Incompressible non-Newtonian Fluid Research Articles

Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

Variable viscosity characteristics of two-layered isothermal calendering phenomena with non-Newtonian fluids

Two-layer calendering using non-Newtonian fluids is used frequently in different industries to improve the working and the quality of the products. In this article, two-layer calendering of incompressible non-Newtonian fluids, that is, couple stress fluid and viscoplastic fluid in the upper and lower layer respectively is investigated. For the simplified governing equations, Lubrication approximation theory is applied. By the use of no-slip condition and non-dimensional variables, the exact solution for pressure gradient, pressure, and velocity profiles for both layers of fluid is calculated. The parameters are important from an engineering point of view like roll separating force, power delivered by rollers, torque acting by each roller, and adiabatic temperature are also calculated analytically. Additionally, the results of a couple stress parameter, viscoplastic Casson parameter, and viscosity ratios on all the parameters are also discussed and investigated in detail. Moreover, all the effects investigated are also verified with the literature results of single-layer calendering of non-Newtonian fluids by using large numeric values for the couple stress parameter and viscoplastic Casson parameter.

Global existence of non-Newtonian incompressible fluid in half space with nonhomogeneous initial-boundary data

In this study, we investigate the global existence of weak solutions of non-Newtonian incompressible fluids governed by (1.1). When u0∈Ḃp,qα−2p(R+n)∩Ḃn+22,n+221−4n+2(R+n)∩Ḃp,11+np(R+n) is given, we will find the weak solutions for the Eq. (1.1) in the function space Cb[0,∞;Ḃp,qα−2p(R+n)∩Cb(0,∞;Ḃn+221−4n+2(R+n))∩L∞(0,∞;Ẇ∞1(R+n)), n+2<p<∞,1≤q≤∞,1+n+2p<α<2. We show the existence of weak solutions in the anisotropic Besov spaces Ḃp,qα,α2(R+n×(0,∞)) (see Theorem 1.2) and we show the embedding Ḃp,qα,α2R+n×(0,∞)⊂Cb[0,∞;Ḃp,qα−2p(R+n) (see Lemma 2.8). For the global existence of solutions, we assume that the extra stress tensor S is represented by S(A)=F(A)A, where F satisfies the assumption (A). Note that S1, S2 and S3 introduced in (1.2) satisfy our assumptions.

Analytical and Computational Modeling of Relaxation Times for Non-Newtonian Fluids

With the availability of efficient and sophisticated finite element analysis (FEA) and computational fluid dynamics (CFD) tools, engineering designs are becoming more software-driven and simulation-based. However, the insights relevant to engineering designs tend to be hidden within massive temporal and spatial data produced with full-fledged three-dimensional simulations. In this paper, we present a preliminary study of the controlled intermittent dispensing of a typical non-Newtonian glue employed in the manufacturing of electric vehicles (EVs). The focus of the study is on the scaling issues derived from different computational and analytical models of interest and importance to the precision control of this non-Newtonian fluid, the lowest dynamic viscosity of which at extremely high shear rates is nearly four million times that of water. More specifically, the abrupt change of the inlet pressure with a constant outlet or ambient pressure and various modeling strategies for transient viscous internal flow with both Newtonian and non-Newtonian fluids are modeled and compared. The analytical and computational results of the developing Newtonian fluid, i.e., water, are derived and computed for validation and verification purposes before the actual applications to the developing non-Newtonian fluid. The concept of a well-established relaxation time before the onset of the steady solution for Newtonian fluids has been validated with both analytical and computational approaches before its expansion and adoption to non-Newtonian fluids with complex rheological behaviors. Other issues attributed to transient operations and precision controls of non-Newtonian fluid delivery involve the pressure pulse and pressure wave propagation within the flexible pipe with compressible or almost incompressible non-Newtonian fluids with a constant pressure at the outlet and a constant mass flow rate or average axial velocity at the inlet, which will be addressed in a separate paper.

Non-Newtonian incompressible fluids with nonlinear shear tensor and hereditary conditions

We consider a mathematical model with delay for non-Newtonian incompressible fluids in a bounded domain. Existence of global weak solutions is proved under suitable regularity on the initial data and the forces. Conditions for uniqueness are also given, but in general the results are stated in a multi-valued framework. Suitable multi-valued dynamical systems are well-posed, using basically L2(Ω)n×L2(−h,0;L2(Ω)n) or C([−h,0];L2(Ω)n) norms. Then the existence of pullback attractors is ensured acting on several universes, some of them of fixed bounded sets and others of tempered type, depending on parameters related to an integrability condition of the force and the delay term. Finally, relationships between these families of attractors are also provided, improving the characterization of attraction with respect to previous results.

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Abstract 1145: A Computational Fluid Dynamics Analysis Of Hemodynamic Differences In Patients With High Grade Asymptomatic Carotid Artery Stenosis

Introduction: Current assessment/management of internal carotid artery (ICA) stenosis is based on estimation of percentage (%) stenosis which does not account for trans-lesional flow, pressure gradient (PG), wall shear stress (WSS), or oscillatory shear index (OSI). Computation fluid dynamics (CFD) can be used to characterize such indices. Hypothesis: We hypothesize that patients asymptomatic >70% ICA stenosis will have hemodynamic differences that are independent of % stenosis. Aims: Evaluate hemodynamic indices in patients with asymptomatic >70% ICA stenosis via CFD. Methods: Patients with asymptomatic >70% ICA stenosis were included. 3D time-of-flight (TOF) and phase-contrast (PC) magnetic resonance imaging (MRI) sequences were obtained. CRIMSON was used to generate CFD models containing the carotid artery (CCA), ICA, and external carotid artery (ECA). PC MRI-derived flow waveforms were prescribed to the CCA and ECA. The ICA outlet was coupled to a three-element Windkessel model. Blood was modeled as an incompressible Non-Newtonian fluid with a dynamic viscosity of 0.004 kg m –1 s –1 and a density of 1,060 kg m -3 . Incompressible Navier-Stokes equations were used to solve for velocity and pressures. Results: Eight patients (average age 73.8 years, 62.5% male) with asymptomatic high-grade ICA stenosis (62.5% left) were included. Hypertension (87.5%), tobacco use (87.5%), and hyperlipidemia (75%) were common. Most patients were medically optimized with anti-hypertensive (100%), statin (87.5%), and aspirin (87.5%). Three patients (37.5%) underwent ICA intervention.. Mean peak systolic velocity was 406 cm/s and mean end-diastolic velocity was 127 cm/s. There was large variability in trans-lesional ICA flow, PG, WSS, and OSI (Table 1). Conclusions: Asymptomatic patients with the same % stenosis have differences in trans-lesional ICA flow, PG, WSS, and OSI. Future work is needed to determine the prognostic value of such differences.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Existence and degenerate regularity of trajectory statistical solution for the 3D incompressible non-Newtonian micropolar fluids

Existence and degenerate regularity of trajectory statistical solution for the 3D incompressible non-Newtonian micropolar fluids

Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions

In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin-Voigt equations with memory, which describes a motion of an incompressible homogeneous non-Newtonian fluids with viscoelastic and relaxation properties. The investigation of these direct problems is related to the study of inverse problems for this system, which requires the continuity and regularity of solutions to these direct problems and their derivatives. The system, in addition to the initial condition, is supplemented with one of the boundary conditions: stick and slip boundary conditions. In both cases of these boundary conditions, the global in time existence and uniqueness of strong solutions to these initial-boundary value problems were proved. Moreover, under suitable assumptions on the data, the regularity of solutions and their derivatives were established.

The Consequence of Velocity Ratio and Curvature of the Surface on MHD Forced Convection Boundary Layer Nanofluid Flow Over an Axisymmetric Cylindrical Surface

The present study has considered the steady laminar incompressible non-Newtonian fluid over an axisymmetric stretching cylindrical surface under the effect of the curvature parameter, Brownian motion parameter, and thermophoresis parameter within the boundary layer region. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the curvature parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving thirdorder ordinary differential equations that include both linear and nonlinear terms. The governing equations have been converted into ordinary differential equations (ODEs) by using appropriate transformations. Runge–Kutta’s fourth-order method is used to find the numerical solutions by exploiting symbolic software MATLAB via the shooting method. It is found that the temperature profile increases for the effect of the thermophoresis parameter and heat generation parameter while decreasing for the effect of the curvature parameter. This study makes an essential contribution to the nanofluids field to solve numerically nonlinear differential equations (DEs). Brownian motion and thermophoresis parameters are considered for the nanofluid effect which plays an important role in the variation of temperature and concentration.

A Study on Oscillatory Micropolar Flow Beyond a Contaminated Micropolar Fluid Sphere

In this paper, the hypothesis of the axisymmetric rectilinear oscillatory flow beyond a micropolar tainted fluid sphere particle in an incompressible non-Newtonian fluid and also the axisymmetric rectilinear oscillatory flow over a viscous tainted fluid sphere particle in an incompressible Newtonian fluid with small amplitude oscillations have been investigated. The velocity field is exhibited in terms of stream functions, and a slip condition is considered on the boundary. The fluid velocities and microrotation components were derived through analytical procedure. The drag force acting on the particle was also computed and verified for special cases. The real drag and imaginary drag values are numerically extracted for varying slip parameter i.e., 2≤s≤30, micro polarity i.e., 8≤e≤32 , and viscosity ratio i.e., 5≤μ≤20 at a fixed parameter values k=0.1,ρ=0.6,ω=0.6,t=0.6. Graphs and tables are used to display the numerical results. It was observed that there was an inverse proportion between slip parameter values, real drag and direct proportion between slip parameter and imaginary drag, for different viscosity ratio and micro polarity values.

Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows

A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of viscosity-splitting procedures and it consists of separating the convection term and incompressibility constraint into two time steps. Unlike the conventional projection methods, the viscosity is not dropped in the last step allowing to enforce the full original boundary conditions on the end-of-step velocity which eliminates any concerns about the numerical boundary layers. We carry out a rigorous error analysis and provide a full first-order error estimate for both the velocity and pressure solutions in the relevant norms. Numerical results are presented for two test examples of non-Newtonian fluid flows to demonstrate the theoretical analysis and confirm the reliability of this viscosity-splitting scheme.

Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids

We present the global modification of the Ladyzhenskaya equations, for incompressible non-Newtonian fluids. This modification is through a cut-off function that multiplies the convective term of the equation and an additional artificial smoothing dissipation term as part of the viscous term of the equation. The goal of this work is the comparative analysis between the modified system and the non-modified system. Therefore, we show the existence and regularity of weak solutions, the existence of global attractors, the estimation of the fractal dimension of the global attractors, and finally, the relationship of the autonomous dynamics between the modified system and the non-modified system.

Inverse problems for nonlinear Navier–Stokes–Voigt system with memory

This paper deals with the unique solvability of some inverse problems for nonlinear Navier–Stokes–Voigt (Kelvin–Voigt) system with memory that governs the flow of incompressible viscoelastic non-Newtonian fluids. The inverse problems that study here, consist of determining a time dependent intensity of the density of external forces, along with a velocity and a pressure of fluids. As an additional information, two types of integral overdetermination conditions over space domain are considered. The system supplemented also with an initial and one of the boundary conditions: stick and slip boundary conditions. For all inverse problems, under suitable assumptions on the data, the global and local in time existence and uniqueness of weak and strong solutions were established.

Numerical investigation of nonlinear radiative flux of non-Newtonian MHD fluid induced by nonlinear driven multi-physical curved mechanism with variable magnetic field

This paper discusses two-dimensional heat flow of an incompressible non-Newtonian hydromagnetic fluid over a power-law stretching curved sheet. The energy equation of the flow problem considers a radiative flux influenced by viscous dissipation and surface frictional heating. Lorentz force and Joule heating are taken in the consequence of applied variable magnetic field satisfying solenoidal nature of magnetism. The governing equations are reduced to boundary-layer regime using dimensionless quantities and the resulting PDEs are converted into ODEs by suitable similarity variables. The flow fields; velocity and temperature are computed numerically by implementing Keller-Box shooting method with Jacobi iterative technique. Error analysis is calculated to ensure solutions' convergence. Interesting flow parameters are examined and plotted graphically. Results show that velocity is increased for large number of fluid rheology and opposite effects are recorded for increasing curvature, Lorentz force, and stretching power. Flow past a flat and curved surfaces are substantial in validation of this present work.

Non-isothermal non-Newtonian fluids: The stationary case

The stationary Navier–Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet-type boundary conditions. The viscosity is supposed to depend on the temperature and the stress depends on the strain through a suitable power law depending on [Formula: see text] (shear thinning case). For this problem we establish the existence of a weak solution as well as we prove some regularity results both for the Navier–Stokes and the Stokes cases. Then, the latter case with the Carreau power law is approximated through a FEM scheme and some error estimates are obtained. Such estimates are then validated through some two-dimensional numerical experiments.

English

Two isothermal unsteady motions of the incompressible Burgers fluids between infinite horizontal parallel plates are analytically and numerically investigated when a differential expression of the shear stress is prescribed on the lower plate. Closed-form expressions are established for the dimensionless permanent velocity fields and the corresponding shear stresses. They seem to be the first exact solutions for such motions of Burgers fluids. The corresponding permanent solutions for Oldroyd-B, Maxwell, second grade and Newtonian fluids performing similar motions can immediately be obtained as limiting cases of general solutions. The obtained velocity fields are used to determine the needed time to reach the steady state for the respective motions. It was found that the steady state for such isothermal motions of the incompressible non-Newtonian fluids is earlier obtained for the Burgers fluids in comparison with Oldroyd-B or Maxwell fluids.

The existence and dimension of the attractor for a 3D flow of a non-Newtonian fluid subject to dynamic boundary conditions

We consider a non-Newtonian incompressible 3D fluid of Ladyzhenskaya type, in the setting of the dynamic boundary condition. Assuming sufficient growth rate of the stress tensor with respect to the velocity gradient, we establish explicit dimension estimate of the global attractor in terms of the physical parameters of the problem.