Thin Cylindrical Layer Research Articles

Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.

Robin-type boundary conditions in transition from reaction-diffusion equations in 3D domains to equations in 2D domains

We consider a singular limit of diffusion equations in 3D domains of thickness converging to zero. In the 2D limit the resulting reaction-diffusion equation has a source term resulting from the Robin-type boundary conditions imposed on boundaries of the original 3D domain. The proposed approach can be applied to constructing approximate solutions of diffusion problems in thin planar, cylindrical, or spherical layers between two membranes. As an example we refer to the problem of activation of B lymphocytes, which typically have large nuclei and a thin cytoplasmic layer which can be considered as a spherical shell. For this example, assuming additionally axial symmetry we provide a rigorous convergence theorem in the language of semigroups of operators.

Second-Harmonic Generation from a Thin Cylindrical Layer: III. No-Generation Conditions

We have presented more than 50 combinations of parameters of the problem on the second-harmonic generation by a plane elliptically polarized electromagnetic wave from a thin optically nonlinear layer on the surface of a cylindrical dielectric particle at which no generation from the lateral surface of the particle is observed. We have also revealed 18 combinations of parameters at which no generation from the butt-end surfaces of the particle is observed. We have determined more than 30 combinations of parameters of the problem at which the second-harmonic radiation generated from the lateral surface (or the butt-end surfaces) of the particle is linearly polarized. Combinations of parameters of the problem have been indicated at which the generation from the entire surface of the cylindrical particle is not observed, as well as parameters at which the polarization of the generated radiation is linear. A method for determining the anisotropy coefficients based on the presented properties has been proposed.

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

Helical Turing patterns in the Lengyel-Epstein model in thin cylindrical layers

The formation of Turing patterns was investigated in thin cylindrical layers using the Lengyel-Epstein model of the chlorine dioxide-iodine-malonic acid reaction. The influence of the width of the layer W and the diameter D of the inner cylinder on the pattern with intrinsic wavelength l were determined in simulations with initial random noise perturbations to the uniform state for W < l/2 and D ∼ l or lower. We show that the geometric constraints of the reaction domain may result in the formation of helical Turing patterns with parameters that give stripes (b = 0.2) or spots (b = 0.37) in two dimensions. For b = 0.2, the helices were composed of lamellae and defects were likely as the diameter of the cylinder increased. With b = 0.37, the helices consisted of semi-cylinders and the orientation of stripes on the outer surface (and hence winding number) increased with increasing diameter until a new stripe appeared.

An improved model of thin cylindrical piezoelectric layers between isotropic elastic media

Radially polarized piezoelectric fibers are now considered to be used in smart composites. The piezoelectric layers in these fibers are generally anisotropic in the transverse direction and therefore difficult to analyze when dynamic loads are involved. The present paper presents a theoretical study of the dynamic behavior of radially polarized cylindrical piezoelectric layers between isotropic elastic media. A new interphase model is developed to provide simple yet accurate evaluation of the dynamic response of such anisotropic elastic layers. Unlike the traditional interface-spring model, the current interphase model satisfies the equations of motion of the layers and can provide reliable prediction of the stress and displacement. A comparison between the developed model, the interface-spring model and the finite element analysis is conducted. The results clearly show the advantages of the current model over the traditional interface-spring model in simulating anisotropic layers. Numerical examples based on this interphase model for different interphase thicknesses, loading frequencies and material combinations are presented to evaluate the dynamic behavior of multilayered elastic media.

Scattering by an array of parallel metallic carbon nanotubes

The scattering of electromagnetic wave by an array of parallel metallic single-walled carbon nanotubes is investigated based on the boundary-value method. Electronic excitations over each nanotube surface are modeled as an infinitesimally thin cylindrical layer of the free-electron gas. The scattering cross section of both transverse magnetic (TM) and transverse electric (TE) uniform plane waves by the system at normal incidences is obtained.

Temperature and Adhesion Influence on the Microbearings Operating Parameters

In presented paper are elaborated the preliminary problems of thermo-hydrodynamic theory of lubrication for dependences between temperature, adhesive forces, and oil dynamic viscosity, in micro-scale inside super thin cylindrical boundary layer arising between two cooperating grooved cylindrical surfaces. In cylindrical micro-bearings are visible the large gradients of temperature changes and adhesion changes in very thin gap height direction. Hence the oil dynamic viscosity changes significantly in gap height direction. This fact implies the visible oil flow velocity changes and friction forces and the hydrodynamic pressure changes during the micro-bearing exploitation. Up to now the influence of adhesion forces simultaneously with temperature on oil viscosity changes and next on hydrodynamic pressure and load carrying capacity changes in cylindrical micro-bearing gap were not considered in analytical and numerical way.

Guided waves characteristics of multi-walled carbon nanotubes

The theoretical analysis of propagation of guided waves in the multi-walled carbon nanotubes is presented within the framework of the classical electrodynamics. Electronic excitations of each wall of the system are modeled as an infinitesimally thin cylindrical layer of the π-electrons, whose dynamics are described by means of the fluid theory. General expressions of dispersion relations are obtained for the electromagnetic wave with the transverse magnetic and transverse electric modes, respectively, by solving Maxwell and fluid equations with appropriate boundary conditions.

Scattering properties of metallic carbon nanotubes in the presence of dielectric media

Scattering properties of a metallic single-walled carbon nanotube that encapsulates a nanowire is studied within the framework of classical electrodynamics. The system is assumed to be illuminated by either a transverse magnetic (TM) or a transverse electric (TE) wave. Electronic excitations on the nanotube's surface are modeled as an infinitesimally thin cylindrical layer of the π-electrons, whose dynamics are described by means of the fluid hydrodynamic theory. The problem is two-dimensional and the solution to both TM and TE uniform plane waves by the system at normal incidences is presented.

Line-source scattering properties of metallic carbon nanotubes

Electromagnetic wave scattering from a metallic multiwalled carbon nanotube is investigated by using the boundary-value approach and modal series expansion of the scattered and transmitted fields. Electronic excitations of each wall of the system are modeled as an infinitesimally thin cylindrical layer of the free electrons, whose dynamics are described by means of the fluid theory. The system is illuminated by a cylindrical wave from a line source that is placed in a direction parallel to the nanotube axis. The problem is two-dimensional, and the solution to both types of polarization (electric and magnetic line source) is presented.

Scattering cross section of metallic two-walled carbon nanotubes

The electromagnetic wave scattering from a metallic two-walled carbon nanotube is studied. The system is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Boundary-value method is used to evaluate the scattering characteristics of the system. Electronic excitations of each wall of nanotube are modeled as an infinitesimally thin cylindrical layer of the free-electron gas described previously by means of the linearized fluid theory. The computed results include the evaluation of the normalized scattering width of both transverse magnetic and transverse electric uniform plane wave by system at normal incidences.

Asymptotic Analysis of Plastic Flow along the Generatrix in a Thin Cylindrical Layer

An analytical solution is found for the problem modeling quasistatic compression and flow of an ideal rigid plastic (under the Mises-Hencky criterion) material along the generatrix in a thin cylindrical layer. This problem is a generalization of the classical Prandtl problem. The small asymptotic parameter is the ratio of the layer thickness to its length. The radii of the cylinders can have any intermediate order of smallness. It is shown that when the radii and thickness of the layer are of the same order of smallness, the solution is asymptotically exact in the sense that the number of terms of the series describing the kinematic and dynamic parameters of the flow is finite. Limiting transitions to the classical Prandtl solution are investigated.

A meshless approach for electromagnetic simulation of metallic carbon nanotubes

In this paper, a study on the electromagnetic behaviour of a single wall carbon nanotube model is described. The electrons available for conduction are treated as a thin cylindrical layer fluid and their motion is described by means of classical hydrodynamics equations in linearized form. These equations are solved in time domain using the Smoothed Particle Hydrodynamics method. The method suitably handled runs on GRID environment.

Support to rock excavations provided by sprayed liners

The support provided to mining excavations by sprayed liners is investigated. A long cylindrical excavation of circular cross-section is considered. Three models to analyse liner mechanisms are presented. In the first model the liner forms a thin cylindrical layer firmly bonded to the surface of the excavation. The rock surrounding the excavation may contain open joints and fractures due to the excavation process. In the second model the liner material penetrates into the fractures to their full extent. In the third model the liner material penetrates some distance into the fractures but the fractures extend well beyond this depth and are taken to extend to infinity. The excavation is subjected to a uniform shear stress at infinity which could represent a perturbation due to mining or a geological disturbance. Two cylindrical regions are considered, an inner region and an outer region which extends to infinity. The stress and displacement in each region are calculated, using plane strain theory of elasticity. In the first model the transfer of stress from the rock to the liner is investigated and the decrease in the stress concentration factor in the rock due to the liner is calculated. In the second and third models the change in the displacement, rotation and stress due to the penetration of the liner material into joints and fractures is investigated. Representative values for the changes in stress and displacement at the surface of the excavation predicted by the three models are presented.

A transmission line model for metallic carbon nanotube interconnects

AbstractA transmission line (TL) model describing the propagation of electric signals along metallic single wall carbon nanotube (CNT) interconnects is derived in a simple and self‐consistent way within the framework of the classical electrodynamics. The conduction electrons of metallic CNTs are modelled as an infinitesimally thin cylindrical layer of a compressible charged fluid with friction, moving in a uniform neutralizing background. The dynamic of the electron fluid is studied by means of the linearized hydrodynamic equations with the pressure assumed to be that of a degenerate spin‐½ ideal Fermi gas. Transport effects due to the electron inertia, quantum fluid pressure and electron scattering with the ion lattice significantly influence the propagation features of the TL. The simplicity and robustness of the fluid model make the derivation of the TL equations more straightforward than other derivations recently proposed in the literature and provide simple and clear definitions of the per unit length (p.u.l.) TL parameters. In particular, this approach has provided a new circuit model that can be used effectively in the analysis of networks composed of CNT transmission lines and lumped elements. The differences and similarities between the proposed model and those given in the literature are highlighted. Copyright © 2006 John Wiley &amp; Sons, Ltd.

An Integral Formulation for the Electrodynamics of Metallic Carbon Nanotubes Based on a Fluid Model

An integral formulation to model, in the frequency domain, the electromagnetic response of three-dimensional (3-D) structures formed by metallic carbon nanotubes and conductors, within the framework of the classical electrodynamics, is described. The conduction electrons of the metallic nanotube are modeled as an infinitesimally thin cylindrical layer of compressible fluid, whose dynamics are described by means of the linearized hydrodynamic equations. The resulting integral equations are solved numerically by the finite element method using the facet elements and the null-pinv decomposition. The proposed formulation is applied to study carbon nanotube interconnects and dipole antennas and some related results are outlined. The solutions highlight the high-frequency effects due to the electron inertia and the fluid pressure. In particular, since the kinetic inductance matrix dominates over the magnetic one, proximity effects are negligible

On features of ferrofluid convection caused by barometrical sedimentation

The experimental and numerical studies of Rayleigh convection in a thin cylindrical layer have been conducted for a ferrofluid containing magnetite particles suspended in kerosene carrier liquid. Near the onset of convection, the wave oscillatory convection was observed both in the experiments and in the numerical finite volume simulations. Time periods of temperature oscillations obtained using thermocouples were investigated using wavelet analysis. Thermosensitive liquid crystal sheet visualizations of flow patterns revealed irregular spatiotemporal behavior of convection, close to the threshold. Numerical simulations using a two-phase mixture model indicated that the initial sedimentation gradient may lead to spatiotemporally chaotic convection. Experimentally observed hysteresis and strong dependence of the measured heat flux from the prehistory of the experiments allude to non-Newtonian nature of ferrocolloids.

GRAVITATIONAL AND MAGNETIC CONVECTION IN MAGNETIC FLUID

Experiments were performed to examine the influence of external homogeneous magnetic field on ferrofluid convection in thin cylindrical layer heated from one wide sidewall and cooled from another. Gravitational and magnetic mechanisms of convection as well as the influence of gravitational sedimentation of particles and their aggregates on stability and structure of fluid flows are studied. The integral and local temperature sensors were used for measurement of heat transport across the layer. Visualization of flow patterns was provided by a temperature-sensitive liquid crystal sheet. The results indicate that with the help of a magnetic field it is possible to control the stability and the form of convection motions. Besides, the concentration gradients of solid phase can have material role to convection instability and heat transfer.

Role of pre-pulse in gas-filled-capillary soft X-ray source

The pre-pulse should ensure that the main current pulse starts (due to skin effect) in a thin cylindrical layer near the capillary wall. Then an axially symmetrical compression (due to pinch effect) takes place that compresses the plasma into a thin, dense, hot, straight plasma fibre, in which there are favourable conditions for amplification of spontaneous emission in soft X-ray region and for lasing. We describe both passive and active generation of the pre-pulse and its influence on the waveform of the capillary discharge current, pinching process, and axial soft X-ray radiation.