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An inverse solidification of pure substance problem in two dimensions

K. Ivaz, T. Nikazad
2005 Applied Mathematics Letters  
This paper is concerned with an inverse problem involving a two-phase moving boundary in two dimensional solidification of pure substance.  ...  Emamizadeh for making valuable comments on the primary version of the paper.  ...  The term "pure substance" is an idealization which allows to neglect the mass diffusion process. In the consequence, solidification is driven by the temperature evolution only.  ... 
doi:10.1016/j.aml.2004.07.030 fatcat:ved4omhryzcijnwecphqzfylxm

Unified derivation of phase-field models for alloy solidification from a grand-potential functional

Mathis Plapp
2011 Physical Review E  
In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found.  ...  In this framework, a complete analogy with phase-field models for the solidification of a pure substance can be established.  ...  ISOTHERMAL ALLOY SOLIDIFICATION A binary alloy is a mixture of two pure substances A and B.  ... 
doi:10.1103/physreve.84.031601 pmid:22060379 fatcat:s7q47or64zgx7kvqisqrk2psei

The phase field technique for modeling multiphase materials

I Singer-Loginova, H M Singer
2008 Reports on progress in physics (Print)  
Then we address in detail dendritic and directional solidification of pure and multicomponent alloys, effects of natural convection and forced flow, grain growth, nucleation, solid-solid phase transformation  ...  In this method, the interface between two phases (e.g. solid and liquid) is treated as a region of finite width having a gradual variation of different physical quantities, i.e. it is a diffuse interface  ...  We are grateful to Professor Bilgram, Swiss Federal Institute of Technology ETH, Zurich, Switzerland for the financial support provided.  ... 
doi:10.1088/0034-4885/71/10/106501 fatcat:4hcyo2spabc23dtzaaquy2kf7m

Solidification problems by the boundary element method

Nicholas Zabaras, Subrata Mukherjee
1994 International Journal of Solids and Structures  
Emphasis is placed on two-dimensional examples. The second part of this paper provides a methodology for the solution of an inverse design Stefan problem.  ...  This paper elaborates on the analysis and design of the solidification of pure metais.  ...  Acknowledgements-N.Z. acknowledges NSF support of his inverse solidification work under grant CRT-8802069 to the University of Minnesota and grant CTS-9115438 to Cornell University.  ... 
doi:10.1016/0020-7683(94)90218-6 fatcat:lplteiceezdi7p4tnrp6uzvsfm

Remarks on some open problems in phase-field modelling of solidification

Mathis Plapp
2011 Philosophical Magazine  
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches.  ...  First, thin-interface limits of two-sided phase-field models are examined, and it is shown that the antitrapping current is in general not sufficient to remove all thin-interface effects.  ...  Orientation-field models for pure substances in two dimensions that work with a single phase field, an orientation field (the local angle of the crystalline structure with respect to a fixed coordinate  ... 
doi:10.1080/14786435.2010.486757 fatcat:tsadcacf45eqnn6yjftvoyshju

Interaction of porosity with a planar solid/liquid interface

Adrian V. Catalina, Subhayu Sen, Doru M. Stefanescu, William F. Kaukler
2004 Metallurgical and Materials Transactions. A  
A two-dimensional numerical model able to accurately track sharp SL interfaces during solidification of pure metals and alloys is proposed.  ...  In this article, an investigation of the interaction between gas porosity and a planar solidniquid (SL) interface is reported.  ...  Samples with typical dimensions of 19 X 4 X 1 mm are placed in the cavity of an X-ray transparent boron nitride crucible.  ... 
doi:10.1007/s11661-004-0260-z fatcat:ngee7naunbagjjm4fwu6n5qhlu

A Front-Tracking Method for Dendritic Solidification

Damir Juric, Grétar Tryggvason
1996 Journal of Computational Physics  
dendritic solidification of pure substances.  ...  The spective. method is based on a finite difference approximation of the heat The process of solidification of a pure substance can equation and explicit tracking of the liquid-solid interface.  ...  From the general method they identify an optiplest case of solidification of a pure substance.  ... 
doi:10.1006/jcph.1996.0011 fatcat:e5ffasvnwfhv3i4nvplglhm5ba

Estimatinig Impurities by Means of the Melting Point Curve

W. P. White
1919 The Journal of Physical Chemistry  
The relation of V to W depends on the form of the double pointed figure CD, which is a characteristic of the combination of substances in question.  ...  Impurities may form solid solutions, or only eutectics, and the crystallization phenomena have significant differences in the two cases.  ...  did solidify, And it is this total heat of solidification of the perfectly pure substance which will be most convenient in the subsequent operations.  ... 
doi:10.1021/j150203a005 fatcat:32ieclzw5vgaxm4cj3evjdryqm

A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Domingo Alberto Tarzia
2000 MAT Serie A  
., "An inverse finite element method for pure and binary solidification problems", J.Comput.Phys., 130 (1997), pp.243-255.  ...  Chemical reactions between two substances II.2.6. Other free boundary problems for the heat equation II.2.6.1. Of an implicit type II.2.6.2.  ... 
doi:10.26422/mat.a.2000.2.tar fatcat:ikpa45typfghzfbj5hhb6dds5q

Simulation of solid deformation during solidification: Compression of a single dendrite

M. Yamaguchi, C. Beckermann
2013 Acta Materialia  
The full model is then applied to simulate in two dimensions the compression of a single dendrite of a pure substance growing in an undercooled melt.  ...  A method is developed to numerically simulate coupled solidification and deformation of dendrites. Dendritic solidification is modeled using the phase-field method.  ...  Acknowledgements This work was financially supported, in part, by NASA under grant no. NNX10AV35G.  ... 
doi:10.1016/j.actamat.2013.03.030 fatcat:cm57u4kkl5afnc3a3gnpu647xu

Thermal Performance Enhancement of Phase Change Materials (PCMs) by Using Metal Foams

Ihsan Y. Hussain, Marwah Abdulkareem Jasim
2017 مجلة النهرين للعلوم الهندسية  
An investigation of thermal conductivity enhancement, melting and solidification processes of Phase Change Materials (PCMs) by using metal foams has been carried out.  ...  Two models have been used in the experiments, model I for measuring the effective thermal conductivity of metal foam embedded in paraffin wax, and model II used as a small scale thermal energy storage  ...  for the same heat flux. 3-Two types of metal foams were used 10 Figure 1 :Figure 2 :Figure 3 : 123 Diagram Model I Geometry (all dimensions are in mm) Model II Geometry (all dimensions are in mm)  ... 
doaj:967c74b24c9f483dab980e8c06833835 fatcat:woinhtv7djbirisaic5w4v6wpu

Page 6274 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
Russian summary) Direct and inverse problems in chemical kinetics ( Russian), 154-175, 286, VO ““Nauka’’, Novosibirsk, 1993.  ...  5-ANU; Canberra) ; Singleton, David (5-ANU-SC; Canberra) Travelling waves in phase field models of solidification.  ... 

A Simple Level Set Method for Solving Stefan Problems

S. Chen, B. Merriman, S. Osher, P. Smereka
1997 Journal of Computational Physics  
physical features of into the liquid phase in a fingerlike or dendritic fashion. dendritic solidification.  ...  Heat is released at the solid/liquid for capturing the front between solid and liquid phases of a pure interface into the liquid region. Undercooling drives the substance.  ...  different phases Before describing some of the numerical approaches of a pure substance.  ... 
doi:10.1006/jcph.1997.5721 fatcat:vihutafxjzgytlmlsjlnmfvq3m

Change of Phase under Pressure. I. The Phase Diagram of Eleven Substances with Especial Reference to the Melting Curve

P. W. Bridgman
1914 Physical Review  
As the liquid crystallizes the pure substance separates, leaving an excess of.impurity in the neighborhood of the freshly formed crystal.  ...  Two crystallizations of acetophenone did not raise the freezing point more than o.5', from I9. x' to z9. 6', although the pure substance melts at ao.g'.  ... 
doi:10.1103/physrev.3.126 fatcat:7f6e3udgxbd5lgzt4iqmijiuty

Crossover from diffusion-limited to kinetics-limited growth of ice crystals

A.A. Shibkov, M.A. Zheltov, A.A. Korolev, A.A. Kazakov, A.A. Leonov
2005 Journal of Crystal Growth  
Experimental study of the free growth of an ice crystal into a supercooled pure water film is presented.  ...  dimension d f of the whole dendrite as functions of initial supercooling of water.  ...  Therefore, at higher supercooling, an ice crystal grows mainly in kinetic regime of solidification.  ... 
doi:10.1016/j.jcrysgro.2005.08.007 fatcat:tbdynjelffhvrl76zecvbq6pla
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