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Conservation Laws in Variational Thermo-Hydrodynamics : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Stanislaw Sieniutycz

Conservation Laws in Variational Thermo-Hydrodynamics


Hardcover Published: April 1994
ISBN: 9780792328025
Number Of Pages: 448

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This volume presents an original, synthesizing approach to the thermal physics of fluid continua based on a novel extension of Hamilton's principle which allows the free flow of entropy, independent of that of matter. The extension, used in the context of NAther's theorem of variational calculus, gives rise to heat and diffusion terms in the conservation laws for the energy, momentum and matter, and may include the effects of thermal inertia. The mass conservation in reacting systems results from their intrinsic symmetries. The role of thermodynamic irreversibility can be investigated through a generalized action functional with Onsager's dissipation potentials. While variational calculus is the basic mathematical tool, the book emphasizes the conservation laws in the context of the underlying thermodynamics (reversible or not) rather than the mathematical formalism. The book can be used as a supplementary text in graduate courses on fluid mechanics, nonequilibrium thermodynamics, transport phenomena and variational calculus. As a reference text for further research it will attract researchers working in various branches of macroscopic physics/chemistry and applied mathematics, especially those in continuum mechanics, nonequilibrium thermodynamics (classical and extended), heat and mass transfer, etc. Applied mathematicians will welcome the use of the field (Lagrangian and Hamiltonian) formalisms for complex physiochemical continua.

Introduction: aims and scope
Physical significance of Nother's symmetries and extremum principlesp. 1
Eulerian and Lagrangian descriptions of perfect fluidsp. 26
Conservation laws for given system of equationsp. 72
Thermodynamics and kinetics of nonequilibrium fluidsp. 87
Lagrangian and Hamiltonian formalism for reversible nonequilibrium fluids with heat flowp. 129
Extended reversible problem involving mass diffusion, heat flow and thermal inertiap. 150
A generalized action with dissipative potentialsp. 194
Thermo-hydrodynamic potentials and geometries: the union of thermodynamics and hydromechanicsp. 241
Intrinsic symmetries and conservation of mass in chemically reacting systemsp. 268
Conservation laws as given constraints for processes at mechanical equilibriump. 312
Generalized minimum dissipation in presence of convection and chemical reactionsp. 356
Some associated relativistic results
Referencesp. 401
Glossary of principal symbolsp. 439
Indexp. 443
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792328025
ISBN-10: 0792328027
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 448
Published: April 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 3.18
Weight (kg): 0.84