Conservation Laws in Variational Thermo-Hydrodynamics

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.

Klappentext

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 Nöther'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.

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