The Classical Stefan Problem

This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives. Under suitable assumptions, a weak solution could be as good as a classical solution. In hyperbolic Stefan problems, the characteristic features of Stefan problems are present but unlike in Stefan problems, discontinuous solutions are allowed because of the hyperbolic nature of the heat equation. The numerical solutions of inverse Stefan problems, and the analysis of direct Stefan problems are so integrated that it is difficult to discuss one without referring to the other. So no strict line of demarcation can be identified between a classical Stefan problem and other similar problems. On the other hand, including every related problem in the domain of classical Stefan problem would require several volumes for their description. A suitable compromise has to be made. The basic concepts, modelling, and analysis of the classical Stefan problems have been extensively investigated and there seems to be a need to report the results at one place. This book attempts to answer that need.

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  • Author : S.C. Gupta
  • Publisher : Elsevier
  • Pages : 404 pages
  • ISBN : 008052916X
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKThe Classical Stefan Problem

The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S.C. Gupta
  • Publisher : Elsevier
  • Release : 22 October 2003
GET THIS BOOKThe Classical Stefan Problem

This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives.

The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S.C. Gupta
  • Publisher : Elsevier
  • Release : 27 July 2017
GET THIS BOOKThe Classical Stefan Problem

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for

The Stefan Problem

The Stefan Problem
  • Author : A.M. Meirmanov
  • Publisher : Walter de Gruyter
  • Release : 01 January 1992
GET THIS BOOKThe Stefan Problem

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board

Free Boundary Problems Involving Solids

Free Boundary Problems Involving Solids
  • Author : J M Chadam,Helen Rasmussen
  • Publisher : CRC Press
  • Release : 22 February 1993
GET THIS BOOKFree Boundary Problems Involving Solids

This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large

Mathematical Modeling Of Melting And Freezing Processes

Mathematical Modeling Of Melting And Freezing Processes
  • Author : V. Alexiades
  • Publisher : Routledge
  • Release : 02 May 2018
GET THIS BOOKMathematical Modeling Of Melting And Freezing Processes

This reference book presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems (LHTES), utilized in a wide range of heat transfer and industrial applications. This topic has spurred a growth in research into LHTES applications in energy conservation and utilization, space station power systems, and thermal protection of electronic equipment in hostile environments. Further, interest in mathematical modeling has increased with the speread of high powered

The One-Dimensional Heat Equation

The One-Dimensional Heat Equation
  • Author : John Rozier Cannon
  • Publisher : Cambridge University Press
  • Release : 28 December 1984
GET THIS BOOKThe One-Dimensional Heat Equation

This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.

The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S. C. Gupta (Ph. D., D. Sc.),S. C. Gupta
  • Publisher : Jai Press
  • Release : 24 January 2022
GET THIS BOOKThe Classical Stefan Problem

For example, the description of some phase-field models in Chapter 4 arose out of this need for a smooth transition between topics. In the mathematical formulation of Stefan problems, the curvature effects and the kinetic condition are incorporated with the help of the modified Gibbs-Thomson relation. On the basis of some thermodynamical and metallurgical considerations, the modified Gibbs-Thomson relation can be derived, as has been done in the text, but the rigorous mathematical justification comes from the fact that this relation

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
  • Author : Michiel Hazewinkel
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKEncyclopaedia of Mathematics

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather

Free Boundary Problems in Continuum Mechanics

Free Boundary Problems in Continuum Mechanics
  • Author : S.N. Antontsev,K.H. Hoffmann,A.M. Khludnev
  • Publisher : Birkhäuser
  • Release : 07 March 2013
GET THIS BOOKFree Boundary Problems in Continuum Mechanics

Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have

Proceedings of the Fourth European Conference on Mathematics in Industry

Proceedings of the Fourth European Conference on Mathematics in Industry
  • Author : U. Wacker,Walter Zulehner
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKProceedings of the Fourth European Conference on Mathematics in Industry

The Fourth ECMI Conference on Industrial Mathematics took place at Strobl in Aus tria, May 29-June 2, 1989. The conference was devoted to the exchange of ideas, models and methods from various fields of industrial applications of mathematics. About 140 people from 21 countries attended the meeting. The aim was to bring together peo ple from industry and from university. In this respect the organizers were only partly successful!. The participance of about 20 people from industry shows that there is still much work to

Free Boundary Problems

Free Boundary Problems
  • Author : Isabel Narra Figueiredo,Lisa Santos
  • Publisher : Springer Science & Business Media
  • Release : 11 January 2007
GET THIS BOOKFree Boundary Problems

This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.

Numerical Simulation in Physics and Engineering: Trends and Applications

Numerical Simulation in Physics and Engineering: Trends and Applications
  • Author : David Greiner,María Isabel Asensio,Rafael Montenegro
  • Publisher : Springer Nature
  • Release : 01 April 2021
GET THIS BOOKNumerical Simulation in Physics and Engineering: Trends and Applications

This book results from the XVIII Spanish-French School 'Jacques Louis Lions' on Numerical Simulation in Physics and Engineering, that took place in Las Palmas de Gran Canaria from 25th to 29th June 2018. These conferences are held biennially since 1984 and sponsored by the Spanish Society of Applied Mathematics (SEMA). They also have the sponsorship of the Société de Mathématiques Appliquées et Industrielles (SMAI) of France since 2008. Each edition is organized around several main courses and talks delivered by

Encyclopedia Of Thermal Packaging, Set 2: Thermal Packaging Tools (A 4-volume Set)

Encyclopedia Of Thermal Packaging, Set 2: Thermal Packaging Tools (A 4-volume Set)
  • Author : Anonim
  • Publisher : World Scientific
  • Release : 23 October 2014
GET THIS BOOKEncyclopedia Of Thermal Packaging, Set 2: Thermal Packaging Tools (A 4-volume Set)

Please click here for information on Set 1: Thermal Packaging Techniques Thermal and mechanical packaging -- the enabling technologies for the physical implementation of electronic systems -- are responsible for much of the progress in miniaturization, reliability, and functional density achieved by electronic, microelectronic, and nanoelectronic products during the past 50 years. The inherent inefficiency of electronic devices and their sensitivity to heat have placed thermal packaging on the critical path of nearly every product development effort in traditional, as well as

Elliptic and Parabolic Problems

Elliptic and Parabolic Problems
  • Author : Josef Bemelmans,Bernard Brighi,Alain Brillard,Michel Chipot,Francis Conrad,Itai Shafrir,Vanda Valente,Giorgio Vergara Caffarelli
  • Publisher : World Scientific
  • Release : 06 August 2002
GET THIS BOOKElliptic and Parabolic Problems

This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis. Contents:Rolduc:Models for Shape Memory Alloys Described by Subdifferentials of Indicator Functions (T Aiki & N Kenmochi)Local Stability Under Changes of Boundary Conditions at a Far Away Location (M Chipot & A Rougirel)Existence of Solutions of a Segregation Model Arising