Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

多相高分子体系中的粘弹相分离行为

相分离广泛存在于各种凝聚态物质中.根据局部浓度的变化形式,可将相分离分为固体模型(model B)和流体模型(model H),这两种模型适用于动力学对称的体系.近年来,Tanaka发现在一些动力学不对称的多组分高分子体系里存在一种新的相分离模式,其相分离过程分为动力学过程可用一个普适的粘弹模型来进行描述.动力学不对称可由体系中两组分间大的尺寸差异或玻璃化温度差异引起.本文介绍了多相高分子体系中产生粘弹相分离的原理及其基本特征,并讨论了模量、粘度、填料等因素对粘弹相分离动力学过程及多相体系微观结构的影响.     

Alternative subcell discretisations for viscoelastic flow: Velocity-gradient approximation

Under subcell discretisation for viscoelastic flow, we have given further consideration to the compatibility of function spaces for stress/velocity-gradient approximation [see F. Belblidia, H. Matallah, B. Puangkird, M.F. Webster, Alternative subcell discretisations for viscoelastic flow: stress interpolation, J. Non-Newtonian Fluid Mech. 146 (2007) 59–78]. This has been conducted through the three scheme discretisations (quad-fe(par), fe(sc) and fe/fv(sc)). In this companion study, we have extended the application of an original implementation for velocity-gradient approximation, being of localised superconvergent recovered form, continuous and quadratic on the parent fe-triangular element. This has led to the consideration of both localised (pointwise) and global (Galerkin weighted-residual) approximations for velocity-gradient, highlighting some of their advantages and disadvantages. The global form is equivalent to the discontinuous elastico–viscous stress splitting (DEVSS-type) technique of Fortin and co-workers. Each representation, local or global, is based on linear/quadratic order upon parent or subcell element stencils. We consider Oldroyd modelling and the contraction flow benchmark, covering abrupt and rounded-corner planar geometries. The localised superconvergent quadratic velocity-gradient treatment affords strong stability and accuracy properties for the three scheme discretisations considered. Through associated analysis and iterative solution processes, we have successfully linked global approximations to their localised counterparts, depicting the inadequacy of inaccurate but stable versions through their corresponding solution features. These issues pervade all formulations, coupled or pressure-correction, and in focusing on velocity-gradient approximation, also apply universally to all discrete representations of stress. The inaccuracy of the global treatment can be somewhat repaired through an increase in (mass) iteration number. The efficiency of localised schemes (and associated properties) is particularly attractive over their global alternatives, being less restrictive to choice of spatial-order (higher-order). Conversely, global implementations are more restrictive in satisfaction of the space inclusion principle. Localised schemes come into their own when chosen to represent strongly localised solution features, such as arise in non-smooth flows. Analysis has also proved helpful in clarifying that space inclusion (extended LBB-condition) is a non-necessary convergence condition in the viscoelastic context.Overall, the localised-quadratic velocity-gradient treatment for both linear (subcell) and quadratic (parent) stress interpolation has achieved both stability and accuracy. Under DEVSS-type approximations (global), once function spaces for stress and velocity-gradients have been selected, this choice dictates the state of system consistency. Additionally, stability gains are recognised through the further application of strain-rate-stabilisation procedures.     

Compression stress relaxation in carbon black reinforced HNBR at low temperatures

Findings of a study of stress relaxation behaviour of hydrogenated nitrile butadiene rubber (HNBR) at nominal compressive strains up to 0.4 and temperatures above and below the glass transition temperature T_g are reported. Two formulations of a model HNBR with 36% acrylonitrile content and carbon black (CB) loading of 0 and 50 phr were investigated. The relaxation function of HNBR is found to be independent of strain at temperatures right above the T_g or at times longer than 10⁻³ s for the deformations employed. CB imparts higher long-term stiffness and also larger relaxation strength at times longer than 10⁻⁴ s to the HNBR, but it does not affect the relaxation behaviour of the rubber in the time span from 10⁻³ – 10⁴ s. In addition, the relationship between the strain energy function of HNBR and temperature is demonstrated to have a complex concave-downward shape which is affected by two competing contributions of entropy elasticity and the stress relaxation.     

Theoretical and experimental analysis of longitudinal wave propagation in cylindrical viscoelastic rods

Wave propagation in viscoelastic rods is encountered in many applications including studies of impact and fracture under high strain rates and characterization of the dynamic behavior of viscoelastic materials. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the rod is of the same order as the wavelength. In this work, we simplify the Pochhammer frequency equation for low and intermediate loss viscoelastic materials and formulate corrections for geometric dispersion for both the phase velocity and attenuation. The formulation is then experimentally verified with measurements of the phase velocity and attenuation in commercial polymethylmethacrylate rods that are 12 and in diameter. Without correcting for geometric dispersion, the usable frequency range for determining the phase velocity and attenuation for the rod is about , and about for the rod. Using the correction procedure developed here, it was possible to accurately determine the phase velocity and attenuation up to frequencies exceeding for the rod and for the rod. These corrections are applicable to many polymers and other viscoelastic materials. From thereon, the viscoelastic properties of the material can be determined over a wide range of frequencies.     

Formulação numérica de estruturas compósitas amortecidas utilizando as teorias da Deformação Cisalhante de Primeira Ordem e de Alta Ordem

Composite materials have been used in the design of the aircrafts structures because their low weight and high mechanical strength. However, structures made in composite material are exposed to dynamical and/or static loading environments. Therefore, a major research effort is undertaken in the development of tools numerical for analysis and design of composite structures. This paper presents a numerical formulation of the composite structures using the Finite Element Method (FEM). The damped composite structures, using inserted viscoelastic devices, and undamped composite structures are formulated by FEM. Viscoelastic materials are applied as continuous layers inserted on composite structures. The intrinsic damping of the composite material is included in the studies, too. The First‐order (FSDT) and Higher‐order Shear Deformation (HSDT) theories are formulated. They are distinguished by order of the approximation functions used in the mechanical displacements field. Both theories are computationally implemented using the Serendipity finite element. This is a rectangular finite element with 8 nodes, 5 or 11 degrees of freedom per node. The results are compared with papers predictions. The advantages and disadvantages of using each theory in the modeling of composite (thin or thick) and thick sandwiches structures, including the intrinsic and the viscoelastic damping, are discusses.     

Numerical solution of an extended White–Metzner model for eccentric Taylor–Couette flow

In this study, we have developed a new numerical approach to solve differential-type viscoelastic fluid models for a commonly used benchmark problem, namely, the steady Taylor—Couette flow between eccentric cylinders. The proposed numerical approach is special in that the nonlinear system of discretized algebraic flow equations is solved iteratively using a Newton–Krylov method along with an inverse-based incomplete lower-upper preconditioner. The numerical approach has been validated by solving the benchmark problem for the upper-convected Maxwell model at a large Deborah number. Excellent agreement with the numerical data reported in the literature has been found. In addition, a parameter study was performed for an extended White–Metzner model. A large eccentricity ratio was chosen for the cylinder system in order to allow flow recirculation to occur. We detected several interesting phenomena caused by the large eccentricity ratio of the cylinder system and by the viscoelastic nature of the fluid. Encouraged by the results of this study, we intend to investigate other polymeric fluids having a more complex microstructure in an eccentric annular flow field.     

Elastodynamic analysis of a thin layer bonded on a visco-elastic medium under combined in-plane and lateral pulse loads

An analytic solution of a thin layer bonded on a visco-elastic medium under the action of in-plane and lateral pulse loads is presented. The analysis is based on double integral transforms with respect to space and time. Representative examples are studied and discussed to determine the influence of the (a) damping and elastic coefficients of visco-elastic medium, and (b) in-plane compression and stretching of the thin layer on wave propagation.     

Electro-osmotic flow of a viscoelastic fluid in a channel : Applications to physiological fluid mechanics

The paper presents a comprehensive theoretical study on the electro-osmotic flow of a viscoelastic fluid past a channel having stretching walls. An attempt has been made to investigate the effect of rheological and electro-osmotic parameters on the kinematics of the fluid. Results presented here pertain to the case where the channel height is much greater than the thickness of electrical double layer comprising the Stern and diffuse layers. The study reveals that an increase in electro-osmotic parameter leads to an increase in the axial velocity throughout the channel for a fluid having viscoelastic coefficient equal to that of blood. This aspect provides a source of novel insight into the process of designing bio-sensing and micro-fluidic devices.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.