubes or microchannels in the membrane. The results indicate that slip flow and Knudsen diffusion make an important contribution to the total gas flow in the microtube, and their weight increases with an increase in the Knudsen number. By substituting the gas flux formula into Darcy’s law for compressible gas, a new apparent permeability model for tight gas reservoirs was proposed, in which the slippage effect and Knudsen diffusion were synthetically considered. The results indicate that the apparent permeability of tight reservoirs strongly depends on the reservoir pressure and pore-throat radius, and an underestimation value may be predicted by the previously published models. This study provides a case study for evaluating these apparent permeability models, which remains a challenging task in the laboratory.

Nanoscale flow-induced nonlinear vibration of multilayer graphene based-resonators: Slip and transition flow regimes

This paper presents a nanoscale fluid-structure interaction (FSI) model for flow-induced nonlinear vibration of multilayer graphene based-resonators in the slip and transition regimes. Based on the multibeam interlayer shear model with von Kármán geometric nonlinearity and nonlocal modified couple stress theory, the size-dependent equations of motion are obtained for beam resonators laminated of NG-graphene layer and (NG−1) interlayer crosslinks. The small-scale effect on effective viscosity and slip boundary conditions of nanoscale flow is formulated by introducing the average velocity correction factor. For unbounded and bounded (by a rigid wall) nanoflows, the closed-form expressions of velocity correction factor in terms of Knudsen number, as a dimensionless discriminant parameter, are developed to correct the pressure distribution predicted by the potential theory. The present FSI model considers the size effects through the length scale parameter for microstructure local rotation, the nonlocal parameter for long-range interatomic interactions, and Knudsen number for slip condition of nanoscale flow. The Galerkin's method in conjunction with the multiple-scale perturbation technique is used to obtain closed-form solutions of frequency ratio and time-history response. The natural frequencies of cantilever multilayer graphene nanostrips are validated with the ones existing in the literature. Parametric studies are carried out to investigate the influences of small-scale, number of layers, interlayer shear modulus, and fluid characteristics on the linear and nonlinear natural frequencies. Findings show that the critical upstream speed for dynamic instability of the coupled system can change considerably by taking into account the size effects of nanoflow and nanostructures. Therefore, the classical FSI model is inadequate for analyzing nanoscale flow-induced vibration of nanoresonators. Also, it is seen that the effect of geometric nonlinearity becomes very significant for multilayer graphene beams with small interlayer shear modulus.

Mechanism of Double-Diffusive Convection on Peristaltic Transport of Thermally Radiative Williamson Nanomaterials with Slip Boundaries and Induced Magnetic Field: A Bio-Nanoengineering Model

The present work has mathematically modeled the peristaltic flow in nanofluid by using thermal radiation, induced a magnetic field, double-diffusive convection, and slip boundary conditions in an asymmetric channel. Peristalsis propagates the flow in an asymmetric channel. Using the linear mathematical link, the rheological equations are translated from fixed to wave frames. Next, the rheological equations are converted to nondimensional forms with the help of dimensionless variables. Further, the flow evaluation is determined under two scientific assumptions: a finite Reynolds number and a long wavelength. Mathematica software is used to solve the numerical value of rheological equations. Lastly, the impact of prominent hydromechanical parameters on trapping, velocity, concentration, magnetic force function, nanoparticle volume fraction, temperature, pressure gradient, and pressure rise are evaluated graphically.

Nematic Liquid Crystal Flow with Partially Free Boundary

We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes equation for the fluid velocity with a transported heat flow of harmonic maps, and both of these parabolic equations are critical for analysis in two dimensions. The boundary conditions are physically natural and they correspond to the Navier slip boundary condition with zero friction for the velocity field and a Plateau-Neumann type boundary condition for the map. In this paper we construct smooth solutions of this coupled system that blow up in finite time at any finitely many given points on the boundary or in the interior of the domain.

Global classical solution to the chemotaxis-Navier-Stokes system with some realistic boundary conditions

In this paper, we consider the chemotaxis-Navier-Stokes model with realistic boundary conditions matching the experiments of Hillesdon, Kessler et al. in a two-dimensional periodic strip domain. For the lower boundary, we impose the usual homogeneous Neumann-Neumann-Dirichlet boundary condition. While, for the upper boundary, since it is open to the atmosphere, we consider three kinds of different mixed non-homogeneous boundary conditions, that is, (i) Neumann-Dirichlet-Navier slip boundary condition; (ii) Zero flux-Dirichlet-Navier slip boundary condition; (iii) Zero flux-Robin-Navier slip boundary condition. For boundary conditions (i) and (iii), the existence and uniqueness of global classical solutions for any initial data and any large chemotactic sensitivity coefficient is established, and for boundary condition (ii), the existence and uniqueness of global classical solutions for any initial data and small chemotactic sensitivity coefficient is proved.

Numerical Study of Unsteady Magnetohydrodynamics Flow and Heat Transfer of Hybrid Nanofluid Induced by a Slendering Surface with Suction and Injection Effects

Since the last two decades, most of the researchers have concentrated on the nanofluids boundary layer flow over a surface of even thickness or flat surface. This article deals with a mathematical model, which describe the hybrid nanofluid (SiO2–MoS2/water) flow over a slendering surface (surface of uneven thickness). The novelty is to study the effects of natural convection and porous medium. The analysis of heat transfer is also accomplished and for the same purpose, the viscous dissipation, heat source/sink, ohmic heating and thermal radiation effects are incorporated. The velocity slip and thermal slip boundary conditions with suction/injection effects are applied. Similarity transformations are utilized to change the prevailing PDEs to ODEs. Numerical investigation is performed to solve the equations. The MATLAB in built function “bvp4c solver” is employed for finding the solution. The velocity and temperature profile were found higher for the injection case in comparison to the suction. The effect of power law index parameter and unsteadiness parameter is to aid the flow velocity. The heat generation parameters, Eckert number and volume fraction of nanoparticles act to augment the flow temperature. For the suction and injection case, the radiation parameter has positive correlation with the heat transfer rate.