Semi-infinite Tube Research Articles

Thermal Spreading/Constriction From an Isothermal Source Into a Multilayer Orthotropic Semi-Infinite Flux Tube

Abstract Thermal spreading and constriction have been widely studied due to relevance in heat transfer across interfaces with imperfect contact and problems such as microelectronics thermal management. Much of the past work in this field addresses an isoflux source, with relatively lesser work on the isothermal source problem, which is of much relevance to heat transfer across rough interfaces. This work presents an analytical solution for thermal spreading/constriction resistance that governs heat flow from an isothermal source into a multilayer orthotropic semi-infinite flux tube. The mixed boundary condition due to the isothermal source is accounted for by writing a convective boundary condition with an appropriately chosen spatially-varying Biot number. A series solution for the temperature field is derived, along with a set of linear algebraic equations for the series coefficients. An expression for the nondimensional thermal spreading resistance is derived for Cartesian and cylindrical problems. It is shown that, depending on the values of various nondimensional parameters, heat transfer in either the thin film or the flux tube may dominate and govern the overall thermal spreading resistance. Results for a single-layered isotropic flux tube are derived as a special case of the general result, for which, good agreement with past work is demonstrated. An easy-to-use polynomial fit for this special case is presented. This work contributes a novel technique for solving mixed boundary problems involving an isothermal source, and may also help solve practical problems related to interfacial heat transfre and thermal management.

Acoustic radiation characteristics of cutoff modes from ducts

The acoustic radiation from a source inside a hard-walled semi-infinite duct or tube, such as for ducted fans and rotors, is investigated. In particular a study of cutoff modes, which have the potential to affect the far-field pressure radiation for sources close to the duct open end, is presented. A large amount of work has been done to mathematically and experimentally investigate propagating cuton acoustic modes. However, there is very little published work on the radiation of cutoff modes. This paper concerns the radiation characteristics of cutoff modes to determine their behaviour, and their likely influence in the far-field directivity for sources close to the duct open end. It is shown that cutoff modes are an essential contributor for the radiation in the rear-arc.

Local field-interaction approach to the Dirac monopole

We introduce the local field interaction approach to Dirac magnetic monopoles. Our analysis reveals two physically different types of a monopole. The first type is free of singularity, and the field angular momentum plays an essential role in the interaction. The second type is described as an endpoint of an invisible semi-infinite flux tube (a Dirac string). Notably, a different phase factor exists between the two types where n is the quantum number of the field angular momentum. Our study provides a realistic description of the two types of monopoles. Various aspects of these monopoles are discussed, including the Maxwell dual of the Dirac string, exchange symmetry, and an analogy to the Coriolis interaction.

The diffusion problem

The study of diffusion processes is relevant in various fields: chemistry, physics, metallurgy, medicine, and others. The paper considers and solves the problem of diffusion of charged particles under the action of an electromagnetic field in a semi-infinite thin tube. The mathematical formulation is a boundary value problem for an inhomogeneous partial differential equation of the parabolic type. To obtain an accurate analytical solution, the operator method is used. The solution is initially obtained in the form of an image, and then the solution of the original problem is obtained using the inverse Laplace transform. The solution of the test example is obtained, a graphical image of the desired function is constructed in the MatLab software package.

Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.

Quantitative Ion Probe Measurements for Application in a Rotating Detonation Engine

Rotating detonation engines (RDEs) are characterized by extremely high temperatures and pressures, with operating frequencies on the order of several kilohertz. This creates an environment that is challenging to implement research diagnostics. The two most common diagnostics implemented in RDEs operating at speeds capable of defining the detonation wave are dynamic pressure transducers and ion probes. In the case of dynamic pressure transducers, hardware cost and excessive temperatures often dictate remotely coupled transducers, such as a semi-infinite tube pressure configuration in order to improve survivability. Ion probes, on the other hand, are much more robust and can be installed directly within the combustion annulus. However, the information obtained by ion probes in RDEs has been largely qualitative, with their primary use being wave tracking for speed and directionality. This paper presents methodology for determining quantitative ion concentrations from raw ion probe current–voltage data, using known geometry and appropriate electrostatic probe theory. Data are presented from a combustion-driven shock tube, demonstrating applicability of various probe theories and providing comparisons with values determined from a Zeldovich–Neumann–Döring simulation using the Shock and Detonation Toolbox. Results are considered from the perspective of future implementation of a flush-mounted device within the combustion annulus of an RDE.

Invariants and Asymptotics of Axisymmetric Swirling Submerged Jets

An axisymmetric laminar swirling jet of a viscous incompressible fluid flowing from a rotating semi-infinite tube in space filled with the same fluid is explored. The inner surface of the tube rotates with a constant angular velocity, and the outer surface is stationary or rotates with the same angular velocity. It is shown that in the first case, the flow field far from the tube orifice is described by the Loitsyansky asymptotic solution, and in the second case (with weak coflow), it is described by the Long-Gol’dshtik-Zubtsov self-similar solution. The Gol’dshtik hidden invariant is generalized to arbitrary axisymmetric swirling jets, and its influence on the jet asymptotics is studied. Strongly swirling jets are calculated, and the dependence of the parameters of the recirculation zone (vortex breakdown in a swirling jet) on the swirl number and the Reynolds number is examined.

Analysis of acoustic radiation force on a rigid sphere in a fluid-filled cylindrical cavity with an abruptly changed cross-section.

This paper studies the acoustic radiation force of a rigid sphere positioned in a fluid-filled cylindrical cavity with an abruptly changed cross-section. This cavity consists of a semi-infinite front tube and a coaxially connected semi-infinite rear tube with different cross-sectional area through a transverse planar junction. Considering a plane wave propagates along the cavity, the exact expression of the acoustic radiation force exerted on the sphere in the front tube is deduced. The effects of the distance between the sphere and the planar junction and the radius ratio of the front tube to the rear tube on acoustic radiation force are analyzed. Numerical results show that the distance influences the acoustic radiation force periodically. Both the distance and the radius ratio of the tubes affect the magnitude and the direction of acoustic radiation force. A finite element model about the calculation for the acoustic radiation force on the sphere in the fluid-filled cylindrical cavity with suddenly changed cross-section is built to validate the theoretical results. The comparison results between the theoretical computation and the finite element simulation are in good agreement with each other. This work can support future studies for the predictive control of a particle in the cavity which has an abruptly changed cross-section.

ACOUSTICS OF PLANE WAVES IN WIND TUNNEL NOZZLES

The problem of propagating plane waves in a subsonic wind tunnel nozzle is considered. The contour of the nozzle is formed by the Witoszynski formula. In the case in which the gas is at rest, a conformal transformation is used to solve the wave equation that leads the system to a cylindrical geometry. This allows using the results of sound emission from a semi-infinite tube to determine the reflection coefficient from the nozzle edge. It is shown that in the conformal coordinates the equations are similar to the equation of sound propagation in thin tubes. In this case, the solutions to both equations give close results. In view of this, the problem is solved within the framework of the thin tube equation. Numerical results show that there are no resonances in the wind tunnel nozzle.

A ring-vortex free-wake model for uniformly loaded propellers. Part I-Model description.

The paper presents a free-wake actuator disk model as applied to uniformly loaded propellers without slipstream rotation. The wake vorticity, originating from the disk edge, is represented by the superposition of a ring vortex sheet and a semi-infinite cylindrical vortex tube modelling the far wake. The shape and the density strength of the sheet are iteratively evaluated using two conditions. Firstly, the vortex sheet stability condition is strongly enforced, that is the static pressures just above and beneath the sheet are required to be equal. Secondly, the vortex sheet is constrained to align with the overall induced flow field, namely it is compelled to be a streamsurface. By doing so, the contraction of the wake is naturally accounted for in the model and no assumptions on its shape are made. The first part of this work deals with the theoretical foundations of the model and with the description of its discrete counterpart. The characteristics of the flow singularities used to model the flow induced by the wake are also presented.

Can one make a laser out of cardboard?

We consider two dimensional and three dimensional semi-infinite tubes made of "Lambertian" material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal vector. If the light source is far away from the opening of the tube then the exiting rays are (approximately) collimated in two dimensions but are not collimated in three dimensions. An observer looking into the three dimensional tube will see "infinitely bright" spot at the center of vision. In other words, in three dimensions, the light brightness grows to infinity near the center as the light source moves away.

Telescopic oscillations of double-walled carbon nanotubes in the presence of an inner semi-infinite tube

Telescopic oscillation of nested carbon nanotubes is capable of generating GHz frequency. A main challenge against their practical applications is how to control and tune such oscillations. In this paper, we demonstrate that by displacing the tip of a semi-infinite tube inside a conventional double-walled oscillatory system, we can change the vdW force distribution acting on the oscillating tube. By changing this distribution, the dynamics of the system is altered; hence, the oscillations are retuned. The positioning of the tip can be controlled externally by moving its other end. The proposed mechanism provides a solution to control and tune this type of oscillatory systems during the course of oscillations. Concerning the different system parameters (i.e. geometrical parameters and initial conditions), we perform a thorough study to reveal how the oscillatory frequency will change by moving the tip of the semi-infinite tube.

Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions

We consider a conservative system consisting of an elastic plate interacting with a gas filling a semi-infinite tube. The plate is placed on the bottom of the tube. The dynamics of the gas velocity potential is governed by the linear wave equation. The plate displacement satisfies the linear Kirchhoff equation. We show that this system possesses an infinite number of periodic solutions with the frequencies tending to infinity. This means that the well-known property of decaying of local wave energy in tube domains does not hold for the system considered.

Spectra of Semi-Infinite Quantum Graph Tubes

The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation $D(\lambda,k_1,k_2)=0$ with $(k_1,k_2)\in(\mathbb{C}/2\pi\mathbb{Z})^2$ subject to the constraint $\alpha k_1 + \beta k_2 \equiv 0$ (mod $2\pi$), where $\alpha$ and $\beta$ are integers. The number of Floquet modes for a given $\lambda\in\mathbb{R}$ is $2\max\left\{ \alpha, \beta \right\}$. Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.

Random Reflections in a High-Dimensional Tube

We consider light ray reflections in a d-dimensional semi-infinite tube, for $$d\ge 3$$ , made of Lambertian material. The source of light is placed far away from the exit, and the light ray is assumed to reflect so that the distribution of the direction of reflected light ray has the density proportional to the cosine of the angle with the normal vector. We present new results on the exit distribution from the tube, and generalizations of some theorems from an earlier article, where the dimension was limited to the cases $$d=2$$ and $$d=3$$ .

Finite Size Effect on the Specific Heat of a Bose Gas in Multi-filament Cables

The specific heat for an ideal Bose gas confined in semi-infinite multifilament cables is analyzed. We start with a Bose gas inside a semi-infinite tube of impenetrable walls and finite rectangular cross section. The internal filament structure is created by applying to the gas two, mutually perpendicular, Kronig-Penney delta-potentials along the tube cross section, while particles are free to move perpendicular to the cross section. The energy spectrum accessible to the particles is obtained and introduced into the grand potential to calculate the specific heat of the system as a function of temperature for different values of the periodic structure parameters such as: the cross section area, the wall impenetrability and the number of filaments. The specific heat as a function of temperature shows at least two maxima and one minimum. The main difference with respect to the infinite case is that the peak associated with the BE condensation becomes a smoothed maximum or in other words, there is not a jump in the specific heat derivative, whose temperature no longer represents a critical point.

Single file diffusion into a semi-infinite tube

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

THE SOLUTION OF THE PROBLEM OF MOTION OF PULSED GAS IN A SEMI-INFINITE TUBE

A method is proposed for solving the problem of non-stationary flow of a pulsating incompressible ( ) insulated ( ) of gas in a semi-infinite cylinder tube (radius ) in the horizontal plane without regard to volume forces. For the case of the periodic law of change of pressure obtained solution of the Navies - Stokes equations on the basis of rapidly convergent double functional series, shows the identity of the decision with the decision of the private boundary value problems of heat conduction.

Wavy Motion of Viscous Bubbly Liquid in Tubes of Orthotropic Material

This article investigates the pulsating flow of a compressible two-phase bubble of viscous fluid contained in an elastic orthotropicle direct axis tube. In this work, one-dimensional linear equations have been used. It is assumed that the tube is rigidly attached to the certain environment. In the case of finite length the pressure is applied at the end of its faces. In the limited process, relations obtained for a very long tube. Such a description, in a sense generalizes and strengthens the work of this type. In the numerical experiment a semi-infinite tube with flowing water containing small amount of air bubbles is considered. The influence of volume fraction of bubbles on wave characteristics is determined.

Numerical computation of thermal and electrical constriction resistance in finite tube

This study presents an analysis of the coupled electrical and thermal constriction phenomena. The finite element method is used to calculate constriction resistance (thermal and electrical) of a conducting semi-infinite cylinder subjected to heat and current spot at the same time. Three fundamental cases are presented successively. The first case deals with the transient thermal constriction in a semi-infinite heat flux tube. The second one deals with the steady state electrical constriction in the same geometry. The third and most important case presents the numerical computation of constriction resistance when the semi-infinite tube is the site of volumetric heat generation resulting from Joule effect (electrical conduction). The preliminary studies are conducted to validate the numerical computation by their comparison to available analytical solutions in the literature. The transient thermal constriction resistance and the steady state electrical constriction resistance are presented and analyzed for different constriction ratio and coupling parameter. All presented examples use a uniform spatial distribution of the electrical density and the heat flux dissipated by the spot.