EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

Hydrothermal analysis of non-Newtonian fluid flow(blood)through the circular tube under prescrib e d non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surface heat flux.After the flow field is determined by solving the continuity and the momentum equations,the energy equation is handled by employing the separation of variables method.The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C.The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,using Duhamel’s Theorem.Furthermore,an approximate analytic solution is determined,employing an integral approach to solve the boundary layer equations.With respect to the comparison,the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%.Interestingly,with decreasing the power-law index,the discrepancy between the two presented methods significantly reduces.Eventually,the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow’s thermal characteristics and structure are elaborately discussed.It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation’s accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube.In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m 2 and when the power-law index is 0.25,the maximum arterial wall temperature is found to be about 311.56 K.

Effects of Hall Current and Ohmic Heating on Non-Newtonian Fluid Flow in a Channel due to Peristaltic Wave

In this paper, the study of non-Newtonian fluid flow with heat transfer in a porous asymmetric channel due to peristaltic wave was taken out. Hall current and Ohmic heating effects were introduced in the present study. A Casson non-Newtonian constitutive model was employed for the transport of fluid. Analytical solutions were obtained for stream function, temperature and heat transfer coefficient. The coupled nonlinear equations have also been solved numerically using MATLAB software (by bvp4c function). The influences of many evolving parameters on the flow characteristic have been explained with the help of 2D and 3D plots. Again the obtained results were compared with the results available in the literature and were found in good agreement.

On the Study of Magneto-Hydrodynamic Non-Newtonian Fluid Flow throughout Curvilinear Channel with Corrugated Walls

This article aims to numerically investigate the flow pattern for Newtonian and power law non-Newtonian fluid in a semi-half circular channel with corrugated walls under the influence of a magnetic field. The results indicate that, presence of a magnetic field affects the flow field in several aspects, especially in the vortex creation and dissipation. In addition, the analysis is carried out for different Reynolds numbers to ascertain the influence of magnetic field on each flow regime. Eventually, the analysis is carried out for a range of power indices including pseudo plastic (shear-thinning) to dilatants (shear-thickening) fluids. The results show that by increasing the power-index, the vortices begin to form and grow gradually so that in the shear-thickening fluid an extra vortex is formed and created nearby the corrugated part of the channel.

Effect of bubble morphology and behavior on power consumption in non-Newtonian fluids’aeration process

Due to a prolonged operation time and low mass transfer efficiency, the primary challenge in the aeration process of non-Newtonian fluids is the high energy consumption, which is closely related to the form and rate of impeller, ventilation, rheological properties and bubble morphology in the reactor. In this perspective, through optimal computational fluid dynamics models and experiments, the relationship between power consumption, volumetric mass transfer rate(kLa) and initial bubble size(d0) was constructed to establish an efficient operation mode for the aeration process of non-Newtonian fluids. It was found that reducing the d0could significantly increase the oxygen mass transfer rate, resulting in an obvious decrease in the ventilation volume and impeller speed. When d0was regulated within 2-5 mm,an optimal kLa could be achieved, and 21% of power consumption could be saved, compared to the case of bubbles with a diameter of 10 mm.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Molecular dynamics simulation of the flow mechanism of shear-thinning fluids in a microchannel

Shear-thinning fluids have been widely used in microfluidic systems,but their internal flow mechanism is still unclear.Therefore,in this paper,molecular dynamics simulations are used to study the laminar flow of shear-thinning fluid in a microchannel.We validated the feasibility of our simulation method by evaluating the mean square displacement and Reynolds number of the solution layers.The results show that the change rule of the fluid system's velocity profile and interaction energy can reflect the shear-thinning characteristics of the fluids.The velocity profile resembles a top-hat shape,intensifying as the fluid's power law index decreases.The interaction energy between the wall and the fluid decreases gradually with increasing velocity,and a high concentration of non-Newtonian fluid reaches a plateau sooner.Moreover,the velocity profile of the fluid is related to the molecule number density distribution and their values are inversely proportional.By analyzing the radial distribution function,we found that the hydrogen bonds between solute and water molecules weaken with the increase in velocity.This observation offers an explanation for the shear-thinning phenomenon of the non-Newtonian flow from a micro perspective.

Study of hybrid nanofluid flow in a stationary cone-disk system with temperature-dependent fluid properties

Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.

Film Flow of Nano-Micropolar Fluid with Dissipation Effect

The physical problem of the thin film flow of a micropolar fluid over a dynamic and inclined substrate under the influence of gravitational and thermal forces in the presence of nanoparticles is formulated.Five different types of nanoparticle samples are accounted for in this current study,namely gold Au,silver Ag,molybdenum disulfide MoS2,aluminum oxide Al2O3,and silicon dioxide SiO2.Blood,a micropolar fluid,serves as the common base fluid.An exact closed-form solution for this problem is derived for the first time in the literature.The results are particularly validated against those for the Newtonian fluid and show excellent agreement.It was found that increasing values of the spin boundary condition and micropolarity lead to a reduction in both the thermal and momentum boundary layers.A quantitative decay in the Nusselt number for a micropolar fluid,as compared to a Newtonian one for all the tested nanoparticles,is anticipated.Gold and silver nanoparticles(i)intensify in the flow parameter as the concentration of nanoparticles increases(ii)yield a higher thermal transfer rate,whereas molybdenum disulfide,aluminum oxide,and silicon dioxide exhibit a converse attitude for both Newtonian and micropolar fluids.The reduction in film thickness for fluid comprising gold particles,as compared to the rest of the nanoparticles,is remarkable.

Flow Field Characteristics of Multi-Trophic Artificial Reef Based on Computation Fluid Dynamics

On the basis of computational fluid dynamics,the flow field characteristics of multi-trophic artificial reefs,including the flow field distribution features of a single reef under three different velocities and the effect of spacing between reefs on flow scale and the flow state,were analyzed.Results indicate upwelling,slow flow,and eddy around a single reef.Maximum velocity,height,and volume of upwelling in front of a single reef were positively correlated with inflow velocity.The length and volume of slow flow increased with the increase in inflow velocity.Eddies were present both inside and backward,and vorticity was positively correlated with inflow velocity.Space between reefs had a minor influence on the maximum velocity and height of upwelling.With the increase in space from 0.5 L to 1.5 L(L is the reef lehgth),the length of slow flow in the front and back of the combined reefs increased slightly.When the space was 2.0 L,the length of the slow flow decreased.In four different spaces,eddies were present inside and at the back of each reef.The maximum vorticity was negatively correlated with space from 0.5 L to 1.5 L,but under 2.0 L space,the maximum vorticity was close to the vorticity of a single reef under the same inflow velocity.

Particulate flow modelling in a spiral separator by using the Eulerian multi-fluid VOF approach

The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.

Influences of double diffusion upon radiative flow of thin film Maxwell fluid through a stretching channel

This work explores the influence of double diffusion over thermally radiative flow of thin film hybrid nanofluid and irreversibility generation through a stretching channel.The nanoparticles of silver and alumina have mixed in the Maxwell fluid(base fluid).Magnetic field influence has been employed to channel in normal direction.Equations that are going to administer the fluid flow have been converted to dimension-free notations by using appropriate variables.Homotopy analysis method is used for the solution of the resultant equations.In this investigation it has pointed out that motion of fluid has declined with growth in magnetic effects,thin film thickness,and unsteadiness factor.Temperature of fluid has grown up with upsurge in Brownian motion,radiation factor,and thermophoresis effects,while it has declined with greater values of thermal Maxwell factor and thickness factor of the thin film.Concentration distribution has grown up with higher values of thermophoresis effects and has declined for augmentation in Brownian motion.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

STABILITY OF BOUNDARY LAYER TO AN OUTFLOW PROBLEM FOR A COMPRESSIBLE NON-NEWTONIAN FLUID IN THE HALF SPACE

This paper investigates the large-time behavior of solutions to an outflow problem for a compressible non-Newtonian fluid in a half space. The main concern is to analyze the phenomena that happens when the compressible non-Newtonian fluid blows out through the boundary. Based on the existence of the stationary solution, it is proved that there exists a boundary layer(i.e., the stationary solution) to the outflow problem and the boundary layer is nonlinearly stable under small initial perturbation.

Non-invasive assessment for intratumoural distribution of interstitial fluid flow

Interstitial fluid plays a vital role in drug delivery and tumour treatment.However,few non-invasive measurement methods are available for measuring low-velocity biological fluid flow.Therefore,this study aimed to develop a novel technology called interstitial flow velocity-MRI.The interstitial flow velocity-MRI sequence consists of a dual inversion recovery preparation and an improved stimulated echo sequence(ISTE)combined with phase-contrast MRI.A homemade flow phantom was used to assess the feasibility and sensitivity of interstitial flow velocity-MRI.In addition,xenografts of female BALB/c mouse models of 4T1 breast cancer administered losartan(40 mg/kg)or saline(n?6)were subjected to imaging on a 7.0 T scanner to assess the in vivo interstitial fluid flow velocity.The results showed a significant correlation(P<0.001)between the theoretical velocities and velocities measured using the flow phantom.Interstitial flow velocity-MRI could detect a velocity as low as 10.21±2.65 mm/s with a spatial resolution of 0.313 mm.The losartan group had a lower mean interstitial fluid velocity than the control group(85±16 vs 113±24 mm/s).In addition,compared to the saline treatment,losartan treatment reduced the proportion of collagen fibres by 10%and 12%in the Masson and Sirius red staining groups,respectively.Interstitial flow velocity-MRI has the potential to determine interstitial fluid flow velocity non-invasively and exhibits an intuitive velocity map.

H4-Boundedness of pullback attractor for a 2D non-Newtonian fluid flow

We prove the H4-boundedness of the pullback attractor for a two- dimensional non-autonomous non-Newtonian fluid in bounded domains.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

Non-Newtonian fluid flow in an axisymmetric channel with porous wall

In the present article Optimal Homotopy Asymptotic Method(OHAM)is used to obtain the solutions of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall for turbine cooling applications.Numerical method is used for validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results.Trusting to this validity,effects of some other parameters are discussed.The results show that Nusselt number increases with increase of Reynolds number,Prandtl number and power law index.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

THE NUMERICAL SIMULATION OF TURBULENT FLOWS OF NEWTONIAN AND A SORT OF NON-NEWTONIAN FLUID IN 180-DEGREE SQUARE SECTIONED BEND

Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.