Large Time Behavior of a Weak Solution for Non-Newtonian Flow

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvaiue of the Stokes operator.

A Remark on the Time Decay of Non-Newtonian Flows in R3

In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at （1 ＋ t）- 3/4 and the error of difference between non-Newtonian fluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods.

Boundary-layer non-Newtonian flow over vertical plate in porous medium saturated with nanofluid

The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brown- ian motion and thermophoresis. The partial differential system governing the problem is transformed into an ordinary system via a usual similarity transformation. The numer- ical solutions of the resulting ordinary system are obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb, and thermophoresis number Nt. For various values of n and Le, the effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

COMPUTER SIMULATION OF NON-NEWTONIAN FLOW AND MASS TRANSPORT THROUGH CORONARY ARTERIAL STENOSIS

A numerical analysis of Newtonian and non-Newtonian flow in an axi-symmetric tube with a local constriction simulating a stenosed artery under steady and pulsatile flow conditions war carried out. Bared on these results, the concentration fields of LDL ( (low-density lipoprotein) and Albumin were discussed. According to the results, in great details the macromolecule transport influences of wall shear stress, non-Newtonian fluid character and the scale of the molecule etc are given. The results of Newtonian fluid flow and non-Newtonian fluid flow, steady flow and pulsatile flow are compared. These investigations can provide much valuable information about the correlation between the flow properties, the macromolecule transport and the development of atherosclerosis.

GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS

The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.

Flow and natural convection heat transfer characteristics of non-Newtonian nanofluid flow bounded by two infinite vertical flat plates in presence of magnetic field and thermal radiation using Galerkin method

The main goal of this paper is to investigate natural convective heat transfer and flow characteristics of non-Newtonian nanofluid streaming between two infinite vertical flat plates in the presence of magnetic field and thermal radiation.Initially,a similarity transformation is used to convert momentum and energy conservation equations in partial differential forms into non-linear ordinary differential equations (ODE) applying meaningful boundary conditions.In order to obtain the non-linear ODEs analytically,Galerkin method (GM) is employed.Subsequently,the ODEs are also solved by a reliable numerical solution.In order to test the accuracy,precision and reliability of the analytical method,results of the analytical analysis are compared with the numerical results.With respect to the comparisons,fairly good compatibilities with insignificant errors are observed.Eventually,the impacts of effective parameters including magnetic and radiation parameters and nanofluid volume fraction on the velocity,skin friction coefficient and Nusselt number distributions are comprehensively described.Based on the results,it is revealed that with increasing the role of magnetic force,velocity profile,skin friction coefficient and thermal performance descend.Radiation parameter has insignificant influence on velocity profile while it obviously has augmentative and decreasing effects on skin friction and Nusselt number,respectively.

Asymptotic Behavior of Solutions to Equations Modelling Non-Newtonian Flows

This paper is concerned with the system of equations that model incompressible non-Newtonian fluid motion with p-growth dissipative potential 1 ＋ 2n/n＋2 〈 p 〈 3 in R^n （n = 2,3）. Using the improved Fourier splitting method, we prove that a weak solution decays in L2 norm at the same rate as （1 ＋ t）^-n/4 as the time t approaches infinity.

ON PRECONDITIONING OF INCOMPRESSIBLE NON-NEWTONIAN FLOW PROBLEMS

This paper deals with fast and reliable numerical solution methods for the incompress- ible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial dif- ferential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equa- tions. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that effects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.

OPTIMAL MIXED H-P FINITE ELEMENT METHODS FOR STOKES AND NON-NEWTONIAN FLOW

Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H[sub h]; Methodology; Results and discussion.

A New Algorithm for Non-Newtonian Flow and Its Application in Mould Filling Process

The simulation of injection molding process requires a stable algorithm to model the molten polymer with non-isothermal non-Newtonian property.In this paper,a staggered and iterative scheme is particularly designed to solve the velocity-pressure-temperature variables.In consideration of the polymer characteristic of high viscosity and low thermal conductivity,the non-Newtonian momentum-mass conservation equations are solved by the Crank-Nicolson method based split (CNBS) scheme,and the energy conservation equation with convective character is discretized by the characteristic Galerkin (CG) method.In addition,an arbitrary Lagrangian Eulerian (ALE) free surface tracking and mesh generation method is introduced to catch the front of the fluid flow.The efficiency of the proposed scheme is demonstrated by numerical experiments including a lid-driven cavity flow problem and an injection molding problem.

Time Decay Rates of the Isotropic Non-Newtonian Flows in R^n

This paper is concerned with time decay rates for weak solutions to a class system of isotropic incompressible non-Newtonian fluid motion in R^n. With the use of the spectral decomposition methods of Stokes operator, the optimal decay estimates of weak solutions in L^2 norm are derived under the different conditions on the initial velocity. Moreover, the error estimates of the difference between non-Newtonian flow and Navier-Stokes flow are also investigated.

4D-Flow MRI在肥厚型心肌病左室流出道血流评估中的价值探索

目的 探索四维血流(four-dimensional flow,4D-Flow)磁共振成像(magnetic resonance imaging,MRI)技术在左心室腔内应用的可行性。材料与方法 本研究为前瞻性、横断面研究,纳入2022年8月至2023年1月于我院接受心脏MRI检查的21例肥厚型心肌病患者,采用3.0 T MRI扫描仪进行二维血流(tow-dimensional flow,2D-Flow)及4D-Flow成像,收集患者一周内进行的超声心动图检查结果。采用组内相关系数(inter-class correlation coefficient,ICC)、变异系数(coefficients of variation,COV)及Bland-Altman分析比较2D-Flow、4D-Flow评估左室流出道峰值流速的可重复性及一致性,并通过Pearson相关性分析探究二者与超声心动图测量结果的关系。结果 2D-Flow和4D-Flow观察者内/观察者间的ICC分别为0.999/0.999和0.995/0.992,COV分别为0.5%/0.5%和2.4%/2.6%。4D-Flow与超声心动图的测量结果呈中度相关,相关系数r值为0.574(P=0.006),但一致性较差,ICC为0.375(P=0.013)。2D-Flow与4D-Flow和超声心动图间无显著的一致性及相关性。结论 4D-Flow技术能够可视化心腔内血流模式,对左室流出道峰值流速的测量具有高度可重复性,且与超声心动图的测量结果具有显著的一致性。

Analysis of one-dimensional rheological consolidation of double-layered soil with fractional derivative Merchant model and non-Darcian flow described by non-Newtonian index

To further investigate the one-dimensional(1D)rheological consolidation mechanism of double-layered soil,the fractional derivative Merchant model(FDMM)and the non-Darcian flow model with the non-Newtonian index are respectively introduced to describe the deformation of viscoelastic soil and the flow of pore water in the process of consolidation.Accordingly,an 1D rheological consolidation equation of double-layered soil is obtained,and its numerical analysis is performed by the implicit finite difference method.In order to verify its validity,the numerical solutions by the present method for some simplified cases are compared with the results in the related literature.Then,the influence of the revelent parameters on the rheological consolidation of double-layered soil are investigated.Numerical results indicate that the parameters of non-Darcian flow and FDMM of the first soil layer greatly influence the consolidation rate of double-layered soil.As the decrease of relative compressibility or the increase of relative permeability between the lower soil and the upper soil,the dissipation rate of excess pore water pressure and the settlement rate of the ground will be accelerated.Increasing the relative thickness of soil layer with high permeability or low compressibility will also accelerate the consolidation rate of double-layered soil.

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.

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.

针对无线控制环境的OpenFlow流表申请优化机制

在无线控制环境下,受限于控制通道的带宽和时延,OpenFlow交换机通过Packet-In消息申请流表的过程耗时较长,这个时段内交换机可能收到同一条流的大量后续报文,并分别产生与首包报文完全相同的Packet-In消息发往控制器,明显浪费网络资源。同时,针对每条流独立发送一个Packet-In报文的方式容易导致控制通道负载以小包为主、包头开销占比过大、网络资源利用率不高的问题。因此,针对无线控制条件下报文粒度Packet-In消息触发和离散化Packet-In消息发送机制存在的问题,提出了一种基于流粒度实现Packet-In消息触发和Packet-In消息聚合发送的方案,并通过仿真试验,验证了方案的效果。

iFlow彩色血流编码成像技术在下肢动脉硬化闭塞症诊断中的应用价值

目的研究iFlow彩色血流编码成像技术在下肢动脉硬化闭塞症(LEASO)诊断中的应用价值。方法选择2022年3月至2023年10月期间确诊的106例LEASO患者作为本研究的LEASO组,以一般资料与LEASO组匹配且无动脉病变的80例志愿者作为对照组。两组受试者均进行数字减影血管造影(DSA)并采用iFlow彩色血流编码成像技术检测股骨头区域和踝关节区域达峰时间(TTP)、计算踝关节区域与股骨头区域TTP的差值,测量踝肱指数(ABI)。结果两组研究对象年龄、性别、体质量指数、吸烟史、高血压病史、糖尿病史、冠心病史、股骨头区域TTP的比较,差异无统计学意义(P>0.05);LEASO组踝关节区域TTP及TTP差值均高于对照组,差异有统计学意义(P<0.05);LEASO组中不同Rutherford分类患者股骨头区域TTP的比较以及左侧病变患者与右侧病变患者股骨头区域TTP、踝关节区域TTP、TTP差值的比较,差异无统计学意义(P>0.05),Rutherford分类越高,踝关节区域TTP及TTP差值越低(P<0.05);经Pearson检验,LEASO患者的踝关节区域TTP、TTP差值与ABI呈负相关(P<0.05);经受试者工作特征(ROC)曲线分析,踝关节区域TTP、TTP差值对LEASO具有诊断效能;经Delong检验,TTP差值诊断的ROC曲线下面积高于踝关节区域TTP(P<0.05)。结论iFlow彩色血流编码成像技术测定踝关节区TTP及TTP差值是诊断LEASO的量化指标。

基于 Moldflow 的汽车中控台框架翘曲变形分析及优化

以某汽车中控台框架为研究对象,测量试模样品发现其翘曲变形量超过了装配要求。通过Moldflow软件模拟了该塑件实际的注塑过程,翘曲变形量的模拟值与实测平均值的最大误差为5.98%,发现该塑件翘曲变形的主要因素为冷却不均和收缩不均。本文在原物料中添加质量分数为25%的玻璃纤维以及优化工艺参数后,翘曲变形量的模拟值与初始方案相比降低了86.22%。试模验证表明,优化后的翘曲变形量模拟值与实测平均值的最大误差为4.35%,证明了Moldflow软件模拟分析的准确性。试模后各检测点的最大翘曲变形量降到了1.6 mm以下,较优化之前降低了80%以上,为类似大型复杂注塑件的翘曲变形分析及优化提供了思路。

Effects of renal artery stenosis on realistic model of abdominalaorta and renal arteries incorporating fluid-structureinteraction and pulsatile non-Newtonian blood flow

The effects of the renal artery stenosis （RAS） on the blood flow and vessel walls are investigated. The pulsatile blood flow through an anatomically realistic model of the abdominal aorta and renal arteries reconstructed from CT-scan images is simulated, which incorporates the fluid-structure interaction （FSI）. In addition to the investigation of the RAS effects on the wall shear stress and the displacement of the vessel wall, it is determined that the RAS leads to decrease in the renal mass flow. This may cause the activation of the renin-angiotension system and results in severe hypertension.