Conservation Laws in Variational Thermo-Hydrodynamics

1. Front Matter

   Pages i-xxiii

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2. Physical significance of Nöther’s symmetries and extremum principles

   • Stanislaw Sieniutycz

   Pages 1-25

3. Eulerian and Lagrangian descriptions of perfect fluids

   • Stanislaw Sieniutycz

   Pages 26-71

4. Conservation laws for given system of equations

   • Stanislaw Sieniutycz

   Pages 72-86

5. Thermodynamics and kinetics of nonequilibrium fluids

   • Stanislaw Sieniutycz

   Pages 87-128

6. Lagrangian and Hamiltonian formalism for reversible nonequilibrium fluids with heat flow

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   Pages 129-149

7. Extended reversible problem involving mass diffusion, heat flow and thermal inertia

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   Pages 150-193

8. A generalized action with dissipative potentials

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   Pages 194-240

9. Thermo-hydrodynamic potentials and geometries: the union of thermodynamics and hydromechanics

   • Stanislaw Sieniutycz

   Pages 241-267

10. Intrinsic symmetries and conservation of mass in chemically reacting systems

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    Pages 268-311

11. Conservation laws as given constraints for processes at mechanical equilibrium

    • Stanislaw Sieniutycz

    Pages 312-355

12. Generalized minimum dissipation in presence of convection and chemical reactions

    • Stanislaw Sieniutycz

    Pages 356-368

13. Some associated relativistic results

    • Stanislaw Sieniutycz

    Pages 369-399

14. Back Matter

    Pages 401-448

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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.

• Dissipation
• Hamilton's principle
• convection
• fluid mechanics
• hydromechanics
• thermodynamics
• fluid- and aerodynamics

• Institute of Chemical Engineering, Warsaw University of Technology, Warsaw, Poland

  Stanislaw Sieniutycz

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