Influence of Anisotropic Permeability and Soret Effect on the Convective Heat and Mass Transfer through a Porous Cavity Saturated by a Non-Newtonian Fluid

In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.

Modeling the Unsteady Flow of a Newtonian Fluid Originating from the Hole of an Open Cylindrical Reservoir

This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir.This reservoir presents a hole on the right bottom wall.Fluid volume variation,heat and mass transfers are neglected.The unsteady governing equations are based on the conservation of mass and momentum.A finite volume technique is used to solve the non-dimensional equations and related boundary conditions.The algebraic system of equations resulting from the discretization process are solved by means of the THOMAS algorithm.For pressure-velocity coupling,the SIMPLE algorithm(Semi Implicit Method for Pressure Linked Equations)is used.Results for laminar flow(Re<1000),including the pressure and velocities profiles as well as the streamlines in the reservoir are presented.Moreover,the effects of the D/d and H0/D ratios and Reynolds number Re on the fluid flow are discussed.It is shown that the velocities and pressure depend essentially on the reservoir size.To validate the model,the present results have been compared with Zhou et al.’s results,Poiseuille’s and Bernoulli’s exact solution.

H^2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.

Dynamic Analysis of Single Pile in Liquefied Soils Considered as Newtonian Fluid

Case histories have shown that the liquefaction-induced soil lateral spreading is one of the main causes of damage to pile foundations subjected to seismic loading. Post-liquefaction soil behaves similarly to a viscous fluid. This study investigated the effect of soil lateral spreading on a single pile based on fluid mechanics in which the liquefied soils were treated as Newtonian fluids. A numerical simulation on a single pile embedded in a fully saturated sandy foundation was conducted and compared with shake table tests. The lateral flow effect and the effect of shear strain rate were discussed. After liquefaction, the acceleration of the foundation shows that there are no obvious spikes and finally reaches a stable state. The presented method can predict the pile response better than p-y curve method. A parametric study was performed to explore the effect of several influence factors on pile behaviors. The results show that the pile head displacement decreases and the maximum bending moment at pile bottom increases with the increase of bending stiffness. With the same pile bending stiffness, the displacement and bending moment of pile increase with the increase of soil viscosity and acceleration amplitude.

The Magnetic Field as Trigger for Disturbances of a Flow of a Newtonian Fluid through a Cylindrical Pipe with a Horizontal Axis

A Fourrier Petrov Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables. It is written in FORTRAN. Systematic studies are presented on the dependence of eigenvalues and other quantities on the axial and azimuthal wave number;the reynolds’ number Re and a new none-dimensional number Ne. The flow will be considered stable if all the real parts of the eigenvalues are negative and unstable if only one of them is positive.

Implementation of Non-Newtonian Fluid Properties for Compressible Multiphase Flows in OpenFOAM

The paper presents the implementation of non-Newtonian fluid properties for compressible multiphase solver in the open source framework OpenFOAM. The transport models for Power Law, Cross Power Law, Casson, Bird-Carreau and Herschel-Bulkley fluids were included in the thermophysical model library. Appropriate non-Newtonian liquids have been chosen from literature, and pressure driven test simulations are carried out. Therefore, the solver compressibleInterFoam is used to compute air-liquid mixture flows over a backward facing step. A validation of the novel models has been performed by means of a sample-based comparison of the strain rate viscosity relation. The theoretical rheological properties of the selected liquids agree well with the results of the simulated data.

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are presented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ, the order of the chemical reaction parameter m, the Soret number S r , the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

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 incompressible non-Newtonian fluid in 3 D 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.

Numerical Simulation of Concentration Field on Liquid Side around Bubble during Rising and Coalescing Process in Non-Newtonian Fluid

根据 Navier-Stockes 方程和传送对流散开方程，与表面紧张和穿入模型，结合了在水泡和周围的非牛顿的液体之间的时刻和集体转移的方程被建立。从从进周围的液体的一个人工地固定的水泡的 1.0 公里直径和集体转移的一张在水下的嘴的一个单个水泡的形成被体积模仿 -- 液体(VOF ) 方法。在模拟结果和试验性的数据之间的好同意证实了数字方法的有效性。而且，在升起附近的集中分发起泡在砍变瘦非牛顿的液体被模仿。当有低于 2.0 的水泡变丑率的一个单个椭圆体的水泡的过程升起时，集中分发是一在水泡的家单个尾巴醒来，但是当水泡变丑率比 2.0 大时，它是分数维的。为追上二个同轴的升起水泡，在二个水泡之间的集中分发区域逐渐地拓宽然后结合发生。集中分发的分叉出现在结果的水泡的尾部。

ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID

This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.

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.

Analytical solutions to the Navier-Stokes equations for non-Newtonian fluid

The pressureless Navier-Stokes equations for non-Newtonian fluid are studied.The analytical solutions with arbitrary time blowup,in radial symmetry,are constructed in this paper.With the previous results for the analytical blowup solutions of the N-dimensional(N ≥ 2) Navier-Stokes equations,we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term ▽·(μ(ρ)|▽ u|α▽ u).

COMPUTATIONALINTELLECTUAL ANALYTICAL THEORYOF COMPUTATIONAL ANALYTICAL APPROACH TOROTATING FLOW OF NON_NEWTONIAN FLUID

A combination of the computational symbolic calculation, mathematical approach and physico_mechanical model leads to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer,also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended,and an unsteady flow of non_Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1st, 2nd and 3rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non_Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non_unique.

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.

Effect of Viscosity on Pumping-Up of Newtonian Fluid Driven by a Rotating Cone

Effect of viscosity on flow patterns of pumping-up of liquid generated by a cone rotating at the liquid surface has been experimentally studied with various concentrations of glycerol aqueous solution. We have previously found that the higher viscous non-Newtonian fluid was lifted-up along the conical surface with a radial filament-wise pattern, which is quite different from the monotonic thin film-wise pattern observed for the lower viscous fluid such as water. In order to elucidate the pumping-up mechanism, a transition diagram indicating the critical rotation rate is obtained as a function of viscosity?of Newtonian fluid in this study, varying from the lower value of water (μ?=?0.890 mPa·s) to the higher one of glycerin (μ?= 910?mPa·s). It is found that there are three categories depending on the viscosity classified as?1) film-wise pumping-up region for the viscosity?μ?≤?134?mPa·s,?2) filament-wise pumping-up one for the viscosity?μ?≥?520?mPa·s, and?3) no pumping-up phenomenon occurs?for 134??μ??mPa·s.

A Novel Blood Coagulation Measuring Method Based on the Viscoelasticity of Non-Newtonian Fluid

There are complex and perfect coagulation, anticoagulation and fibrinolysis systems in the human body and their fine regulatory mechanisms. Once the coagulation system and its regulatory mechanisms are destroyed, bleeding or thrombosis will occur very soon. In the blood coagulation, the blood viscoelasticity changes. Therefore, the thrombus elasticity measurement technology can be used to continuously monitor the changing blood viscoelasticity in order to study the process of coagulation. The results of the interaction among the various components of the blood can be obtained from coagulation to fibrinolysis by bedside detection. The traditional electromagnetic induction sensors, based on conventional coil inductance, are manufactured complexly, high cost and non-linear. Therefore, this paper proposes a non-Newtonian fluid viscoelasticity measurement method based on the piezoelectric effect. We use the piezoelectric bimorphs with the diameter of 21 mm and the total thickness of 0.38 mm and DSM coupling probes with the length of 3 mm, 5 mm and 7 mm to design the piezoelectric bimorphs driver. The viscoelasticity of different non-Newtonian fluids is tested. The vibration amplitudes of the piezoelectric bimorphs and liquid surfaces range from 0.43 μm to 3.52 μm. Consequently, the feasibility of in vitro detection of thrombus is confirmed in principle and the above scheme is validated theoretically and experimentally, which provides the basis for the measurement of blood viscoelasticity, the in vitro detection of thrombus and the manufacture of blood coagulation instrument.