The Classical Stefan Problem

1st Edition

basic concepts, modelling and analysis

Print ISBN: 9780444510860
eBook ISBN: 9780080529165
Imprint: JAI Press
Published Date: 22nd October 2003
Page Count: 404
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Table of Contents

Chapter 1. The Stefan Problem and its Classical Formulation
1.1 Some Stefan and Stefan-like Problems
1.2 Free Boundary Problems with Free Boundaries of Codimension- two
1.3 The Classical Stefan Problem in One-dimension and the Neumann Solution
1.4 Classical Formulation of Multi-dimensional Stefan Problems
1.4.1 Two-Phase Stefan problem in multipledimensions
1.4.2 Alternate forms of the Stefan condition
1.4.3 The Kirchhoff's transformation
1.4.4 Boundary conditions at the fixed boundary
1.4.5 Conditions at the free boundary
1.4.6 The classical solution
1.4.7 Conservation laws and the motion of the melt
Chapter 2. Thermodynamical and Metallurgical Aspects of Stefan Problems
2.1 Thermodynamical Aspects
2.1.1 Microscopic and macroscopic models
2.1.2 Laws of classical thermodynamics
2.1.3 Some thermodynamic variables and thermal parameters
2.1.4 Equilibrium temperature; Clapeyron's equation
2.2 Some Metallurgical Aspects of Stefan Problems
2.2.1 Nucleation and supercooling
2.2.2 The effect of interface curvature
2.2.3 Nucleation of melting, effect of interface kinetics, and glassy solids
2.3 Morphological Instability of the Solid-Liquid Interface
2.4 Non-material Singular Surface : Generalized Stefan Condition
Chapter 3. Extended Classical Formulations of n-phase Stefan Problems with n>1
3.1 One-phase Problems


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© JAI Press 2003
JAI Press
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The book is well organized, so that, in spite of its complexity, the exposition is seemingly effortless and reading is greatly facilitated by a very judicions mixing of phemenomenology and mathematics. A book like this, bridging physics and mathematics in a concrete and readable way, was very much needed. Prof. Gupta's book fulfills that task nicely."
Antonio Fasano (Firenze) in: Zentralblatt MATH Database 1931 - 2005.