Brian Straughan - Böcker

This volume is a substantially revised new edition of the earlier book of the same title. Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems. The book presents convection studies in a variety of fluid and porous media contexts. It begins at an elementary level and should be accessible to a wide audience of applied mathematicians, physicists, and engineers.

This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.

This book is a revised edition of my earlier book of the same title. The cur­ rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex­ plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta­ bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.

This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.

This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.

This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations.

Several other important topics are incorporated, including:Guyer-Krumhansl termsKelvin-Voigt fluid theoryNavier-Stokes theoryHigher gradient fluid theoriesThermal Convection with a Cattaneo Flux Law will appeal to researchers interested in exploring this active area.

This monograph provides an account of thermal convection with a focus on Cattaneo’s heat flux equation. Various applications of the equation are analyzed, such as those pertaining to nanoscale mechanics, nuclear engineering, the treatment of various diseases, and more. The influence it has had on problems in the field of thermal convection is highlighted as well. Several other important topics are incorporated, including:Guyer-Krumhansl termsKelvin-Voigt fluid theoryNavier-Stokes theoryHigher gradient fluid theoriesThermal Convection with a Cattaneo Flux Law will appeal to researchers interested in exploring this active area.

This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations. The author's analysis of these equations concentrates on thermal convection in a layer of incompressible fluid. Readers will learn how the Navier-Stokes equations, the Kelvin-Voigt equations, and the Navier-Stokes-Voigt equations are special cases of the generalized Oskolkov system. Thermal convection and double-diffusive convection are studied in Navier-Stokes-Voigt fluids and in various Kelvin-Voigt and Oskolkov fluids. Cutting edge research is included on magnetohydrodynamic convection in a Navier-Stokes-Voigt fluid and in a Kelvin-Voigt fluid of order one.Oskolkov Equations and Thermal Convection will serve as a timely resource for students and researchers interested in this active topic, as well as those studying the broader area of fluid dynamics.

This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.

This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.

This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement.

This topical volume reviews applications of continuum mechanics to systems in geophysics and the environment. Part of the text is devoted to numerical simulations and modeling. The topics covered include soil mechanics and porous media, glacier and ice dynamics, climatology and lake physics, climate change as well as numerical algorithms. The book, written by well-known experts, addresses researchers and students interested in physical aspects of our environment.

Also in vogue in the mathematical literature are studies of blow-up in systems of partial differen­ tial equations, partial differential equations with non-linear convection terms, and systems of partial differential equations which contain convection terms.

This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer­ sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark­ ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his PhD, Professor Hutter returned to Europe where he worked as a senior scientist at the Labor­ atory for Hydraulics, Hydrology and Glaciology, ETH Zurich, being involved in glacier flow, physical limnology, avalanche research and granular media. At the same time he maintained scientific contact with the Mechanics Institute of the Vienna University of Technology. In both European cities he received a habil­ itation degree: In Vienna for Mechanics, in Zurich for Theoretical Glaciology and Limnology. Since 1987 Professor Hutter has been the successor to Professor Becker at the Department of Mechanics, Darmstadt University of Technology. Professor Hutter's work has always been relevant to reallife, and a feature of the man is his attention to experiments and matching theory. He has built up an internationally respected laboratory in Darmstadt which concentrates on both experimental and theoretical aspects.