Equations For Velocity Field Research Articles

Hydrodynamic analysis of the magnetic field dependent viscous fluid flow and thermosolutal convection between rotating channels

According to research, exposing a person to a magnetic field enhances blood flow and minimizes their risk of suffering a heart attack. Ferrohydrodynamics is the study of fluid motion mechanics that is affected by strong magnetic polarisation forces (FHD). Ferrofluids may transmit heat in a variety of ways by using magnetic fluids. This behaviour is demonstrated by liquid-cooled speakers, which utilise less ferrofluid to prevent heat from reaching the speaker coil. This modification boosts the coil’s ability to expand, which enables the loudspeaker to create high-fidelity sound. It is investigated how the fluid dynamics of spinning, squeezing plates are affected by thermosolutal convection and a magnetic field dependent (MFD) viscosity. Standard differential equations are used to represent the equations of the modified form of Navier Stokes, Maxwell’s, and thermosolutal convection. The magnetic field, modified velocity field equations, and thermosolutal convection equations all yield suitable answers. Additionally computed and thoroughly detailed are the MHD torque and fluid pressure that are imparted to the top plate. To create a technique with quick and certain convergence, the resulting equations for uniform plates are solved using the Homotopy Analysis Method (HAM) with appropriate starting estimates and auxiliary parameters. The validity and reliability of the HAM outcomes are shown by comparing the HAM solutions with the BVP4c numerical solver programme. It has been found that a magnetic Reynolds number lowers the temperature of the fluid as well as the tangential and axial components of the velocity field. Additionally, when the fluid’s MFD viscosity rises, the axial and azimuthal components of the magnetic field behave in opposition to one another. This study has applications in the development of new aircraft take-off gear, magnetorheological airbags for automobiles, heating and cooling systems, bio-prosthetics, and biosensor systems.

Аutomatisation of Calculation Method of Technological Parameters of Wiredrawing with Account of Speed Factor and Material Properties

The article presents the mathematical model worked out for calculating the operating force of the wire drawing. The solution of the problem was achieved by dividing the wire work piece material in the deformation zone into an infinitely small finite elements ij; and, by parting the working area of the die geometry, consisting of crimping cone, drawing cylinder and the radius of curvature between them into infinitely small linear sections. The authors described the conditions for continuity at the finite element line, the dependencies required to determine the geometric grid sizes. To determine the total modified draw force, the authors obtained formulas to describe the stress condition at each point of the finite element, based on the motion equations, equations of velocity fields, the incompressibility condition, the deformation rate intensity, taking into account the speed factor and viscoplastic properties of the work material. The article presents the adequacy of the proposed model.

BiconeDrag—A data processing application for the oscillating conical bob interfacial shear rheometer

BiconeDrag is a software package that allows one to perform a flow field based data processing of dynamic interfacial rheology data pertaining to surfactant laden air–fluid interfaces obtained by means of a rotational bicone shear rheometer. MATLAB and Python versions of the program are provided. The bicone fixture is widely used to transform a conventional bulk rotational rheometer into an interfacial shear rheometer. Typically, such systems are made of a bicone bob, which is mounted on the rheometer rotor, and a cylindrical cup. Usually, the experiment consists of measuring the response of the interface under an oscillatory stress. The program takes the values of the torque/angular displacement amplitude ratio and phase difference to compute the interfacial dynamic moduli (or complex viscosity) by consistently taking into account the hydrodynamic flow both at the interface and the subphase. This is done by numerically solving the Navier–Stokes equations for the subphase velocity field together with the Boussinesq–Scriven boundary condition at the interface, and no slip boundary conditions elsewhere. Furthermore, the program implements a new iterative scheme devised by solving for the complex Boussinesq number in the rotor’s torque balance equation. Program summaryProgram Title: BiconeDragProgram Files doi:http://dx.doi.org/10.17632/c245bmgf5n.1Licensing provisions: GPLv3Programming language: MATLAB (compatible with GNU Octave) and PythonNature of problem: Obtaining the interfacial dynamic moduli, or the complex viscosity, of a surfactant laden air–liquid interface from the experimental data obtained by means of a bicone fixture mounted on the rotor of a conventional bulk rotational rheometer. The experimental data consist in the amplitude ratio and phase difference between the torque and the angular displacement of the rotor. The coupling between the surface and subphase fluid flows requires a proper representation of the hydrodynamic velocity field both at the surface and at the liquid subphase.Solution method:: We use a proper hydrodynamic model of the problem through the Navier–Stokes equations for the velocity field at the subphase, supplemented with the Boussinesq–Scriven boundary condition at the interface and no slip conditions elsewhere. The hydrodynamic equations are solved by means of a centered second order finite difference method and the flow field is used to compute the hydrodynamic drags exerted by the subphase and the interface on the bicone probe. Both calculated drags are later used in the rotor torque balance equation together with the rotor inertia term. Solving for the Boussinesq number in the torque balance equation then allows one to devise an iterative scheme that yields improved values of the complex Boussinesq number: starting from a convenient seed one obtains a converged value of the complex Boussinesq number such that the experimental and calculated values of the torque/angle amplitude ratio coincide within a user selected tolerance. The values of the rheological variables are obtained directly from the value of the complex Boussinesq number.Additional comments including restrictions and unusual features: The program is valid only for air/fluid interfaces. The interface may have or not a thin film either newtonian or viscoelastic. The subphase fluid may be newtonian or viscoelastic (having non negligible storage and loss moduli) though the user must take care of the possible frequency dependence of the dynamic moduli.

Ergodicity of a Galerkin approximation of three-dimensional magnetohydrodynamics system forced by a degenerate noise

Magnetohydrodynamics system consists of a coupling of the Navier-Stokes and Maxwell's equations and is most useful in studying the motion of electrically conducting fluids. We prove the existence of a unique invariant, and consequently ergodic, measure for the Galerkin approximation system of the three-dimensional magnetohydrodynamics system. The proof is inspired by those of [E. Weinan and J.C. Mattingly, Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finitedimensional approximation, Comm. Pure Appl. Math. LIV (2001), pp. 1386–1402; M. Romito, Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise, J. Stat. Phys. 114 (2004), pp. 155–177] on the Navier-Stokes equations; however, computations involve significantly more complications due to the coupling of the velocity field equations with those of magnetic field that consists of four non-linear terms.

Analysis of thin film flow over a vertical oscillating belt with a second grade fluid

An analysis is performed to study the unsteady thin film flow of a second grade fluid over a vertical oscillating belt. The governing equation for velocity field with appropriate boundary conditions is solved analytically using Adomian decomposition method (ADM). Expressions for velocity field have been obtained. Optimal asymptotic method (OHAM) has also been used for comparison. The effects of Stocks number, frequency parameter and pressure gradient parameters have been sketched graphically and discussed.

Plane Stress Equations for the Von Mises–Schleicher Yield Criterion

Systems of equations for plastic stresses and velocities based on the von Mises–Schleicher criterion are obtained for plane stresses. The regions of ellipticity and hyperbolicity of these systems are found, and the limiting stresses and fracture directions identified with the characteristics of the velocity field equations are determined. The results agree well with experimental data for plastic and brittle materials.

A quasianalytical model for LT-GaAs and LT-Al0.3Ga0.7As MISFET devices

This paper describes a quasianalytical model for the calculation of the current–voltage characteristics of LT–GaAs and LT–Al0.3Ga0.7As MISFET devices. The model is derived from basic semiconductor charge analysis. Poisson's equation, the current continuity equation, and the Chang–Fetterman velocity-field equations have been solved analytically. When the devices are operating in the linear region and the knee region, the one-dimensional Poisson equation is considered. When the devices are in the saturation regime, the two-dimensional Poisson equation is solved analytically. The resulting output current–voltage characteristics are in good agreement with experimental data. This model has been used to predict the RF performance and RF power capability of these MISFETs. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 61–66, 2000.

Velocity field equations and strain localization in rigid-plastic materials

The velocity field equations are set up for a standard rigid-plastic material. They allow a direct determination of the velocity field, and therefore correspond to the Navier-Stokes equations of a Newtonian fluid. Under conditions of plane strain or axisymmetric deformation, the velocity field equations lead, using the Lévy-Huber-von Mises flow law, to the principal lines—i.e. to the trajectories of the principal strain-rates as characteristics. However, an incipient strain localization, combined with a velocity discontinuity, cannot be expected to occur along a principal line. Rather, a degeneration of the velocity field equations, shown to exist for certain rate-sensitive materials. might be responsible for such a localization effect.

Nonisothermal Axisymmetric Forging

An approximate solution for nonisothermal upset forging is presented. A finite difference thermal analysis and an upper-bound deformation solution are used for this purpose. The thermal analysis is for a homogeneous state of strain, it ignores deformation heating, but accounts for all modes of heat flow during the transfer of the billet to the tooling and throughout the deformation. The upper-bound solution is based on admissible velocity field equations, the recorded temperature data from the thermal analysis, and constitutive equations for temperature, strain, and strain rate-dependence of flow stress. The size of the chilled zone is determined by minimization of total power for the deformation process. Theoretical predictions for load-displacement behavior and the size of the chilled zone are compared with the experimental results for 304 stainless and AISI 1042 steels.

Velocity field equations and strain localization

The velocity field equations of a hypo-elastic material are derived using arbitrary curvilinear coordinates in the actual configuration of the body, and emphasizing “higher order” terms which would disappear in an infinitesimal strain theory. As an example, bifurcation analyses are carried out with the help of the velocity field equations, for the thin rod and the thin plate under uniaxial tension. The results agree with those from the literature, at least if the “higher order” terms are disregarded. Differences may result from the way these terms are incorporated in the hypo-elastic approach.

Analysis of axisymmetric upsetting based on flow pattern observations

A flow-based model for upset forging of cylindrical billets is presented. Four deformation zones are recognized. The size of the elastic zone (Zone I) is determined from empirical equations. Kinematically admissible velocity field equations are obtained for the other three zones. These equations are in terms of two arbitrary parameters which are optimized based on flow pattern observations. From the numerical solution of the velocity and strain rate equations the deformed grid patterns and the localized strains are determined. In general, good agreement with FEM solutions is observed. The phenomenon of side-surface foldover is also predicted with sufficient accuracy by the present solution.

Higher order heat transfer from a rotating sphere

Asymptotic expansions are used to study the higher order heat transfer from a sphere rotating in a fluid at low Reynolds number,R, about thez-axis when the free stream velocity is directed along thex-axis. Navier-Stokes equations involving the effect of the azimuthal velocity both in the Stokes (inner) and the Oseen (outer) regions give the velocity field equations which are used to determine the forced convection field for the above asymmetric case. It is found that the Nusselt number is affected by the rotation at terms of 0(σ2R2) where σ is the Prandtl number of the fluid.

Some generalizations and applications of the velocity field concept: Trip patterns in idealized cities

This paper discusses the velocity field concept and seeks to extend its descriptive power by introducing the continuous analogue of the traditional link speed-flow relations used in transportation studies. By solving the resulting velocity field equations self-consistently in terms of land use and socio-economic factors, and various policy variables, the profile of this field, which reflects the spatial distribution of congestion in an urban area, may be found. The velocity field is computed in a circular city with a single ring road in order to identify its optimal radius. Car parking and public transport “no fares” policies are also considered to illustrate various aspects of our approach.

Axially symmetric plastic deformations in soils

A theoretical investigation is given of quasi-static axially symmetric plastic deformations in soils.The mechanical behaviour of a natural soil is approximated by that of an ideal soil which obeys Coulomb’s yield criterion and associated flow rule, with restriction to rigid, perfectly plastic deformations. There are considerable variations in the structure of the associated stress and velocity field equations for the various plastic regimes, but it is noteworthy that real families of characteristics occur in all non-trivial cases. Attention is focused on those plastic régimes agreeing with the heuristic hypothesis of Haar & von Kármán as being seemingly of application to certain classes of problems, in particular to those of indentation. The stress and velocity fields are then hyperbolic with identical families of characteristics, and the stress field is statically determinate under appropriate boundary conditions. In applications of the theoretical analysis, attention is confined to situations involving only the Haar & von Kármán plastic regimes. First, possible velocity fields are obtained for the incipient plastic flow of a right circular cylindrical sample of soil subjected to uni-axial compressive stress parallel to its axis. Secondly, a complete solution is obtained for the incipient plastic flow in a semi-infinite region of soil, bounded by a plane surface, due to load applied through a flat-ended,smooth, rigid, circular cylinder; numerical results obtained for this problem include the variation of yield-point load with angle of internal friction of the ideal soil. These applications relate to problems of the mechanical testing of soil samples and of load-bearing capacity in foundation engineering.