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Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.
Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.
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Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.
The contents of this book covers the material required in the Fluid Mechanics Graduate Core Course (MEEN-621) and in Advanced Fluid Mechanics, a Ph. D-level elective course (MEEN-622), both of which I have been teaching at Texas A&M University for the past two decades. While there are numerous undergraduate fluid mechanics texts on the market for engineering students and instructors to choose from, there are only limited texts that comprehensively address the particular needs of graduate engineering fluid mechanics courses. To complement the lecture materials, the instructors more often recommend several texts, each of which treats special topics of fluid mechanics. This circumstance and the need to have a textbook that covers the materials needed in the above courses gave the impetus to provide the graduate engineering community with a coherent textbook that comprehensively addresses their needs for an advanced fluid mechanics text. Although this text book is primarily aimed at mechanical engineering students, it is equally suitable for aerospace engineering, civil engineering, other engineering disciplines, and especially those practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self study, provided that the reader has a sufficient knowledge of calculus and differential equations. In the past, because of the lack of advanced computational capability, the subject of fluid mechanics was artificially subdivided into inviscid, viscous (laminar, turbulent), incompressible, compressible, subsonic, supersonic and hypersonic flows.
This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
One of the major achievements in fluid mechanics in the last quarter of the twentieth century has been the development of an asymptotic description of perturbations to boundary layers known generally as 'triple deck theory'. These developments have had a major impact on our understanding of laminar fluid flow, particularly laminar separation. It is also true that the theory rests on three quarters of a century of development of boundary layer theory which involves analysis, experimentation and computation. All these parts go together, and to understand the triple deck it is necessary to understand which problems the triple deck resolves and which computational techniques have been applied. This book presents a unified account of the development of laminar boundary layer theory as a historical study together with a description of the application of the ideas of triple deck theory to flow past a plate, to separation from a cylinder and to flow in channels. The book is intended to provide a graduate level teaching resource as well as a mathematically oriented account for a general reader in applied mathematics, engineering, physics or scientific computation.
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.
Written by experts in the field, this book, "Boundary Layer Flows - Theory, Applications, and Numerical Methods" provides readers with the opportunity to explore its theoretical and experimental studies and their importance to the nonlinear theory of boundary layer flows, the theory of heat and mass transfer, and the dynamics of fluid. With the theory's importance for a wide variety of applications, applied mathematicians, scientists, and engineers - especially those in fluid dynamics - along with engineers of aeronautics, will undoubtedly welcome this authoritative, up-to-date book.