Computational Model of Phase Transformations in Thermo-Chemical Cathodes Using Kinetic Approach

2012 ◽  
Vol 510-511 ◽  
pp. 9-14
Author(s):  
A.A. Kavokin ◽  
I.H. Kazmi ◽  
B. Munir
Keyword(s):  
Heat Equation ◽  
Solid Phase ◽  
State Diagram ◽  
Two Phase ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
Solid Phases ◽  
Kinetics Of ◽  
Liquid And Solid Phases

The paper presents the results of modeling of the processes of phases transformations occurring in cathode of plasmatron with zirconium insertion. Model describes temperature and liquid-solid phase transformation in cathode considering kinetics of transformation in accordance with a state diagram. The comparison between one-dimensional mathematical models was exploited for estimation of the kinetics coefficient. First model is based on well-known heat equation with Stefans condition on the free boundary between liquid and solid phases [. The standard analytical self-similar solution for two-phase case is applied. In the second model, for heat equation instead of Stefans conditions, differential equations of kinetics are used.

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

On backward self-similar blow-up solutions to a supercritical semilinear heat equation

2010 ◽  
Vol 140 (4) ◽  
pp. 821-831 ◽  
Author(s):  
Noriko Mizoguchi
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Blow Up ◽  
Radial Solution ◽  
Similar Solution ◽  
Semilinear Heat Equation ◽  
Blowing Up ◽  
Self Similar Solution ◽  
Self Similar ◽  
Image Position

We are concerned with a Cauchy problem for the semilinear heat equationthen u is called a backward self-similar solution blowing up at t = T. Let pS and pL be the Sobolev and the Lepin exponents, respectively. It was shown by Mizoguchi (J. Funct. Analysis257 (2009), 2911–2937) that k ≡ (p − 1)−1/(p−1) is a unique regular radial solution of (P) if p > pL. We prove that it remains valid for p = pL. We also show the uniqueness of singular radial solution of (P) for p > pS. These imply that the structure of radial backward self-similar blow-up solutions is quite simple for p ≥ pL.

scholarly journals Application of equilibrium phase diagrams for calculation of segregation kinetics during two-component melt cooling

2020 ◽  
Vol 63 (2) ◽  
pp. 129-134
Author(s):  
A. D. Drozin ◽  
E. Yu. Kurkina
Keyword(s):  
Liquid Phase ◽  
Equilibrium State ◽  
Cross Section ◽  
Diffusion Coefficients ◽  
Solid Phase ◽  
Equilibrium Phase ◽  
Minimum Size ◽  
Two Component ◽  
Solid Phases ◽  
Liquid And Solid Phases

According to the equilibrium state diagrams, when the melt is cooled to a certain temperature below liquidus, compositions of liquid and solid phases are uniquely determined by corresponding curves in the diagram. However, it does not happen in reality. For equilibrium (which the diagram describes), it is necessary that the melt is maintained indefinitely at each temperature, or thermal conductivity of liquid and solid phases, and the diffusion coefficients of their components, are infinitely large. We made an attempt to find out how these processes occur in reality. In this work, we consider the growth of individual crystal during cooling of a two-component melt. Mathematical model is constructed based on the following. 1. The melt area with volume corresponding to one grain, the periphery of which is cooled according to a certain law, is considered. 2. At the initial instant of time, a crystal nucleus of a certain minimum size is in the liquid. 3. At the surface of crystal, compositions of liquid and solid phases correspond to equilibrium state diagram at a given temperature on its surface. 4. Changes in temperature and composition in liquid and solid phases occur according to the laws of heat conduction and diffusion, respectively. As the melt gets cold and the crystal grows, the liquid phase is enriched in one component and depleted in another, the solid phase – on the contrary. Since the diffusion coefficients of the components in the solid phase are small, the composition of the crystal does not have time to completely equalize its cross section. The model proposed in the work allows us to study this phenomenon, to calculate for each cooling mode how the composition of the crystal will vary over its cross section. The calculations have shown that the temperature equalization occurs almost instantly, and composition of the liquid phase equalizes much slower. Equalization of the solid phase composition does not occur in the foreseeable time. The results of the work will help to improve technology of generation of alloys with an optimal structure.

scholarly journals Formation of Interfacial Reaction Layers in Al2O3/SS 430 Brazed Joints Using Cu-7Al-3.5Zr Alloys

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 990 ◽  
Author(s):  
Hoejun Heo ◽  
Hyeonim Joung ◽  
Keeyoung Jung ◽  
Chung-Yun Kang
Keyword(s):  
Liquid Phase ◽  
Interfacial Reaction ◽  
Eutectic Temperature ◽  
Liquid Phases ◽  
430 Stainless Steel ◽  
Brazed Joints ◽  
Solid Phases ◽  
Α Al2o3 ◽  
Kinetics Of ◽  
Liquid And Solid Phases

The formation of interfacial reaction layers was investigated in an α-Al2O3/430 stainless steel (SS430) joint brazed using a Cu-7Al-3.5Zr active brazing alloy. Brazing was conducted at above its eutectic temperature of 945 °C and below liquidus 1045 °C, where liquid and solid phases of the brazing alloys coexists. At 1000 °C, the liquid phase of the brazing alloy was wet onto the α-Al2O3 surface. Zr in the liquid phase reduced α-Al2O3 to form a continuous ZrO2 layer. As the dwell time increased, Zr in the liquid phases near α-Al2O3 interface was used up to thicken the reaction layers. The growth kinetics of the layer obeys the parabolic rate law with a rate constant of 9.25 × 10−6 cm·s−1/2. It was observed that a number of low yield strength Cu-rich particles were dispersed over the reaction layer, which can release the residual stress of the joint resulting in reduction of crack occurrence.

Minimal blow-up asymptotics of quasilinear heat equations

2001 ◽  
Vol 131 (6) ◽  
pp. 1297-1321
Author(s):  
M. Chaves ◽  
Victor A. Galaktionov
Keyword(s):  
Heat Equation ◽  
Blow Up ◽  
Asymptotic Properties ◽  
Basin Of Attraction ◽  
Boundary Function ◽  
Similar Solution ◽  
Heat Equations ◽  
Blowing Up ◽  
Self Similar Solution ◽  
Self Similar

We study the asymptotic properties of blow-up solutions u = u(x, t) ≥ 0 of the quasilinear heat equation , where k(u) is a smooth non-negative function, with a given blowing up regime on the boundary u(0, t) = ψ(t) > 0 for t ∈ (0, 1), where ψ(t) → ∞ as t → 1−, and bounded initial data u(x, 0) ≥ 0. We classify the asymptotic properties of the solutions near the blow-up time, t → 1−, in terms of the heat conductivity coefficient k(u) and of boundary data ψ(t); both are assumed to be monotone. We describe a domain, denoted by , of minimal asymptotics corresponding to the data ψ(t) with a slow growth as t → 1− and a class of nonlinear coefficients k(u).We prove that for any problem in S11−, such a blow-up singularity is asymptotically structurally equivalent to a singularity of the heat equation ut = uxx described by its self-similar solution of the form u*(x, t) = −ln(1 − t) + g(ξ), ξ = x/(1 − t)1/2, where g solves a linear ordinary differential equation. This particular self-similar solution is structurally stable upon perturbations of the boundary function and also upon nonlinear perturbations of the heat equation with the basin of attraction .

scholarly journals Electromagnetic Field as Agent Moving Bioactive Cations. A New Antimicrobial System in Architecture Technology

2021 ◽  
Vol 11 (18) ◽  
pp. 8320
Author(s):  
Andrzej Chlebicki ◽  
Wojciech Spisak ◽  
Marek W. Lorenc ◽  
Lucyna Śliwa ◽  
Konrad Wołowski
Keyword(s):  
Electromagnetic Field ◽  
Cultural Heritage ◽  
Two Phase ◽  
Galvanic Cells ◽  
Solid Phases ◽  
Cultural Heritage Objects ◽  
Liquid And Solid Phases ◽  
Protection Of Cultural Heritage

There is a new described antifungal system (GALVI) involving the moving of bioactive ions of Zn, Cu and Bi for the protection of cultural heritage objects such as buildings, sculptures and stretchers. There were two kinds of galvanic cells that were used: the first composed of a two-electrodes system, Zn, Cu, and second one composed of a three-electrodes system, Zn, Bi and Cu. Moreover, two-phase media are proposed with various kinds of rocks used in architectonical objects. Microorganisms inhabit the boundaries of two liquid and solid phases. This enables the investigation of the process of rock colonization. Possible applications of the suggested GALVI system are mentioned.

scholarly journals Solid-liquid phase equilibria in the ternary systems H2O+ZnCl2+NaCl at temperatures of 298, 313 and 333 K

2021 ◽  
pp. 53-53
Author(s):  
Sevilay Demirci ◽  
Vedat Adiguze ◽  
Omer Sahin
Keyword(s):  
Liquid Phase ◽  
Phase Equilibria ◽  
Solid Phase ◽  
Ternary Systems ◽  
Viscosity Data ◽  
Isothermal Method ◽  
Chloride Water ◽  
Solid Phases ◽  
Solid Liquid ◽  
Liquid And Solid Phases

In this study, an economic separation method was suggested with the use of phase equilibria in order to ensure the recycling of ZnCl2 whose industrial waste amount is very high and to prevent it to form an environmental pollution. Sodium chloride-zinc chloride-water systems were examined with the isothermal method at temperatures of 298, 313 and 333 K. The analyses of the liquid and solid phases were used to determine the composition of the solid phase using the Schreinemakers graphic method. The solid-liquid phase equilibrium and viscosity data belonging to all ternary systems were identified and the solubility and viscosity changes with temperature were compared. The viscosity values were inversely proportional to the temperature as the amount of ZnCl2 in the solution increased. NaCl, 2NaCl ZnCl2 nH2O (n: 2, 0), ZnCl2 salts were observed at 298, 313, 333 K in the solid phases which are at equilibrium with the liquid phase at the invariant point.

scholarly journals One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

1984 ◽  
Vol 138 ◽  
pp. 417-429 ◽  
Author(s):  
D. Rivas ◽  
J. Meseguer
Keyword(s):  
Computing Time ◽  
Stability Limit ◽  
Static Stability ◽  
Industrial Processes ◽  
Liquid Bridges ◽  
High Melting Point ◽  
Singular Perturbation Method ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar

Liquid bridges appear in a large variety of industrial processes such as the so-called floating-zone technique, used in recent years in crystal growth and in purification of high-melting-point materials.In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.

Self-similar and asymptotic solutions for a one-dimensional Vlasov beam

1983 ◽  
Vol 29 (1) ◽  
pp. 139-142 ◽  
Author(s):  
J. R. Burgan ◽  
M. R. Feix ◽  
E. Fijalkow ◽  
A. Munier
Keyword(s):  
Asymptotic Solution ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Asymptotic Solutions ◽  
One Dimensional ◽  
Self Similar Solution ◽  
Self Similar ◽  
New Equation

Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.

A Solidification Front Monitor for Metal Casting

1998 ◽  
Vol 120 (3) ◽  
pp. 515-522 ◽  
Author(s):  
M. M. Hytros ◽  
J.-H. Chun ◽  
R. C. Lanza ◽  
N. Saka
Keyword(s):  
Solidification Front ◽  
First Generation ◽  
Metal Casting ◽  
Two Phase ◽  
Front Position ◽  
Solid Phases ◽  
Ct System ◽  
Two Phases ◽  
Future Work ◽  
Liquid And Solid Phases

A feasibility study was performed to assess computed tomography (CT) as a method of detecting the position of the solidification front during metal casting. Since the liquid and solid phases of metals differ in density by 4 to 12 percent, CT has the ability to differentiate the two phases. The motivation for this work is the development of a real-time solidification sensor for the continuous casting of metals. A first-generation CT system for reconstructing two-dimensional images of solidifying tin was developed. The performance of the CT system was evaluated by reconstructing images of objects of known geometries. For the solidification experiment, CT scans were conducted on an actively heated and cooled crucible filled with pure tin. The tin existed in both liquid and solid phases, with the solidification front position tracked by thermocouples. The image of the two-phase tin experiment had poor contrast resolution, but a quantitative analysis of the image does indicate an approximate 7 percent difference between the liquid and the solid portions of the melt. However, the size of the liquid phase was not as large as that determined by thermocouple measurements. This is a result of temperature fluctuations in the melt during data acquisition, as well as the relatively low spatial resolution. Future work to improve system performance will include using a linear accelerator (linac) as the radiation source.

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