Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.     

Stress–strain state of flexible ring plates of variable stiffness in a magnetic field

A nonlinear two-dimensional model of a magnetoelastic flexible current-carrying ring plate is developed.Asystem of nonlinear equations describing the stress–strain state of flexible current-carrying plates in nonstationary mechanical and electromagnetic fields is derived. The stress state of a flexible plate of variable stiffness in a magnetic field is determined     

Anisotropic hardening – numerical application of a cubic yield theory and consideration of variable r-values for sheet metal

The first part of this paper contains a polynomial yield condition of third order connected with evolution equations for material tensors of higher orders. They are formulated by formal generalisation of an approach by Danilov. The second part presents a possibility of taking into account the rotation of the yield surface as a result of a variable planar anisotropy (r-value) in sheet metal. This is done by an extension of the evolution equations, based on a quadratic yield function. The corresponding deformation law and the set of evolution equations are numerically integrated for selected loading paths in the subspaces σ₁,σ₂ and σ,τ. Some of the experimentally observed effects, such as the increasing curvature of the yield locus curve in the loading direction or the specific rotation of the yield surface, are correctly reproduced.     

Chemical reaction and variable viscosity effects on flow and mass transfer of a non-Newtonian visco-elastic fluid past a stretching surface embedded in a porous medium

This work deals with the study of the boundary layer flow and mass transfer of a visco-elastic fluid immersed in a porous medium over a stretching surface in the presence of surface slip, chemical reaction and variable viscosity. The partial differential equations governing the flow have been transformed by similarity transformation into a system of coupled nonlinear ordinary differential equations which is solved numerically by means of the fourth order Runge-Kutta integration scheme coupled with the shooting technique. The effects of various involved interesting parameters on the velocity fields and concentration fields are shown graphically and investigated. In addition, tabulated results for the local skin-friction coefficient and the local Sherwood number are presented and discussed.     

Evolution of optical solitary waves in a generalized nonlinear Schr?dinger equation with variable coefficients

We derive two types of exact analytical solutions in terms of rational-like functions for a generalized nonlinear Schr?dinger equation with variable coefficients via the methods of similarity transformation and direct ansatz. Based on these solutions, several novel optical solitary waves are constructed by selecting appropriate functions, and the main evolution features of these waves are shown by some interesting figures with computer simulation.     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Soliton-like solutions of a derivative nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers

Under investigation in this paper is a derivative nonlinear Schrödinger equation with variable coefficients, which governs the propagation of the subpicosecond soliton pulses in inhomogeneous optical fibers. Through the nonisospectral Kaup–Newell scheme, the Lax pair is constructed with some constraints on the variable coefficients. Under the integrable conditions, bright one- and multi-soliton-like solutions are derived via the Hirota method. By suitably choosing the dispersion coefficient function, several types of inhomogeneous solitons are obtained in, respectively: (1) exponentially decreasing dispersion profile, (2) linearly decreasing dispersion profile, (3) exponentially increasing dispersion profile, and (4) periodically fluctuating dispersion profile. The intensity of the inhomogeneous soliton can be controlled by means of modifying the loss/gain term. Asymptotic analysis of the two-soliton-like solution is performed, which shows that the changes of the widths, amplitudes, and energies before and after the collision are completely caused by the variable coefficients, but have nothing to do with the collision between two soliton-like envelopes. Through suitable choices of variable coefficients, figures are plotted to illustrate the collision behavior between two inhomogeneous solitons, which has some potential applications in the real optical communication systems.     

Stochastic thermal stresses in an FGM annular disc of variable thickness with spatially random heat transfer coefficients

The second-order statistics (i.e. mean and standard deviation) of the temperature and thermal stresses are evaluated in an axisymmetrically heated functionally graded annular disc of variable thickness with spatially random heat transfer coefficients (HTCs) on the major surfaces of the disc. This annular disc is assumed to have arbitrary variations in the HTCs and material composition along the radial direction only. The randomness in the HTCs is considered to be a random field. The stochastic temperature field is analysed by considering the annular disc to be a multilayered one with stepwise thickness variation, where each layer is assumed to have constant deterministic material properties and random HTCs. In order to evaluate the statistics, the Monte Carlo simulation method is applied to analytical solutions for the deterministic temperature and thermal stresses. The analytical solution for the thermal stresses is obtained through the use of a piecewise power function approximation for Young’s modulus. Numerical results demonstrate the effects of the magnitude of the HTC means, volume fraction distributions of the constitutive materials and thickness variation on the statistics of the temperature and thermal stresses.     

An application of the k-ɛ model with variable Prandtl number to heat transfer computations in air flows

The two-equation `low Reynolds number' k-? model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Pr_t in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 10⁴?4. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.     

Viscoelastic blood flow through arterial stenosis—Effect of variable viscosity

Current theoretical investigation deals with mathematical model of unsteady non-Newtonian flow of blood through a stenosed artery. The flowing blood is considered as a viscoelastic fluid having shear-thinning rheology and characterized by generalised Oldroyd-B model. The arterial wall is considered to be rigid having cosine shaped stenosis in its lumen. The governing equations of motion accompanied by appropriate choice of the initial and boundary conditions are solved numerically by MAC (Marker and Cell) method and the results are checked for numerical stability with desired degree of accuracy. The quantitative analysis has been carried out finally which includes the respective profiles of the flow-field. The key factors like the wall shear stress and flow separation are also examined for further qualitative insight into the flow through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.     

Equivalence transformations and differential invariants of a generalized cubic–quintic nonlinear Schrödinger equation with variable coefficients

Nonlinear Dynamics - In this paper, a variable-coefficient cubic–quintic nonlinear Schrödinger equation involving five arbitrary real functions of space and time is analyzed from the...     

Synthesis and surface modification of magnetic particles for application in biotechnology and biomedicine

Magnetic particles have numerous applications in biotechnology and biomedicine. In this paper we reviewed the synthesis, surface modification and some applications of magnetic particles with focus on their synthesis and surface modification. Various methods have been developed for the production of magnetic particles （magnetic nanoparticles and magnetic composite particles）. For future application magnetic particles must be modified to obtain stability and surface functional groups. Finally, the application of magnetic particles in magnetic separation, drug delivery, hyperthermia, and magnetic resonance imaging are discussed.     

Investigation of Aerodynamic Drag of Two Bodies in Trans‐ and Supersonic Flows

Results of experimental investigations of trans or supersonic flow around two bodies (cone–disk or sphere–disk) connected by a cylindrical rod along the axis of symmetry are presented. The special features of the flow are analyzed. It is found that the dependence of the drag coefficient C_x of a pair of bodies on the Mach number within the range 0.6 M 1.7 is nonmonotonic. The reasons for the hysteresis in the dependences C_x(M) for two bodies at the stages of flow acceleration and deceleration and discrete variation of the Mach number are clarified. The influence of cone angles and sizes of both bodies on the drag coefficient is estimated.     

A Physical Model of the Structure and Attenuation of Shock Waves in Metals

In this paper,a physical model of the structure and attenuation of shockwaves in metals is presented.In order to establish the constitutive equa-tions of materials under high velocity deformation and to study the struc-ture of transition zone of shock wave.two independent approaches are in-volved.Firstly,the specific internal energy is decomposed into the elasticcompression energy and elastic deformation energy,and the later is represent-ed by an expansion to third-order terms in elastic strain and entropy.includ-ing the coupling effect of heat and mechanical energy.Secondly,a plasticrelaxation function describing the behaviour of plastic flow under high tem-perature and high pressure is suggested from the viewpoint of dislocationdynamics.In addition.a group of ordinary differential equations has beenbuilt to determine the thermo-mechanical state variables in the transitionzone of a steady shock wave and the thickness of the high pressure shockwave.and an analytical solution of the equations can be foun     

Characteristics of elemental carbon and organic carbon in PM10 during spring and autumn in Chongqing, China

PM10 （particulate matter with aerodynamic diameter less than 10 μm） samples were collected simultaneously at nine urban sites and one urban background site during two intensive observation campaigns in 2006. Concentrations of elemental carbon （EC） and organic carbon （OC） in PM10 were analyzed using an element analyzer. The characteristics regarding spatial and seasonal distribution patterns of OC and EC concentrations and their contributions to PM10 mass, as well as correlation between OC and EC, were investigated in detail. The average OC and EC concentrations for urban sites were 57.5 ± 20.8 and 8.3 ± 3.9 μg/m^3, respectively, both being around three times higher than those for urban background site. As a whole, EC concentrations did not show distinct seasonal variations, though OC concentrations were generally higher in autumn than in spring. For urban sites, total carbonaceous aerosol （TCA） accounted for 33.2% in spring and 35.0% in autumn of PM10 mass. The OC and EC concentrations were found significantly correlated to each other both in spring and in autumn, implying the existence of similar emission sources such as coal combustion. The OC/EC ratios generally exceeded 2.0, indicating the presence of secondary organic carbon （SOC）, whose estimated concentration for urban Chongqing was 26.7 and 39.4μg/m^3, accounting for 48.9 and 61.9% of the total OC observed in the samples, in spring and in autumn, respectively.     

Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies

The mathematical modelling of highly compressible unsteady flows has been of interest for some years. In order to obtain tractable solutions of the governing equations, investigators have made various simplifying assumptions such as presuming isothermal or isentropic flow of ideal gases, etc. The present review, with dense phase gas tranmission systems of particular interest, briefly develops the basic equations without such assumptions and includes the effects of wall friction and heat transfer. After re-expressing the equations in terms of the measurable quantities of pressure, temperature and velocity, previously published work is reviewed for their solution. Relevant experimental work is somewhat limited but contributions from 20 references are included.     

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.     

Eulerian–Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian–Lagrangian model, where the particles are modeled by the discrete element method (DEM) and the gas by the Navier–Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution (RTD) of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser but a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.     

Enhancement of energy efficiency for mechanical production of fine and ultra-fine particles in comminution

This paper presents the energy requirements for mechanical production of fine and ultra-fine particles in comminution. Recent approaches for effective size reduction and energy saving in comminution are described, viz., （a） development and application of new mills/classifiers, （b） adjustment of the bead characterization in stirred bead mills, （c） hybrid comminution systems with roller-press and media mill, （d） assisted methods, and （e） simulation.2007 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.