Free [2021] And Moving Boundary Problems Crank Pdf
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Free And Moving Boundary Problems Crank Pdf: A Comprehensive Guide
Free and moving boundary problems are mathematical problems that involve finding the shape and position of a boundary that separates two or more regions with different physical properties. These problems arise in many fields of science and engineering, such as hydrology, metallurgy, chemical engineering, soil science, molecular biology, materials science, and steel and glass production.
One of the most authoritative books on this topic is Free and Moving Boundary Problems by John Crank, published by Oxford University Press in 1984. This book provides a wide-ranging and detailed account of the formulation, analysis, and numerical solution of various types of free and moving boundary problems. It covers topics such as Stefan problems, Hele-Shaw flows, phase change problems, solidification and melting problems, seepage problems, variational inequalities, and more. It also discusses modern computer techniques that can handle multidimensional and multiphase practical problems.
If you are looking for a free and moving boundary problems crank pdf, you can find it online on several websites. However, you should be aware that some of these websites may not have the permission to distribute the book or may contain viruses or malware. Therefore, it is advisable to download the pdf only from trusted sources or purchase the book from reputable online or offline bookstores.
In this article, we will give you a brief overview of the contents of the book and some of its main features. We will also provide you with some links where you can find more information about the book and its author.
Contents of the Book
The book consists of 12 chapters and 3 appendices. The chapters are organized as follows:
Chapter 1: Introduction. This chapter gives a general introduction to free and moving boundary problems and their applications. It also defines some basic concepts and notation used throughout the book.
Chapter 2: Formulation. This chapter presents the mathematical formulation of various types of free and moving boundary problems in terms of partial differential equations, boundary conditions, initial conditions, and compatibility conditions.
Chapter 3: Analytical Solutions. This chapter discusses some analytical methods for solving free and moving boundary problems, such as similarity solutions, integral methods, perturbation methods, asymptotic methods, and transform methods.
Chapter 4: Numerical Methods for One-Dimensional Problems. This chapter describes some numerical methods for solving one-dimensional free and moving boundary problems, such as finite difference methods, finite element methods, method of lines, method of characteristics, front-fixing methods, marker methods, and enthalpy methods.
Chapter 5: Numerical Methods for Two-Dimensional Problems. This chapter extends the numerical methods for one-dimensional problems to two-dimensional problems. It also introduces some special techniques for dealing with curved boundaries, such as coordinate transformations, grid generation methods, boundary-fitted grids, adaptive grids, and immersed boundary methods.
Chapter 6: Numerical Methods for Three-Dimensional Problems. This chapter further extends the numerical methods for two-dimensional problems to three-dimensional problems. It also discusses some challenges and difficulties that arise in three-dimensional problems, such as computational complexity, stability issues, accuracy issues, convergence issues, and visualization issues.
Chapter 7: Stefan Problems. This chapter focuses on a specific class of free and moving boundary problems that involve phase change phenomena. It covers topics such as one-phase Stefan problems,
two-phase Stefan problems,
mushy zone Stefan problems,
nonlinear Stefan problems,
convection-diffusion Stefan problems,
and Stefan problems with surface tension.
Chapter 8: Hele-Shaw Flows. This chapter focuses on another specific class of free and moving boundary problems that involve viscous flows in narrow gaps between two plates. It covers topics such as basic Hele-Shaw flows,
Hele-Shaw flows with injection or suction,
Hele-Shaw flows with surface tension,
Hele-Shaw flows with gravity,
Hele-Shaw flows with chemical reactions,
and Hele-Shaw flows with phase change.
Chapter 9: Solidification and Melting Problems. This chapter focuses on another specific class of free and moving boundary problems that involve solidification or melting processes in materials science. a474f39169