Conservation Laws in Variational Thermo-Hydrodynamics

ISBN-13: 9789401044738 / Angielski / Miękka / 2012 / 448 str.

S. Sieniutycz

Opis

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 Nother'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. "

Spis treści

Preface. Introduction: aims and scope. 1. Physical significance of Nöther's symmetries and extremum principles. 2. Lagrangian and Eulerian descriptions of perfect fluids. 3. Conservation laws for given system of equations. 4. Thermodynamics and kinetics of nonequilibrium fluids. 5. Lagrangian and Hamiltonian formalism for reversible nonequilibrium fluids with heat flow. 6. Extended reversible problem involving mass diffusion, heat flow and thermal inertia. 7. A generalized action with dissipative potentials. 8. Thermohydrodynamic potentials and geometries: the union of thermodynamics and hydromechanics. 9. Intrinsic symmetries and conservation of mass in chemically reacting systems. 10. Conservation laws as given constraints for processes at mechanical equilibrium. 11. Generalized minimum dissipation in presence of convection and chemical reactions. 12. Some associated relativistic results. References. Glossary of principal symbols. Index.