The general goal of this book is to deduce rigorously, from the first principles, the partial differential equations governing the thermodynamic processes undergone by continuum media under forces and heat. Solids and fluids are considered in a unified framework. Reacting mixtures of fluids are also included for which general notions of thermodynamics are recalled, such as the Gibbs equilibrium theory.
Linear approximate models are mathematically obtained by calculating the derivatives of the constitutive response functions. They include the classical models for linear vibrations of thermoelastic solids and also for wave propagation in fluids (dissipative and non-dissipative acoustics and internal gravity waves).
General Definitions, Conservation Laws.- Lagrangian Coordinates.- Constitutive Laws.- The Principle of Material Frame-Indifference.- Replacing Entropy with Temperature.- Isotropy.- Equations in Lagrangian Coordinates.- Linearized Models.- Quasi-static Thermoelasticity.- Fluids.- Linearized Models for Fluids, Acoustics.- Perfect Gases.- Incompressible Fluids.- Turbulent Flow of Incompressible Newtonian Fluids.- Mixtures of Coleman-Noll Fluids.- Chemical Reactions in a Stirred Tank.- Chemical Equilibrium of a Reacting Mixture of Perfect Gases in a Stirred Tank.- Flow of a Mixture of Reacting Perfect Gases.- The Method of Mixture Fractions.- Turbulent Flow of Reacting Mixtures of Perfect Gases, The PDF Method.