一类非牛顿系统弱解的长时间性态

本文讨论一类非牛顿系统弱解的长时间性态,证明解在L2 范数下的衰减速率为(1 t)-n/4 达到和线性热方程一致.     

Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows

In this paper we investigate the exponential dichotomy of linear skew-product semiflows over semiflows by considering the operators generated by the integral equation related to strongly continuous cocycles over metric spaces acting on Banach bundles. We characterize the existence of exponential dichotomy by properties of these operators and use this characterization to prove the robustness of exponential dichotomy.     

Solutions to the Equation of Non－Newtonian Polytropic Filtration Under Optimal Condition On Initial Values

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Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

A numerical method for the calculation of incompressible,steady, separated flows around aerofoils

The present work deals with the numerical calculation of the incompressible turbulent flow around aerofoils. An orthogonal curvilinear grid of ‘C’ type is used for the solution of the time averaged equations and Reynolds stresses are modelled according to the κ-ε turbulence model. PISO and SIMPLE algorithms are used to solve the strongly coupled system of the derived finite volume equations and convergence is improved by applying the method of variable local underrelaxation factors. Comparisons between the calculated and measured pressure distributions are presented for NACA 0012 and NACA 4412 wing sections. The formation of separation bubbles according to calculations is also shown.     

A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.     

Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid

Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.     

On the case when steady converging/diverging flow of a non-Newtonian fluid in a round cone permits an exact solution

This communication considers the steady converging/diverging flow of a non-Newtonian viscous power-law fluid in a round cone. The motion is driven by a sink/source of mass at the origin. It is shown that the problem permits exact similarity solution for a particular value (n=4/3) of the fluid index. In this case a complete set of governing equations can be reduced to an ordinary differential equation, which is solved numerically for different values of the main non-dimensional parameters (the cone angle and the dimensionless sink/source intensity).     

On the shear-thinning and viscoelastic effects of blood flow under various flow rates

The aim of this paper is to describe and discuss the results of numerical comparative study performed in order to demonstrate and quantify some of the most relevant non-Newtonian characteristics of blood flow in medium-sized blood vessels, namely its shear-thinning and viscoelastic behavior.The models studied in this work are the classical Newtonian and Oldroyd-B models, as well as their generalized (shear-thinning) modifications. Numerical tests are performed on three-dimensional geometries, namely an idealized axisymmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images. The numerical solution of the system of governing equations is obtained by a finite-volume method on a structured grid. Model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non-Newtonian effects.