The Classical Stefan Problem

Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods

S.C. Gupta

• Publisher: Elsevier
• Year: 2017
• eBook ISBN: 9780444635822
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides fundamental theory, concepts, modelling and analysis of the physical, mathematical, thermodynamical and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems involving 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 an in-depth background reading on theorems. This new edition includes more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems.- Provides both the phenomenology and mathematics of Stefan problems- Bridges physics and mathematics in a concrete and readable manner- Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading- Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• List of Symbols
• Preface to the New Edition
• Preface
• Acknowledgements
• Chapter 1: The Stefan Problem and Its Classical Formulation
• Chapter 2: Thermodynamical and Metallurgical Aspects of Stefan Problems
• Chapter 3: Extended Classical Formulations of n-Phase Stefan Problems With n ≥ 1
• Chapter 4: Stefan Problem With Supercooling: Classical Formulation and Analysis
• Chapter 5: Superheating due to Volumetric Heat Sources: The Formulation and Analysis
• Chapter 6: Steady-State and Degenerate Classical Stefan Problems
• Chapter 7: Elliptic and Parabolic Variational Inequalities
• Chapter 8: The Hyperbolic Stefan Problem
• Chapter 9: Inverse Stefan Problems
• Chapter 10: Analysis of the Classical Solutions of Stefan Problems
• Chapter 11: Regularity of the Weak Solutions of Some Stefan Problems
• Chapter 12: Quasi-Analytical Solutions and Methods
• Appendix A: Preliminaries
• Appendix B: Some Function Spaces and Norms
• Appendix C: Fixed Point Theorems and Maximum Principles
• Appendix D: Sobolev Spaces
• Bibliography
• Index