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N88-21509 - NASA Technical Report Server (NTRS)

Language: English ...

Homotopy Perturbation Method for Solving the Two-Phase Inverse Stefan Problem

problem similar to the Stefan problem in heat conduction [19]. ..... as the Stefan problem. Although the Stefan problem and the creep rupture ...

The Stefan Problem of Detonation Theory,

Not Available

2011-01-01

Relation of the One-Phase Stefan Problem to the Seepage of ...

... Accession Number : ADP004921. Title : The Stefan Problem of Detonation Theory,. Corporate Author : CORNELL UNIV ...

1985-02-01

Indian Academy of Sciences - Summer Fellowships 2005

... Accession Number : ADA079641. Title : Relation of the One-Phase Stefan Problem to the Seepage of Liquids and Electrochemical Machining,. ...

1979-12-01

Indian Academy of Sciences (India)

kodali, mr (iii b.tech.) anil neerukonda inst. of science and chandrashekaran ramachandra reddy shekhar c mande lang="en-gb">kandavelmani, reg. cancer cen., trivandrum panda panda lang="en-gb">dr anand imtech, chandigarh lang="en-gb">ravichandran, reg. cancer cen., trivandrum reg. cancer cen., trivandrum chandrasekar, dr (lecturer) psg college of arts & science, imtech, chandigarh ...

The two-dimensional Stefan problem with slightly varying heat flux

The authors solve the two-dimensional stefan problem of solidification in a half-space, where the heat flux at the wall is a slightly varying function of positioning along the wall, by means of a large Stefan number approximation (which turns out to be equivalent to a small time solution), and then by means of the Heat Balance Integral Method, which is valid for all time, and which agrees with the large Stefan number solution for small times. A representative solution is given for a particular form of the heat flux perturbation.

1995-09-01

Numerical Optimization

Direct and Iterative One-Dimensional Front Tracking Methods for the Two-Dimensional Stefan Problem.

... been possible to prove the existence and uniqueness of a classical solution which tends to the well-known solution of the Stefan problem as the ...

1989-01-01

Two-Phase Stefan Problem with Interfacial Energy and Entropy.

No abstract available.

1978-01-01

The Bidimensional Stefan Problem with Convection: The Time-Dependent Case.

The classical Stefan theory for the melting of a solid or the freezing of a liquid is too simplistic to describe phenomena such as supercooling, in which a liquid supports temperatures below its freezing point, or superheating, the analog for solids, or d...

1985-01-01

Stefan Problem of Detonation Theory.

This paper considers the time dependent Stefan problem with convection in the fluid phase governed by the Stokes equation, and with adherence of the fluid on the lateral boundaries. The existence of a weak solution is obtained via the introduction of a te...

1982-01-01

Relation of the One-Phase Stefan Problem to the Seepage of Liquids and Electrochemical Machining.

A certain model of one-dimensional detonation waves leads to a Stefan problem: the unknown f satisfies Burgers equations on the two sides of a moving discontinuity at which it is given (f, say) and the jump in it derivative (corresponding to the exothermi...

1985-01-01

Test API: Class SearchCriteria

The flow of water through a dam of fairly arbitrary shape is examined in the limit of large frictional drag on the flow. The relation of the problem to the one-phase Stefan problem and a problem of anodic smoothing is explored. Monotonicity and uniqueness...

1979-01-01

THE EFFECT OF THE ICE-SEPARATION CURVE ON THE ...

Stability and Thermal Influences in Nonlinear Continuum ...

... However, the solution of the Stefan problem in this context becomes abruptly complicated, since within each zone, the differential equations ...

Mathematical Sciences Division 1992 Programs

... The general two-phase Stefan problem with supercooling, superheating, and capillarity, was studied [T19] in collaboration ...

1990-11-01

Application of the combined integral method to Stefan problems

... Progress: For a one-dimensional two-phase degenerate Stefan problem, it was proved that the boundary and the solutions up to the boundary are C ...

1992-10-01

British Library Electronic Table of Contents (United Kingdom)

In this paper we present a new, accurate form of the heat balance integral method, termed the combined integral method (CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

2011-01-01

A method of fundamental solutions for the one-dimensional inverse Stefan problem

British Library Electronic Table of Contents (United Kingdom)

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T,T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

2011-01-01

Solution of vector Stefan problems with cross-diffusion

Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusive phase. Several numerical schemes for the solution of the Stefan problem are proposed and compared. It turns out that diagonalization is useful for numerical purposes. However, for the case of position-dependent diffusion coefficients one has to use a different scheme. Here, we analyze stability and workload of several time integration methods.

2005-04-01

1 2 3 4

The Development of New Methods for Solving the Target ...

A hyperbolic Stefan problem based on the linearized Gurtin-Pipkin heat conduction law is considered. The temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results are proved in all the cases. Uniqueness is also shown, except in the situation corresponding to the ideal switch.

1999-03-15

Parameter Estimation in Moving Boundary Problems

... and 7 survey papers. On the inverse Stefan problem he wrote 3 research papers and 1 survey paper. The papers on inverse ...

1984-07-18

Nonlinear Wave and Diffusion Equations

... Finally, the one dimensional, one phase Stefan problem is well known as a model for the melting of ice (see, eg, [5]). There are many approaches to ...

1988-05-01

N95. 14209 - NASA Technical Report Server (NTRS)

... A. Fasano, SD Howison. JR Ockendon & M. Primicerio. Some remarks on the regularisation of the supercooled one-phase Stefan problem. Quart. ...

1990-08-01

Stefan problem with a convective boundary condition

coupled heat/mass transfer Stefan problem. Taking the diffusion coefficient of Bi as a free parameter, the best fit was observed for the published value, ...

On the Stefan Problem with Volumetric Energy Generation

We study the one-phase Stefan problem on a semi-infinite strip x> or =0, with the convective boundary condition -KT/sub x/(0,t) = h[T/sub L/--T(0,t)]. Points of intrest include: a) behavior of the surface temperature T(0,t); b) asymptotic behavior as h#->#infinity; c) uniqueness, and d) bounds on the phase change front and total system energy.

1982-01-01

Test API: Class ImageIDParseBean

This paper presents results of solid-liquid phase change, driven by volumetric energy generation, in a vertical cylinder. We show excellent agreement between a quasi-static, approximate analytical solution valid for Stefan numbers less than one, and a computational model solved using the CFD code FLUENT®. A computational study also shows the effect that the volumetric energy generation has on both the mushy zone thickness and convection in the melt during phase change.

2009-11-01

Computational experience with an explicit difference scheme for a one phase Stefan problem

User Manual for the NASA Glenn Ice Accretion Code ... - GLTRS - NASA

The results of a computational scheme of Rose (a method for calculating solutions of parabolic equations with free boundary, Math. Comp., 14: 249-256(1960)) are compared with the known analytic solution of a single-phase Stefan problem with constant boundary temperature. Rose's scheme was implemented in FORTRAN on a DEC PDP-10. Computations were performed for Stefan numbers St = 0.01, 0.1, 1, 10, and 100. Three relative mesh sizes (..gamma.. = DT/(DX)/sup 2/ = 1/2, 1/6, and 1/25) were used. For each St, the relative mesh size had very little effect on accuracy. However, taking ..gamma.. = 1/25 resulted in dramatically increased computing time. The relative errors of temperature were large near the phase change front. 11 figures, 5 tables.

1980-07-01

Fourth Order Accurate Discretization for the Laplace and Heat Equations on Arbitrary Domains, with Applications to the Stefan Problem.

eling of the Stefan Problem, AIAA J., vol. 22, Nov. 1984, pp. 1685-1690. Schlichting, H., Boundary-Layer Theory. F. J. Cerra, ED. ...

In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an i...

2004-01-01

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The Stefan problem of evaporation of a volatile component from a binary liquid mixture

nt method for the Stefan problem, Int. J. Num. Meth. in . . (25) G. STKANG AND G.J. FIX, A n v s i s of the F U L L. Element, Prentice-Hall, 1973. ...

Perturbation solution to heat conduction in melting or solidification with heat generation

The study is concerned with the Stefan problem of evaporation of a volatile component from its solution with a virtually non-volatile material. The analysis provides an analytical solution to the problem based on mass-transfer fundamentals. Results yield the evaporation rate, interfacial mole fractions, concentration profiles in the gas and liquid phases, and the location of the evaporation front. The analysis can be used to provide the binary liquid diffusion coefficient of the volatile component based on experimental data for the liquid gas interface position as a function of time. The requirements for such a measurement are discussed in terms of the volatility of the evaporating component and its initial concentration in the liquid mixture.[Figure not available: see fulltext.

2006-01-01

Instrumentation, controls and automation in the power industry. Volume 45

The Stefan problem involving a source term is considered in this technical note. As an example, planar solidification with time-dependent heat generation in a semi-infinite plane is solved by use of a perturbation technique. The perturbation solution is validated by reducing the problem to the case without heat generation whose exact solution is available. An application to the case with constant heat generation is presented, for which a closed-form solution is obtained. The effects of heat generation and Stefan number on the evolution of solidification are examined using the perturbation solution.

2010-04-01

Optimal control of the free boundary in a two-phase Stefan problem

Sessions covered economic and management, advance control technologies (including pulverized coal dynamic balancing-activator and control strategy by B. DeMarcy and X.Ollat), nuclear technologies, environmental (including purge considerations for seasonal SCR systems by D.P. Evely, NOx and heat rate supervisory control at NRG-Huntley operations by G Lange, comparison of gypsum dewatering technologies at flue gas desulfurization plants by B.A. Perlmutter, beta gauge particulate monitoring by J.L. Arnold), improving performance at nuclear power plants, network security, and emerging applications.

2002-07-01

Modeling of snow melting and uniform wetting front migration in a layered subfreezing snowpack

We present an optimal control approach for the solidification process of a melt in a container. The process is described by a two phase Stefan problem with the free boundary (interface between the two phases) modelled as a graph. We control the evolution of the free boundary using the temperature on the container wall. The control goal consists in tracking a prescribed evolution of the free boundary. We achieve this goal by minimizing a appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method with step size control, where the gradient of the cost functional is expressed in terms of the adjoint variables. Several numerical examples are presented which illustrate the performance of the method. The novelty of the approach presented consists in using a sharp interface model for the control of the free boundary. This guarantees direct access to the free boundary as optimization variable in terms of its ...

2007-05-01

Approximate solutions to the Stefan problem with internal heat generation

A method of modeling freeze-thaw cycles of naturally deposited snowpacks is presented. The model involves the Stefan condition as an independent governing equation on the exterior moving boundary to calculate snowpack thinning, flow of water through a variably saturated layered porous medium as described by the Richards equation, and heat conduction with a phase change. The heat conduction problem was treated in two ways. Local heat conduction between a snow grain and its surrounding water film was treated by using a simple energy balance. Global heat conduction with a phase change (the Stefan problem) was introduced to calculate the space-time temperature distribution. In order to handle multiple interior moving boundaries, a specific form of the enthalpy formulation was used for heat conduction with a phase change. Changing material properties were considered according to the calculated meltwater refreezing. 48 refs., 11 figs., 2 tabs.

1994-08-01

Stentgraftimplantationen im Aortenbogen

Using a quasi-static approach valid for Stefan numbers less than one, we derive approximate equations governing the movement of a phase change front for materials which generate internal heat. These models are applied for both constant surface temperature and constant surface heat flux boundary conditions, in cylindrical, spherical, plane wall and semi-infinite geometries. Exact solutions with the constant surface temperature condition are obtained for the steady-state solidification thickness using the cylinder, sphere, and plane wall geometries which show that the thickness depends on the inverse square root of the internal heat generation. Under constant surface heat flux conditions, closed form equations can be obtained for the three geometries. In the case of the semi-infinite wall, we show that for constant temperature and constant heat flux out of the wall conditions, the solidification layer grows then remelts. (orig.)

2008-05-15

British Library Electronic Table of Contents (United Kingdom)

Zusammenfassung Hintergrund Endograftimplantationen im oder am Aortenbogen stellen besondere Herausforderungen an die Implantationstechnik und an die mechanischen Eigenschaften von Stentgrafts und ihren Einf?hrungssystemen, bedingt durch die Notwendigkeit, die Prothesen punktgenau abzusetzen und durch die mit der Biegung im Aortenbogen zunehmende Reibungswiderst?nde innerhalb der Einf?hrungssysteme. Die Endograftsysteme der 1. Generation (Talent?, Zenith TX 1?, TAG?) zeigten in dieser Lokalisation technisch bedingte Limitationen. Neue Prothesen Bei den seit 2004 und 2005 verf?gbaren neuen Stentgrafts (E-vita?, Zenith TX 2?, Valiant?, Relay?) sind diese Limitationen weitgehend ?berwunden. Durch technische Verbesserungen von Stentgrafts und Einf?hrungssystemen ist es nun m?glich, auch lange ...

2006-01-01

Soft factor 'felt comfort'. Room air quality, an important element; Soft-Factor Wohlbefinden. Raumluftqualitaet als wichtige Grundlage

Healthy room air - the new Thermal Insulation Ordinance creates a demand for domestic ventilation systems; Gesunde Raumluft - die neue WSchVO weckt den Bedarf an Wohnungslueftungen

Facility management has long been regarded as a cost reduction measure, but it is also a means of raising the financial worth of a building so that landlords can get higher rents or sell the building at a better price. [German] Lange Zeit wurde Facility Management als eine Massnahme zur Kostensenkung angesehen. Heutzutage zeigt sich immer mehr, dass das Facility Management sehr viel umfassender zu verstehen ist: Der Wert eines Gebaeudes bemisst sich nicht allein an einer niedrigen Kostenquote, sondern er soll umfassend Investoren wie Mietern den hoechst moeglichen Nutzen bringen. Nicht allein der kostenguenstige Betrieb ist entscheidend, sondern der Wert des Gebaeudes muss insgesamt gesteigert werden. (orig.)

2002-07-01

1 2 3 4

a Kinetic Model of Interface Motion

Mechanical ventilation in private homes was for many years a stepchild of air conditioning engineers. A decisive impulse for change came in January 1995 with the enactment of the new Thermal Insulation Ordinance which for the first time allows house owners to exceed the usual admissible annual heating requirement by a certain amount on the condition that they equip the house with mechanical ventilation systems. (orig.) [Deutsch] Ueber lange Jahre war die mechanische Wohnungslueftung ein Stiefkind der Raumlufttechnik. Einen entscheidenden Impuls gab erst die seit Januar 1995 gueltige Waermeschutzverordnung, die erstmals zulaesst, dass ein gewisses Quantum des Jahres-Heizwaermebedarfs durch den Einbau mechanischer Wohnungslueftungen kompensiert werden kann. (orig.)

1996-10-01

The lichens, tritium and carbon 14 integrators; Les lichens, integrateurs de tritium et de carbone 14

We study a kinetic model for a system of two species of particles interacting via a repulsive long range potential and with a reservoir at fixed temperature. The interaction between the particles is modeled by a Vlasov term and the thermal bath by a Fokker-Planck term. We show that in the diffusive and sharp interface limit the motion of the interfaces at low temperature is described by a Stefan problem or a Mullins-Sekerka motion, depending on the time scale.

2004-01-01

Spin-up of He II in a cylindrical vessel of finite height

The present report concerns a research for the tritium and for the carbon 14 in lichens in a spirit of bio-indication: the first results appear in Daillant and al (2004 ) and additional results were presented to the congress B.I.O.M.A.P. in Slovenia, organized collectively by the institute Josef Stefan from Ljubljana and the international atomic energy agency from Vienna (Daillant and al 2003). (N.C.)

2007-07-01

Simulation of laser melting and evaporation of superconducting ceramics

The spin-up problem of He II in a cylindrical container of infinite and finite height is considered on the basis of the Hall-Vinen-Bekarevich-Khalatnikov equations. The boundary conditions include the assumption of the generation of superfluid vorticity at the walls of the container. In the lowest order approximation with respect to viscosity, the problem is reduced to a Stefan problem for a single diffusion-type equation. Examples of solutions are given which show that the method used gives a good insight into the physical development of the spin-up flow.

1990-01-01

Optimal Control of Thermo--Fluid Phenomena in Variable Domains

The peculiarities of pulsed laser melting and evaporation of the superconducting ceramics are analyzed by means of numerical simulation. The appearance of the overheated metastable states in solid and liquid phases is shown as a result of the phase front dynamics and volume nature of laser energy release. A method of dynamic adaptation for the multifront Stefan problem is proposed.

1994-11-01

Models in detail. Analysis and assessment of models and methods to determine the air quality along highways; Modellen onder de loep. Analyse en beoordeling van modellen en methoden voor de bepaling van de luchtkwaliteit langs snelwegen

This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an ...

2008-11-01

Numerical methods for solving problems with a free boundary. Chislennye metody resheniia zadach so svobodnoi granitsei

An overview is given of several computer models in use in the Netherlands to determine and analyze the quality of air and the effect of air pollution abatement measures. [Dutch] Voor het vaststellen van de luchtkwaliteit of het bepalen van het effect van emissiereducerende maatregelen op die luchtkwaliteit zijn in ons land meerdere computermodellen beschikbaar. In het kader van het Vooronderzoek Innovatieprogramma Luchtkwaliteit (VIPL) wilde het ministerie van Verkeer en Waterstaat meer inzicht in de betrouwbaarheid en specifieke eigenschappen van deze modellen. Deze studie geeft daarom een overzicht en analyse van de verschillen, overeenkomsten en voor- en nadelen van de meest gangbare Nederlandse computermodellen om de luchtkwaliteit rond snelwegen te bepalen. Dit zijn: Het Voorspellingssysteem Luchtkwaliteit Wegtraces (VLW); CAR-II; Het TNO-verkeersmodel; Het Heaven-model van TNO; Urbis (air); en NNM+ (KEMA-STACKS)

2003-12-15

Method for the approximate solution of a two-phase stefan problem with reverse motion of the front

Approximate methods are presented for solving nonlinear boundary value problems with an unknown (free) boundary, such as the Stefan problem in heat conductivity. Examples of this kind of problems in thermal physics, hydrodynamics, elasticity, and plasma physics are examined. Attention is given to the principal computational methods for solving stationary problems for second- and fourth-order elliptic equations, such as the domain transformation and penalty methods. To illustrate the capabilities of the methods presented here, examples of numerical solutions are presented for various specific applied problems. 255 references.

1987-01-01

Ground temperatures surrounding a molten fuel pool

Determination of the trajectory of a phase transition front moving in a forward or reverse direction is reduced to the solution of an ordinary differential equation. A numerical check of the results shows the method to be highly accurate. The method was used recently over a period of several years to solve various problems connected with the thawing of frozen rocks and their refreezing; among the problems considered was that of the ablation of rocks during the channeling of well, in which the method invariably proved its effectiveness. This furnishes a basis for recommending it for broader usage.

1988-03-01

Freezing phenomena in ice-water systems

In the analysis of the consequences of a hypothetical meltdown accident in an LMFBR, it is important to estimate the final location of the molten fuel pool in the concrete and ground underlying the reactor vessel. The GROWS program and the AYER program have been developed to calculate the final location of the molten fuel pool as the culmination of the transient analysis of this unusual Stefan problem but these programs require extensive computational resources. The solution is provided to the concrete and ground temperatures surrounding the stationary fuel pool and the related heat flux from the pool to the ground surface outside the containment building. This solution can be used to estimate the final location of the fuel pool and to check the end results of the sophisticated programs.

1977-06-01

Drop freezing on a substrate

The characteristics of solidification and melting are reviewed. The properties of water and ice and the phase diagram of water are discussed with special emphasis on ice density. A concise account of the freezing process and the Stefan problem is presented. To this end, the four stages of freezing are identified, supercooling, nucleation and the formation of dendritic ice, the growth of concentric rings of solid ice at 0{sup o}C and the final cooling of the solid ice are treated in some detail. The subject of bursting of pipes is given particular emphasis. Attention is drawn to a common misconception on pipe bursting and to misleading relationships for the computation of freezing time for ice blockage. Several current applications of melting and freezing systems are outlined. (author)

2002-09-01

Thermal and heat transfer characteristics in a latent heat storage system using lauric acid

The freezing of liquid in the form of a granule on a cooled substrate is considered. On the basis of a hypothesis regarding the form of the isotherms in the granule, an analytical solution of the Stefan problem is obtained for two limiting cases: when a/sub d/ >> a/sub s/ and a/sub d/ << a/sub s/, where a/sub s/ and a/sub d/ are the thermal conductivity of the substrate and drop, respectively. The results of calculating the crystallization times of the granules as a function of their dimensions (height and diameter) and the substrate temperature, and also the dynamics of temperature variation at the base of the granule in the course of crystallization, are in good agreement with the experimental data.

1988-07-01

The Stefan Problem Revisited: A Continuum Model of Frost Heave

The thermal and heat transfer characteristics of lauric acid during the melting and solidification processes were determined experimentally in a vertical double pipe energy storage system. In this study, three important subjects were addressed. The first one is temperature distributions and temporal temperature variations in the radial and axial distances in the phase change material (PCM) during phase change processes. The second one is the thermal characteristics of the lauric acid, which include total melting and total solidification times, the nature of heat transfer in melted and solidified PCM and the effect of Reynolds and Stefan numbers as inlet heat transfer fluid (HTF) conditions on the phase transition parameters. The final one is to calculate the heat transfer coefficient and the heat flow rate and also discuss the role of Reynolds and Stefan numbers on the heat transfer parameters. The experimental results proved that the PCM melts ...

2002-12-01

The Stefan problem solved via conjugate gradient-like iterative methods on a parallel vector machine

The classical Stefan problem describes the motion of a solidification front through a uniform half-space in response to a step change in temperature on its boundary. The predictions of such a model can be applied quite accurately to the freezing of water in a porous medium so long as the pore geometry remains unaltered by the passing solidification front. It is observed, however, that in fine-grained porous media, ice has a tendency to form in segregated horizontal bands, known as ice lenses, that disrupt the regular pattern of heat flow through their enhanced consumption of latent heat. This process, known as frost heave, causes significant ground deformation in regions subject to prolonged freezing, and is one of the most important weathering processes in polar and alpine regions. Recent improvements to our understanding of the mechanics of ice lens nucleation and growth are applied here to predict the conditions and characteristics of frost heave in a ...

2005-12-01

Study of Nordgren's equation of hydraulic fracturing

The aim of this paper is to illustrate the validity and efficiency of iterative methods for solving large linear systems arising from the finite element discretization of the equation governing conduction-controlled solidification processes. Starting from the basic enthalpy equation, two alternative formulations are obtained and fixed-grid finite element discretizations are developed. These discretizations yield a set of nonlinear equations that are linearized using the Newton-Raphson scheme. The linearized equations are used as a basis for evaluating different iterative methods of the conjugated gradient type. Symmetric scaling and incomplete factorization preconditioning of the linear equations are used to improve the convergence properties of the iterative methods. Vectorization and parallelization are also employed to make full use of the CRAY-2 supercomputer. The results indicate that the implementation of currently available iterative solvers leads to efficient solution ...

1991-01-01

Radius of thawing around an injection well and time of complete freezeback

A nonlinear partial differential equation modeling the propagation of a vertical hydraulic fracture first derived by Nordgren is studied. When properly posed, Nordgren's derivation constitutes a Stefan problem and requires another boundary condition-namely, that the velocity of the fluid at the crack tip equals the velocity of crack propagation. With this addition, Nordgren's similarity solution in the no-leakoff case is perfected by a power-series solution. New shut-in solutions are derived in the large-and-no-leakoff cases where the crack of the large-leakoff shut-in solution retracts and the crack of the no-leakoff shut-in solution extends forever. This study ignores the effect of crack-tip rock strength on crack propagation.

1990-08-01

Post-lens tear-film depletion due to evaporative dehydration of a soft contact lens

An approximate method of calculating the radius of thawing around an injection well is presented. The method is based on the assumption that for a cylindrical system the position of the phase interface in the Stefan problem can be approximated through two functions: one function determines the position of the melting-temperature isotherm in the problem without phase transitions and the second function does not depend on time. The adjusted heating time concept was used to describe the first function. The second function is a known analytical relationship and is expressed in terms of ice content, thermal properties of thawed/frozen formations, formation temperature and the temperature of the injected fluid. Simple approximate formulae are suggested to estimate the duration of the freezeback period. To verify the proposed formulae, the results of numerical solutions were used. An example which shows that the duration of the 'safety period' (free from freezing of water ...

2006-06-01

British Library Electronic Table of Contents (United Kingdom)

For a soft-contact-lens (SCL) wearer, corneal health and comfort are strongly influenced by water transport through the polymeric materials used in lens fabrication. In particular, evaporative water loss at the anterior lens surface is a potential cause of contact-lens dehydration and of post-lens tear-film depletion, which in turn, may lead to discomfort, dryness syndrome, and/or lens adhesion.We present a solution-diffusion model for transport of water through soft-contact-lens materials to mimic evaporative dehydration from a contact lens during blinking and to access possible SCL adhesion to the corneal surface under a variety of environmental conditions (e.g., wind speed and relative humidity). To describe the water-transport process, we use an extended version of the Maxwell-Stefan m...

2006-01-01

On the solid-fluid transition zone in welding analysis

Numerical modeling of scanning laser-induced melting, vaporization and resolidification in metals subjected to step heat flux input

Equilibrium and energy equations have been developed in describing the solid-fluid transition zone during the melting and solidification of the binary alloys. Due to the existence of the transition region exhibited both solid and fluid phases at the same material point from continuum point of view, mixture theory was utilized to analyze the region. Unlike the Stefan problem, the latent heat due to the phase change appears as a source term in the heat equation. The molten fluid is treated as a thermoviscous and incompressible fluid, whereas the solid is thermoviscoplastic described by the Bodner-Partom/Walker type of constitutive equations. Thermal mechanical behaviors of the solid and the fluid phases are determined separately because of insignificant mechanical interactions between them. Volume fractions of the phases are obtained according to the equilibrium phase diagram. The simulation process of the transition zone and the welding process was carried out by ...

1993-01-01

Numerical analysis of melting/solidification phenomena using a moving boundary problem analysis method X-FEM

We present a 1-D heat transfer, melting, vaporization and resolidification model describing the interaction of a scanning continuous-wave laser with a metal surface wherein the beam power is constant. A physical model based on the Stefan problem is developed with appropriate boundary conditions. The effects of processing parameters on process variables are investigated numerically by varying beam diameters, scan speeds and substrate temperatures for Nickel. Relations are derived for the times to initiate melting, to initiate vaporization, to reach maximum melting depth, for melting-resolidification, and for maximum melting and vaporization depths. Surface temperatures are compared with approximate closed form solutions. (Author)

2004-09-01

1 2 3 4

Analysis of the dynamics of coal char combustion with ignition and extinction phenomena: Shrinking core model

A numerical analysis method for melting/solidification phenomena has been developed to evaluate a feasibility of several candidate techniques in the nuclear fuel cycle. Our method is based on the eXtended Finite Element Method (X-FEM) which has been used for moving boundary problems. Key technique of the X-FEM is to incorporate signed distance function into finite element interpolation to represent a discontinuous gradient of the temperature at a moving solid-liquid interface. Construction of the finite element equation, the technique of quadrature and the method to solve the equation are reported here. The numerical solutions of the one-dimensional Stefan problem, solidification in a two-dimensional square corner and melting of pure gallium are compared to the exact solutions or to the experimental data. Through these analyses, validity of the newly developed numerical analysis method has been demonstrated. (author)

2008-06-01

A one-dimensional, two-phase model for direct methanol fuel cells - Part I: Model development and parametric study

Single-particle combustion of coal char is analyzed using a generalized shrinking core model. Finite volume method, which was earlier employed by the authors in solving moving boundary problems involving fluid-solid noncatalytic reactions in general, is used to solve fully transient mass and energy equations. The model takes into account convection and diffusion inside the particle as well as in the boundary layer. The computed results are compared with the experimental data of the authors for combustion of coal char in a fluidized bed combustor. The effects of parameters such as bulk temperature and initial particle radius on the combustion dynamics are examined. The phenomena of ignition and extinction are also investigated. Finally, the importance of Stefan flow, originating due to nonequimolar counterdiffusion, on combustion of coal char is analyzed.

2008-09-15

British Library Electronic Table of Contents (United Kingdom)

A one-dimensional, steady-state, two-phase direct methanol fuel cell (DMFC) model is developed to precisely investigate complex physiochemical phenomena inside DMFCs. In this model, two-phase species transport through the porous components of a DMFC is formulated based on Maxwell-Stefan multi-component diffusion equations, while capillary-induced liquid flow in the porous media is described by Darcy's equation. In addition, the model fully accounts for water and methanol crossover through the membrane, which is driven by the effects of electro-osmotic drag, diffusion, and the hydraulic pressure gradient. The developed model is validated against readily available experimental data in the literature. Then, a parametric study is carried out to investigate the effects of the operating temperat...

2010-01-01

The new 2.2 l ECOTEC aluminium engine by Opel; Der neue 2,2-l-ECOTEC-Aluminium-Motor von Opel

Enzyme-induced growth of silver nanoparticles studied on single particle level

The ECOTEC combustion system and the architecture of the new Opel 2.2 l aluminum engine have been configured to achieve low noise and exhaust emissions. This power unit, employed in Germany for the first time in the Astra Coupe, already complies with the Euro IV emissions standard. It features minimum maintenance requirements and a long operating life. The DOHC spark-ignition engine with four valves per cylinder has two chain-driven camshafts, valve gear with roller cam followers and hydraulic lash adjusters. Two chain driven balancer shafts have been integrated into the engine block. The cylinder head and block, lower crankcase, oil pan, and cylinder head cover are all made of aluminum. A modular concept makes it possible to adapt the engine effectively to different vehicle concepts and markets. (orig.) [German] Das ECOTEC-Verbrennungssystem und die Motorarchitektur des neuen 2,2-l-Aluminium-Triebwerks von Opel sind auf niedrige Geraeusch- und Abgasemissionen ausgelegt. Das in ...

2000-09-01

Total hemispherical emittance of niobium-1% zirconium fuel cladding for the SP-100 space reactor. Master's thesis

Based on their interesting properties, metal nanoparticles show the potential as an analytical tool in electronic (Burmeister et al. 2004), optical (Yguerabide and Yguerabide 1998), and catalytic applications (Liu 2006). Their characteristics depend on the composition, shape, and size of the single particles. These various properties are utilized in many different approaches such as optics, magnetics (Lang et al. 2007), and laser technology (Csaki et al. 2007). We investigated an alternative method for the synthesis of nanoparticles. In this case, an enzyme, horseradish peroxidase, induces a silver deposition and replaces a metal nanoparticle as the reaction seed. Depending on the reaction time, we could obtain particles in a range of few nanometers up to more than 250 nm. For a better understanding of the enzymatic silver deposition process, the silver particles produced by this process were analyzed by SEM, TEM, and atomic force microscopy (AFM) on a single ...

2009-05-15

Single-pulse excimer laser nanostructuring of silicon: A heat transfer problem and surface morphology

Total hemispherical emittance was measured for the SP-100 reactor fuel cladding alloy (Nb-l% Zr). Based on a standard test method (ASTM C 835-82), experiments were conducted on a reference sample of oxidized stainless steel and then on a sample of actual cladding. The sample is heated in a vacuum by passing DC current through it until reaching equilibrium. Measurements are made of the electrical power dissipated in the sample and of the surface temperature. Using the Stefan-Boltzmann Law and some key assumptions concerning conductive and radiative heat transfer, the measured quantities are used to calculate emittance. Calculated values for unoxidized cladding range from 0.159 +/- 5.35% at 913 K to 0.200 +/- 4.51% at 1091 K. Highest value measured after onset of visible oxidation was 0.339 +/- 3.92% at 1269 K.... SP-100, Reactor, Emittance, Niobium, Fuel cladding, Emissivity.

1992-12-01

Moving finite element codes in one and two dimensions. Final report

We present computer modeling along with experimental data on the formation of sharp conical tips on silicon-based three-layer structures that consist of a single-crystal Si layer on a 1 {mu}m layer of silica on a bulk Si substrate. The upper Si layers with thicknesses in the range of 0.8-4.1 {mu}m were irradiated by single pulses from a KrF excimer laser focused onto a spot several micrometers in diameter. The computer simulation includes two-dimensional time-dependent heat transfer and phase transformations in Si films that result from the laser irradiation (the Stefan problem). After the laser pulse, the molten material self-cools and resolidifies, forming a sharp conical structure, the height of which can exceed 1 {mu}m depending on the irradiation conditions. We also performed computer simulations for experiments involving single-pulse irradiation of bulk silicon, reported by other groups. We discuss conditions under which different types of structures (cones ...

2008-05-01

Interaction of energetic beams with metals and semiconductors - a computational approach

Many problems in physics necessitate the solution of equations which develop sharp gradients, such as shocks. These include atmospheric shocks near the earth's surface, plasma physics phenomena, both in the laboratory and in space, combustion, petroleum reservoir modelling, and light propagation in glass fibers. To deal with this situation, methods are needed which place a high density of nodes in the neighborhoods of the steep gradients. One of the most promising of these methods is the moving finite element method which was first invented by Miller. This approach, in which the nodes are moved so as to minimize the residual error, has been used successfully by Gelinas, Doss, and co-workers to study several different one-dimensional problems and shows great promise as well in dealing with two dimensions. A paper describing the one-dimensional results has already been published, and a paper describing the two-dimensional results is in preparation. The remainder of this report ...

1985-10-01

A boundary integral approach to unstable solidification

In a vacuum insulator, the narrow electron beam emitted from the cathode impinges on the anode and raises its temperature and also may produce high thermal stress. This high thermal stress, in conjuction with the surface electrostatic pressure may rupture the surface and detach particles from it. In this thesis, the interaction of high energy electron and laser beams with metals and semiconductors is investigated. The differential equations governing the physical processes involved in the interaction are solved by the finite element method. Effects of beam penetration into the material, variable beam reflectance at the surface, finite beam size and dependence of material properties on temperature are accounted for. The two-phase moving boundary problem, also known as the Stefan problem, is solved by an enthalpy formulation of the heat equation. Material deformation by thermal stresses caused by high temperature gradients and electrostatic forces induced by space ...

1984-01-01

Magnetic resonance imaging in the evaluation of pneumonia; Nachweis von pneumonischen Infiltraten mit der MRT

We consider the supercooled Stefan problem with a general anisotropic curvature- and velocity-dependent boundary condition on the moving interface. We present numerical methods, based on an integral equation formulation and including a new algorithm for moving curves with curvature-dependent velocity. These methods compute a periodic interface with {ital O}({Delta}{ital t}) accuracy, where {Delta}{ital t} is the time step. Previous work has been limited to short time spans and achieved slightly less than {ital O}({Delta}{ital t}{sup 1/2}) accuracy. Accurate numerical results are seen to agree with the predictions of linear stability theory. This agreement has eluded previous authors, because their numerical methods suffered from grid effects and their linear stability theory was incorrect. We study the long-time evolution of an unstable interface. Our computations exhibit the beginnings of a sidebranching instability when the boundary condition includes anisotropy ...

1989-12-01

Impacts of climate change in the Netherlands; Effecten van klimaatverandering in Nederland

Magnetic resonance imaging (MRI) of the lung is challenging because of substantial drawbacks. However, lung pathologies that are associated with increased attenuation values in CT enhance visualization in MRI: proton density is increased and tissue-air interfaces, resulting in susceptibility artifacts, are reduced in pneumonia, pneumonitis, edema, and carcinoma. On the other hand, many lung diseases result in shortness of breath, so that patients cannot hold their breath for long periods. Therefore, fast imaging techniques are required which should also allow for high spatial resolution so that small lesions can be detected. Calcifications and air pockets within lesions are not readily recognized with MRI. Thin section CT is standard for the diagnosis of pneumonia. With parallel imaging techniques, MRI examination of the lungs can be performed with short periods of breath holding, which allow for sub-centimeter resolution in the z-axis. Especially for follow-up examinations in ...

2006-04-15

Globalisation of the nuclear fuel cycle - impact of developments on fuel management

The main conclusion of the study on the title subject is that the impacts of climatic change in the Netherlands are still limited. However, the impacts will be stronger in the next decades and will be even problematic at the end of this century. In this book an overview is given of probable changes in the climate for the Netherlands, danger for flooding in specific areas of the Netherlands, changes of the nature, impacts for agriculture, tourism and recreation, and industry and businesses, and risks for public health. [Dutch] De effecten van klimaatverandering in Nederland zijn nu nog beperkt. Ze zullen echter de komende decennia toenemen, maar pas tegen het eind van deze eeuw problematisch worden. Dat is de hoofdboodschap van de titelstudie. De studie is opgesteld in samenwerking met een reeks instellingen, die zijn verenigd in het Platform Communicatie Klimaatverandering (PCCC). Het klimaat verandert: de zeespiegel stijgt, de afvoeren van de rivieren nemen toe. De natuur reageert al ...

2005-10-01

TRIGA reactor spent fuel pool under severe earthquake conditions

Nuclear energy will have to cope more and more with a rapid changing environment due to economic competitive pressure and the deregulatory progress. In current economic environment, utilities will have to focus strongly on the reduction of their total generation costs, covering the fuel cycle costs, which are only partly under their control. Developments in the fuel cycle will be in the short-term rather evolutionary addressing the current needs of utilities. However, within the context of sustainable development and more and more inclusion of externalities in energy generation costs, more performing developments in the fuel cycle could become important and feasible. A life-cycle design approach of the fuel cycle will be requested in order to cover all factors in order to decrease significantly the nuclear energy generation cost to complete with other alternative fuels in the long-term. This paper will report on some of the trends one could distinguish in the fuel cycle with emphasis ...

2000-02-01

Study of the mass of the electron neutrino in Japan

Supplemental criticality safety analysis of a pool type storage for TRIGA spent fuel at 'Jozef Stefan' Institute in Ljubljana, Slovenia, is presented. Previous results (Ravnik, M, Glumac, B., 1996) have shown that subcriticality is not guaranteed for some postulated accidents. To mitigate this deficiency, a study was made about replacing a certain number of fuel elements in the rack with absorber rods (Glumac, B., Ravnik, M., Logar, M., 1997) to lower the supercriticality probability, when the pitch is decreased to contact (as a consequence of a severe earthquake) in a square arrangement. The criticality analysis for the hexagonal contact pitch is presented in this paper, following the same scenario as outlined above. The Monte Carlo computer code MCNP4B with ENDF-B/VI library and detailed three dimensional geometry was used. First, the analysis about the influence of the number of triangular fuel piles on the bottom that could appear, if the fuel rack, made of ...

1998-07-01

An emerging field of high-velocity friction and its implication for dynamic fault motion during large earthquakes

This report describes a study of the mass of the electron neutrino using electron capture in {sup 163}Ho in Japan for the period from 1981 to 1994. This monograph has two purposes, one is to supplement the papers on the mass of the electron neutrino already published by us and another is to make a record on some details of our experiments for future. Electron capture in a nucleus takes place in a rather small space inside an atom, where atomic physics, nuclear physics and particle physics work closely together. Therefore, this study needed an intimate collaboration of atomic physicists, nuclear physicists and particle physicists. In addition, it was necessary for this study to use various fine techniques, including metallurgy, production of {sup 163}Ho activity, micro-analysis by wet chemistry, isotope-dilution mass spectrometry, undulator radiation source technology, the soft X-ray monochromator technology, a counting technique for very intense soft X-rays and so on. As a result, our ...

1996-02-01