The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies.

This series of books forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations such as the incompressible and compressible NavierStokes equations. The main emphasis in the first volume is on the mathematical analysis of incompressible models. The second volume is an attempt to achieve a mathematical understanding of compressible Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes entirely new material on compactness properties of solutions for the Cauchy problem, the existence and regularity of stationary solutions, and the existence of global weak solutions. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.

One of the most challenging topics in applied mathematics over the past decades has been the developent of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc lead to such equations when formulated in mathematical terms. However, despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogenous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contiatns many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University of Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.

Microscale and Nanoscale Heat Transfer: Analysis, Design, and Applications features contributions from prominent researchers in the field of micro- and nanoscale heat transfer and associated technologies and offers a complete understanding of thermal transport in nano-materials and devices. Nanofluids can be used as working fluids in thermal systems; the thermal conductivity of heat transfer fluids can be increased by adding nanoparticles in fluids. This book provides details of experimental and theoretical investigations made on nanofluids for use in the biomechanical and aerospace industries. It examines the use of nanofluids in improving heat transfer rates, covers the numerical approaches for computational fluid dynamics (CFD) simulation of nanofluids, and reviews the experimental results of commonly used nanofluids dispersed in both spherical and nonspherical nanoparticles. It also focuses on current and developing applications of microscale and nanoscale convective heat transfer. In addition, the book covers a wide range of analysis that includes: Solid-liquid interface phonon transfer at the molecular level The validity of the continuum hypothesis and Fourier law in nanochannels Conventional methods of using molecular dynamics (MD) for heat transport problems The molecular dynamics approach to calculate interfacial thermal resistance (ITR) A review of experimental results in the field of heat pipes and two-phase flows in thermosyphons Microscale convective heat transfer with gaseous flow in ducts The application of the lattice Boltzmann method for thermal microflows A numerical method for resolving the problem of subcooled convective boiling flows in microchannel heat sinks Two-phase boiling flow and condensation heat transfer in mini/micro channels, and more Microscale and Nanoscale Heat Transfer: Analysis, Design, and Applications addresses the need for thermal packaging and management for use in cooling electronics and serves as a resource for researchers, academicians, engineers, and other professionals working in the area of heat transfer, microscale and nanoscale science and engineering, and related industries.

Contains Fluid Flow Topics Relevant to Every Engineer Based on the principle that many students learn more effectively by using solved problems, Solved Practical Problems in Fluid Mechanics presents a series of worked examples relating fluid flow concepts to a range of engineering applications. This text integrates simple mathematical approaches that clarify key concepts as well as the significance of their solutions, and fosters an understanding of the fundamentals encountered in engineering. Comprised of nine chapters, this book grapples with a number of relevant problems and asks two pertinent questions to extend understanding and appreciation: What should we look out for? and What else is interesting? This text can be used for exam preparation and addresses problems that include two-phase and multi-component flow, viscometry and the use of rheometers, non-Newtonian fluids, and applications of classical fluid flow principles. While the author incorporates terminology recognized by all students of engineering and provides a full understanding of the basics, the book is written for engineers who already have a rudimentary understanding and familiarity of fluid flow phenomena. It includes engineering concepts such as dimensionless numbers and requires a fluency in basic mathematical skills, such as differential calculus and the associated application of boundary conditions to reach solutions. Solved Practical Problems in Fluid Mechanics thoroughly explains the concepts and principles of fluid flow by highlighting various problems frequently encountered by engineers with accompanying solutions. This text can therefore help you gain a complete understanding of fluid mechanics and draw on your own practical experiences to tackle equally tricky problems.

Reactive flows encompass a broad range of physical phenomena, interacting over many different time and space scales. Such flows occur in combustion, chemical lasers, the earth's oceans and atmosphere, and in stars. Because of a similarity in their descriptive equations, procedures for constructing numerical models of these systems are also similar, and these similarities can be exploited. Moreover, using the latest technology, what were once difficult and expensive computations can now be done on desktop computers. This new edition of a highly successful book presents algorithms useful for reactive flow simulations, describes trade-offs involved in their use, and gives guidance for building and using models of complex reactive flows. It takes account of the explosive growth in computer technology and the greatly increased capacity for solving complex reactive-flow problems that has occurred since the previous edition was published more than fifteen years ago. An indispensable guide on how to construct, use, and interpret numerical simulations of reactive flows, this book will be welcomed by advanced undergraduate and graduate students, and a wide range of researchers and practitioners in engineering, physics, and chemistry.

Waves and oscillations are found in large scales (galactic) and microscopic scales (neutrino) in nature. Their dynamics and behavior heavily depend on the type of medium through which they propagate. Waves and Oscillations in Nature: An Introduction clearly elucidates the dynamics and behavior of waves and oscillations in various mediums. It presents different types of waves and oscillations that can be observed and studied from macroscopic to microscopic scales. The book provides a thorough introduction for researchers and graduate students in assorted areas of physics, such as fluid dynamics, plasma physics, optics, and astrophysics. The authors first explain introductory aspects of waves and electromagnetism, including characteristics of waves, the basics of electrostatics and magnetostatics, and Maxwell's equations. They then explore waves in a uniform media, waves and oscillations in hydrodynamics, and waves in a magnetized medium for homogeneous and nonhomogeneous media. The book also describes types of shock waves, such as normal and oblique shocks, and discusses important details pertaining to waves in optics, including polarization from experimental and observational points of view. The book concludes with a focus on plasmas, covering different plasma parameters, quasilinear and nonlinear aspects of plasma waves, and various instabilities in hydrodynamics and plasmas.

First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineering

From the foreword to the third edition written by Charles Meneveau: ..". this meticulously assembled and significantly enlarged description of the many aspects of LES will be a most welcome addition to the bookshelves of scientists and engineers in fluid mechanics, LES practitioners, and students of turbulence in general."

Many diverse materials, from man-made plastics to slurry, behave in ways that cannot be predicted using straightforward 'classical' equations. This book provides a guide, with examples, for those who wish to make predictions about the mechanical and thermal behaviour of non-Newtonian materials in engineering and processing technology. There is an emphasis on the practical solution of problems using computer methods, and on the correlation between theory and experimental work.

The theory of water waves has been a source of intriguing and often difficult mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and non-linear water-wave theory. This sets the ground for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and help to make this an ideal text for a beginning graduate course on water waves.

Based on the author's many years of lectures and tutorials at Novosibirsk State University and the University of Manchester, Physics of Continuous Media: Problems and Solutions in Electromagnetism, Fluid Mechanics and MHD, Second Edition takes a problems-based approach to teaching continuous media. The book's problems and detailed solutions make it an ideal companion text for advanced physics and engineering courses. Suitable for any core physics program, this revised and expanded edition includes a new chapter on magnetohydrodynamics as well as additional problems and more detailed solutions. Each chapter begins with a summary of the definitions and equations that are necessary to understand and tackle the problems that follow. The text also provides numerous references throughout, including Landau and Lifshitz's famous course of theoretical physics and original journal publications.

This book offers a practical, application-oriented introduction to computational fluid dynamics (CFD), with a focus on the concepts and principles encountered when using CFD in industry. Presuming no more knowledge than college-level understanding of the core subjects, the book puts together all the necessary topics to give the reader a comprehensive introduction to CFD. It includes discussion of the derivation of equations, grid generation and solution algorithms for compressible, incompressible and hypersonic flows. The final two chapters of the book are intended for the more advanced user. In the penultimate chapter, the special difficulties that arise while solving practical problems are addressed. Distinction is made between complications arising out of geometrical complexity and those arising out of the complexity of the physics (and chemistry) of the problem. The last chapter contains a brief discussion of what can be considered as the Holy Grail of CFD, namely, finding the optimal design of a fluid flow component. A number of problems are given at the end of each chapter to reinforce the concepts and ideas discussed in that chapter. CFD has come of age and is widely used in industry as well as in academia as an analytical tool to investigate a wide range of fluid flow problems. This book is written for two groups: for those students who are encountering CFD for the first time in the form of a taught lecture course, and for those practising engineers and scientists who are already using CFD as an analysis tool in their professions but would like to deepen and broaden their understanding of the subject.

The advancements in micro- and nano-fabrication techniques, especially in the last couple of decades, have led research communities, over the world, to invest unprecedented levels of attention on the science and technology of micro- and nano-scale devices and the concerned applications. With an intense focus on micro- and nanotechnology from a fluidic perspective, Microfluidics and Microscale Transport Processes provides a broad review of advances in this field. A comprehensive compendium of key indicators to recent developments in some very active research topics in microscale transport processes, it supplies an optimal balance between discussions of concrete applications and development of fundamental understanding. The chapters discuss a wide range of issues in the sub-domains of capillary transport, fluidic resistance, electrokinetics, substrate modification, rotational microfluidics, and the applications of the phenomena of these sub-domains in diverse situations ranging from non-biological to biological ones like DNA hybridization and cellular biomicrofluidics. The book also addresses a generic problem of particle transport in nanoscale colloidal suspensions and includes a chapter on Lattice-Boltzmann methods for phase-changing problems which represents a generic particle based approach that may be useful to address many microfluidic problems of interdisciplinary relevance.

This book covers specific aspects of submarine hydrodynamics in a very practical manner. The author reviews basic concepts of ship hydrodynamics and goes on to show how they are applied to submarines, including a look at the use of physical model experiments. The book is intended for professionals working in submarine hydrodynamics, as well as for advanced students in the field. This revised edition includes updated information on empirical methods for predicting the hydrodynamic manoeuvring coefficients, and for predicting the resistance of a submarine. It also includes new material on how to assess propulsors, and includes measures of wake distortion, which has a detrimental influence on propulsor performance. Additional information on safe manoeuvring envelopes is also provided. The wide range of references has been updated to include the latest material in the field.

Wax Deposition: Experimental Characterizations, Theoretical Modeling, and Field Practices covers the entire spectrum of knowledge on wax deposition. The book delivers a detailed description of the thermodynamic and transport theories for wax deposition modeling as well as a comprehensive review of laboratory testing for the establishment of appropriate field control strategies. Offering valuable insight from academic research and the flow assurance industry, this balanced text: Discusses the background of wax deposition, including the cause of the phenomenon, the magnitude of the problem, and its impact on petroleum production Introduces laboratory techniques and theoretical models to measure and predict key parameters of wax precipitation, such as the wax appearance temperature and the wax precipitation curve Explains how to conduct and interpret laboratory experiments to benchmark different wax deposition models, to better understand wax deposition behaviors, and to predict wax deposit growth for the field Presents various models for wax deposition, analyzing the advantages and disadvantages of each and evaluating the differences between the assumptions used Provides numerous examples of how field management strategies for wax deposition can be established based on laboratory testing and modeling work Wax Deposition: Experimental Characterizations, Theoretical Modeling, and Field aids flow assurance engineers in identifying the severity and controlling the problem of wax deposition. The book also shows students and researchers how fundamental principles of thermodynamics, heat, and mass transfer can be applied to solve a problem common to the petroleum industry.

This book introduces methodologies for subsurface imaging based upon asymptotic and trajectory-based methods for modeling fluid flow, transport and deformation. It describes trajectory-based imaging from its mathematical formulation, through the construction and solution of the imaging equations, to the assessment of the accuracy and resolution associated with the image. Unique in its approach, it provides a unified framework for the complete spectrum of physical phenomena from wave-like hyperbolic problems to diffusive parabolic problems and non-linear problems of mixed character. The practical aspects of imaging, particularly efficient and robust methods for updating high resolution geologic models using fluid flow, transport and geophysical data, are emphasized throughout the book. Complete with online software applications and examples that enable readers to gain hands-on experience, this volume is an invaluable resource for graduate-level courses, as well as for academic researchers and industry practitioners in the fields of geoscience, hydrology, and petroleum and environmental engineering.

As global consumption of fossil fuels such as oil increases, previously abundant sources have become depleted or plagued with obstructions. Asphaltene deposition is one of such obstructions which can significantly decrease the rate of oil production. This book offers concise yet thorough coverage of the complex problem of asphaltene precipitation and deposition in oil production. It covers fundamentals of chemistry, stabilization theories and mechanistic approaches of asphaltene behavior at high temperature and pressure. Asphaltene Deposition: Fundamentals, Prediction, Prevention, and Remediation explains techniques for experimental determination of asphaltene precipitation and deposition and different modeling tools available to forecast the occurrence and magnitude of asphaltene deposition in a given oil field. It discusses strategies for mitigation of asphaltene deposition using chemical inhibition and corresponding challenges, best practices for asphaltene remediation, current research, and case studies.

The complex flows in the atmosphere and oceans are believed to be accurately modeled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems and that describe, for example, the dynamics of cyclones and ocean eddies. The simplifications often result in models that are amenable to solution both analytically and numerically. The volume examines and explains why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations, such as groups of transformations, Hamiltonian structure and stability.

This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided and coupling of SPH and molecular dynamics is discussed for multiscale simulation, making this a friendly book for readers and SPH users.

This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

The second of two volumes concentrating on the dynamics of slender bodies within or containing axial flow, Volume 2 covers fluid-structure interactions relating to shells, cylinders and plates containing or immersed in axial flow, as well as slender structures subjected to annular and leakage flows. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes, with increased coverage of computational techniques and numerical methods, particularly for the solution of non-linear three-dimensional problems.

Presenting a comprehensive description of the theory and physics of high-intensity ultrasound, this book also deals with a wide range of problems associated with the industrial applications of ultrasound, mainly in the areas of metallurgy and mineral processing. The book is divided into three sections, and Part I introduces the reader to the theory and physics of high-intensity ultrasound. Part II considers the design of ultrasonic generators, mechanoacoustic radiators and other vibrational systems, as well as the control of acoustic parameters when vibrations are passed into a processed medium. Finally, Part III describes problems associated with various uses of high-intensity ultrasound in metallurgy. The applications of high-intensity ultrasound for metal shaping, thermal and thermochemical treatment, welding, cutting, refining, and surface hardening are also discussed here. This comprehensive monograph will provide an invaluable source of information, which has been largely unavailable in the West until now.

Most of the equations governing the problems related to science and engineering are nonlinear in nature. As a result, they are inherently difficult to solve. Analytical solutions are available only for some special cases. For other cases, one has no easy means but to solve the problem must depend on numerical solutions. Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions presents the current theoretical developments of boundary layer theory, a branch of transport phenomena. Also, the book addresses the theoretical developments in the area and presents a number of physical problems that have been solved by analytical or numerical method. It is focused particularly on fluid flow problems governed by nonlinear differential equations. The book is intended for researchers in applied mathematics, physics, mechanics and engineering.