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Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
Coulson and Richardson's Chemical Engineering has been fully revised and updated to provide practitioners with an overview of chemical engineering. Each reference book provides clear explanations of theory and thorough coverage of practical applications, supported by case studies. A worldwide team of editors and contributors have pooled their experience in adding new content and revising the old. The authoritative style of the original volumes 1 to 3 has been retained, but the content has been brought up to date and altered to be more useful to practicing engineers. This complete reference to chemical engineering will support you throughout your career, as it covers every key chemical engineering topic. Coulson and Richardson’s Chemical Engineering: Volume 1A: Fluid Flow: Fundamentals and Applications, Seventh Edition, covers momentum transfer (fluid flow) which is one of the three main transport processes of interest to chemical engineers. Covers momentum transfer (fluid flow) which is one of the three main transport processes of interest to chemical engineers Includes reference material converted from textbooks Explores topics, from foundational through technical Includes emerging applications, numerical methods, and computational tools
This book offers a tutorial on the response of materials to lasers, with an emphasis on simple, intuitive models with analytical and mathematical solutions, using techniques such as Laplace Transformation to solve most complex heat conduction equations. It examines the relationship between existing thermal parameters of simple metals and looks at the characteristics of materials and their properties in order to investigate and perform theoretical analysis from a heat conduction perspective mathematically. Topics discussed include optical reflectivity of metals at infrared (IR) wavelengths, laser-induced heat flow in materials, the effects of melting and vaporization, the impulse generated in materials by pulsed radiation, and the influence of the absorption in the blow-off region in irradiated material. Written for engineers, scientists, and graduate-level engineering and physics students, Thermal Effects of High Power Laser Energy on Materials provides an in-depth look at high energy laser technology and its potential industrial and commercial applications in such areas as precision cutting, LIDAR and LADAR, and communications. The knowledge gained from this allows you to apply spaced-based relay mirror in order to compensate laser beam divergence back to its original coherency by preventing further thermal blooming that takes place during laser beam propagation through the atmosphere. Examines the state-of-the-art in currently available high energy laser technologies; Includes computer codes that deal with the response of materials to laser radiation; Provides detailed mathematical solutions of thermal response to laser radiation.
This book takes a holistic approach to plasma physics and controlled fusion via Inertial Confinement Fusion (ICF) techniques, establishing a new standard for clean nuclear power generation. Inertial Confinement Fusion techniques to enable laser-driven fusion have long been confined to the black-box of government classification due to related research on thermonuclear weapons applications. This book is therefore the first of its kind to explain the physics, mathematics and methods behind the implosion of the Nd-Glass tiny balloon (pellet), using reliable and thoroughly referenced data sources. The associated computer code and numerical analysis are included in the book. No prior knowledge of Laser Driven Fusion and no more than basic background in plasma physics is required.
Nuclear engineers advancing the energy transition are understanding more about the next generation of nuclear plants; however, it is still difficult to access all the critical types, concepts, and applications in one location. Advanced Reactor Concepts (ARC): A New Nuclear Power Plant Perspective Producing Energy gives engineers and nuclear engineering researchers the comprehensive tools to get up to date on the latest technology supporting generation IV nuclear plant systems. After providing a brief history of this area, alternative technology is discussed such as electromagnetic pumps, heat pipes as control devices, Nuclear Air-Brayton Combined Cycles integration, and instrumentation helping nuclear plants to provide dispatchable electricity to the grid and heat to industry. Packed with examples of all the types, benefits, and challenges involved, Advanced Reactor Concepts (ARC) delivers the go-to reference that engineers need to advance safe nuclear energy as a low-carbon option. Describes theory and concepts on generation IV technology such as advanced reactor concepts (ARC) and electromagnetic pumps, and compares different types and sizes. Sets out the energy transition with critical carbon-free technology that can supplement intermittent power sources such as wind and solar. Explains alternative heat storage technology, including Nuclear Air-Brayton Combined Cycles. Introduces advanced main instrumentation systems for in-core probes.
The rapid growth of modern industry has resulted in a growing demand for construction materials with excellent operational properties. However, the improved features of these materials can significantly hinder their manufacture and, therefore, they can be defined as hard-to-cut. The main difficulties during the manufacturing/processing of hard-to-cut materials are attributed especially to their high hardness and abrasion resistance, high strength at room or elevated temperatures, increased thermal conductivity, as well as resistance to oxidation and corrosion. Nowadays, the group of hard-to-cut materials is extensive and still expanding, which is attributed to the development of a novel manufacturing techniques (e.g., additive technologies). Currently, the group of hard-to-cut materials mainly includes hardened and stainless steels, titanium, cobalt and nickel alloys, composites, ceramics, as well as the hard clads fabricated by additive techniques. This Special Issue, “Advances in Hard-to-Cut Materials: Manufacturing, Properties, Process Mechanics and Evaluation of Surface Integrity”, provides the collection of research papers regarding the various problems correlated with hard-to-cut materials. The analysis of these studies reveals the primary directions regarding the developments in manufacturing methods, characterization, and optimization of hard-to-cut materials.
Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Mathematical modeling - the ability to apply mathematical concepts and techniques to real-life systems has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the challenging problems sections found at the ends of several chapters.