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
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2. Thermodynamical and Metallurgical Aspects of Stefan Problems
3. Extended Classical Formulations of n-phase Stefan Problems with n>1
4. Stefan Problem with Supercooling: Classical Formulation and Analysis
5. Superheating Due to Volumetric Heat Sources: Formulation and Analysis
6. Steady-State and Degenerate Classical Stefan Problems
7. Elliptic and Parabolic Variational Inequalities
8. The Hyperbolic Stefan Problem
9. Inverse Stefan Problems
10. Analysis of the Classical Solutions of Stefan Problems
11. Regularity of the Weak Solutions of Some Stefan Problems
12. Quasi-Analytical Solutions and Methods
Professor S.C. Gupta retired in 1997 from the Department of Mathematics, Indian Institute of Science, Bangalore, India. He holds a PhD in Solid Mechanics and a DSc in "Analytical and Numerical Solutions of Free Boundary Problems. His areas of research are inclusion and inhomogeneity problems, thermoelasticity, numerical computations, analytical and numerical solutions of free boundary problems and Stefan problems. He has published numerous articles in reputed international journals in many areas of his research.