Mathematics and Its Applications

Conservation Laws in Variational Thermo-Hydrodynamics

Authors: Sieniutycz, S.

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About this book

This study is one of the first attempts to bridge the theoretical models of variational dynamics of perfect fluids and some practical approaches worked out in chemical and mechanical engineering in the field newly called thermo-hydrodynamics. In recent years, applied mathematicians and theoretical physicists have made significant progress in formulating analytical tools to describe fluid dynamics through variational methods. These tools are much loved by theoretists, and rightly so, because they are quite powerful and beautiful theoretical tools. Chemists, physicists and engineers, however, are limited in their ability to use these tools, because presently they are applicable only to "perfect fluids" (i. e. those fluids without viscosity, heat transfer, diffusion and chemical reactions). To be useful, a model must take into account important transport and rate phenomena, which are inherent to real fluid behavior and which cannot be ignored. This monograph serves to provide the beginnings of a means by which to extend the mathematical analyses to include the basic effects of thermo-hydrodynamics. In large part a research report, this study uses variational calculus as a basic theoretical tool, without undo compromise to the integrity of the mathematical analyses, while emphasizing the conservation laws of real fluids in the context of underlying thermodynamics --reversible or irreversible. The approach of this monograph is a new generalizing approach, based on Nother's theorem and variational calculus, which leads to the energy-momentum tensor and the related conservation or balance equations in fluids.

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Physical significance of Nöther’s symmetries and extremum principles

    Pages 1-25

    Sieniutycz, Stanislaw

  • Eulerian and Lagrangian descriptions of perfect fluids

    Pages 26-71

    Sieniutycz, Stanislaw

  • Conservation laws for given system of equations

    Pages 72-86

    Sieniutycz, Stanislaw

  • Thermodynamics and kinetics of nonequilibrium fluids

    Pages 87-128

    Sieniutycz, Stanislaw

  • Lagrangian and Hamiltonian formalism for reversible nonequilibrium fluids with heat flow

    Pages 129-149

    Sieniutycz, Stanislaw

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-94-011-1084-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $99.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Conservation Laws in Variational Thermo-Hydrodynamics
Authors
Series Title
Mathematics and Its Applications
Series Volume
279
Copyright
1994
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-1084-6
DOI
10.1007/978-94-011-1084-6
Hardcover ISBN
978-0-7923-2802-5
Softcover ISBN
978-94-010-4473-8
Edition Number
1
Number of Pages
XXIII, 448
Topics