This text provides a modern introduction to the mathematical formulation and physical applications of Stefan problems. With a careful balance of theory and practice, it is suitable for both graduate students and experienced researchers in applied math, engineering, physics, and chemistry. The formulation of the Stefan problem and several analytical and approximate solution methods are described in the first three chapters. Applied mathematical techniques needed for later chapters, such as non-dimensionalization, perturbation methods, and lubrication theory, are also covered. The remaining chapters are more specialized and explore formulations going beyond the classical Stefan problem, for example where the material properties and phase change temperatures vary. The theory is always motivated by physical situations and examples: phase change with a flowing liquid in the context of microvalves and ice accretion on aircraft; the solidification of a supercooled liquid, the melting or growth of nanoparticles and nanocrystals and phase change when the heat flow no longer follows Fourier’s law.
Introduction.- Exact and approximate solutions.- Solidification of a
thin liquid layer.- Variable property Stefan problem.- Variable interface
conditions.- Non-Fourier Stefan problems.- Hints to Exercises.- Index.
Tim Myers is a Senior Researcher at the Centre de Recerca Matemàtica in Barcelona, Adjunct Professor at the Universitat Politècnica de Catalunya, and Adjunct Professor of Industrial Mathematics at the University of Limerick. Previously he has worked in universities in the UK, South Africa, Australia, Canada, Argentina and South Korea. He has over 30 years of experience in applying mathematics to practical problems and, for now, is focussed on environmental applications. He is currently the co-ordinator for all European Study Groups with Industry and involved in a number of initiatives to spread practical mathematics to the Global South.
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