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Vector Fields with Applications to Thermodynamics and Irreversibility

Author: Luis Manuel Braga da Costa Campos

Publisher: CRC Press

Published: 2022-11-30

Total Pages: 279

ISBN-13: 1000415988

Vector Fields with Applications to Thermodynamics and Irreversibility is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass and electricity; and their interactions. This is the first book of the volume. The second book of volume V continues this book on thermodynamics, focusing on the equation of state and energy transfer processes including adiabatic, isothermal, isobaric and isochoric. These are applied to thermodynamic cycles, like the Carnot, Atkinson, Stirling and Barber-Brayton cycles, that are used in thermal devices, including refrigerators, heat pumps, and piston, jet and rocket engines. In connection with jet propulsion, adiabatic flows and normal and oblique shock waves in free space and nozzles with variable cross-section are considered. The equations of fluid mechanics are derived for compressible two-phase flow in the presence of shear and bulk viscosity, thermal conduction and mass diffusion. The thermodynamic cycles are illustrated by detailed calculations modelling the operation of piston, turbojet and rocket engines in various ambient conditions, ranging from sea level, the atmosphere of the earth at altitude and vacuum of space, for the propulsion of land, sea, air and space vehicles. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics. This book: Simultaneously covers rigorous mathematics, general physical principles and engineering applications with practical interest Provides interpretation of results with the help of illustrations Includes detailed proofs of all results L.M.B.C. Campos was chair professor and the Coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and also the director (and founder) of the Center for Aeronautical and Space Science and Technology until retirement in 2020. L.A.R.Vilela is currently completing an Integrated Master's degree in Aerospace Engineering at Institute Superior Tecnico (1ST) of Lisbon University.

Compressible Flow with Applications to Engines, Shocks and Nozzles

Author: Luis Manuel Braga da Costa Campos

Publisher: CRC Press

Published: 2022-11-30

Total Pages: 294

ISBN-13: 1000415996

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Compressible Flow with Application to Shocks and Propulsion is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass and electricity; and their interactions. This is the second book of the volume. The first book of volume V starts with the classification of partial differential equations and proceeds with similarity methods that apply in general to linear equations with constant coefficients and all derivatives of the same order, such as the Laplace and Biharmonic equations, without and with forcing. The similarity solutions are also applied to Burger's non-linear diffusion equation. First-order linear and quasi-linear partial differential equations with variable coefficients are considered, with application to the representation of conservative/non-conservative, solenoidal/rotational and Beltrami/helical vector fields by one, two or three scalar and/or one vector potential in relation with exact, inexact and non-integrable differentials. The latter appear in the first and second principles of thermodynamics that specify the constitutive and diffusive properties of matter as concerns thermal, mechanical, elastic, flow, electrical, magnetic and chemical phenomena and their interactions. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics. This book: Simultaneously covers rigorous mathematics, general physical principles and engineering applications with practical interest Provides interpretation of results with the help of illustrations Includes detailed proofs of all results L.M.B.C. Campos was chair professor and the Coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and also the director (and founder) of the Center for Aeronautical and Space Science and Technology until retirement in 2020. L.A.R. Vilela is currently completing an Integrated Master's degree in Aerospace Engineering at Institute Superior Tecnico (1ST) of Lisbon University.

Beyond Equilibrium Thermodynamics

Author: Hans Christian Öttinger

Publisher: John Wiley & Sons

Published: 2005-05-13

Total Pages: 651

ISBN-13: 0471727911

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Beyond Equilibrium Thermodynamics fills a niche in the market by providing a comprehensive introduction to a new, emerging topic in the field. The importance of non-equilibrium thermodynamics is addressed in order to fully understand how a system works, whether it is in a biological system like the brain or a system that develops plastic. In order to fully grasp the subject, the book clearly explains the physical concepts and mathematics involved, as well as presenting problems and solutions; over 200 exercises and answers are included. Engineers, scientists, and applied mathematicians can all use the book to address their problems in modelling, calculating, and understanding dynamic responses of materials.

Extended Irreversible Thermodynamics

Author: David Jou

Publisher: Springer Science & Business Media

Published: 2010-09-16

Total Pages: 484

ISBN-13: 9048130743

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The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

Extended Irreversible Thermodynamics

Author: D. Jou

Publisher: Springer Science & Business Media

Published: 2011-06-27

Total Pages: 475

ISBN-13: 3642565654

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Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

Irreversible Thermodynamics

Author: Katrine Seip Førland

Publisher: John Wiley & Sons

Published: 1988

Total Pages: 304

ISBN-13:

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Irreversible thermodynamics is an extension of classical thermodynamics to give a unified method of treating transport processes. This book develops the theoretical basis and relates it to reality by examples. These theories are then applied to solve some important problems within varied fields of science and technology. To facilitate understanding, the basic equations are derived in a simple manner, using a minimum of mathematics.

Understanding Non-equilibrium Thermodynamics

Author: Georgy Lebon

Publisher: Springer Science & Business Media

Published: 2008-01-12

Total Pages: 331

ISBN-13: 3540742522

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Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.

Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities

Author: Marco Bramanti

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 136

ISBN-13: 0821849034

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"March 2010, Volume 204, number 961 (end of volume)."

Irreversible Thermodynamics

Author: K.S. Forland

Publisher: Akademika Pub

Published: 2001-01-01

Total Pages: 281

ISBN-13: 9788251916349

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Irreversible thermodynamics is an extension of classical thermodynamics which provides a unified method of examining transport processes and, in particular, cases where simultaneous transport processes need to be studied together. These are common in various fields such as electrochemistry, chemical engineering, biochemistry and biophysics, metallurgy and geology. In this book, the basic equations of irreversible thermodynamics are derived simply, using a minimum of mathematics firstly for very simple systems, and by example extended into more complex cases. The second part of the book then utilizes this theoretical background to discuss the applications in different fields. Important problems are used as case studies to highlight the use of irreversible thermodynamics in, for example, ion selective electrodes, biological systems and frost heave situations. Irreversible thermodynamics is an increasingly important tool in a number of disciplines and this volume will provide an ideal introduction for those using it for the first time. *** The now deceased Katrine Seip Forland and Tormod Forland served as professors at the Norwegian University of Science and Technology, in inorganic and physical chemistry, respectively. At an early stage, Katrine Seip Forland investigated non-stoichiometric oxides, while Tormod Forland developed thermodynamic models for salt melts and slags. Both invested a large effort in creating chemical engineering education in East Africa, and in 1990 T. Forland became honorary doctor of the University of Tanzania. He was the 1988 recipient of the Guldberg-Waage medal. In the 70's they took an interest in irreversible thermodynamics, and were joined by Signe Kjelstrup (previously Kjelstrup Ratkje). She has been professor of physical chemistry since 1985. Many of her early works in irreversible thermodynamics concern electrochemical systems. Since 1995 she has also studied entropy production minimisation in process equipment. She is honorary doctor of the University of North East China, and has been teaching irreversible thermo-dynamics also in Kyoto University.

Non-Equilibrium Entropy and Irreversibility

Author: C. Lindblad

Publisher: Springer Science & Business Media

Published: 2001-11-30

Total Pages: 184

ISBN-13: 9781402003202

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The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems.