Continuum Thermomechanics

Alfredo Bermúdez de Castro (auth.)9783764372651, 3764372656

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).

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Table of contents :
General Definitions, Conservation Laws….Pages 1-12
Lagrangian Coordinates….Pages 13-15
Constitutive Laws….Pages 17-25
The Principle of Material Frame-Indifference….Pages 27-31
Replacing Entropy with Temperature….Pages 33-35
Isotropy….Pages 37-42
Equations in Lagrangian Coordinates….Pages 43-45
Linearized Models….Pages 47-56
Quasi-static Thermoelasticity….Pages 57-59
Fluids….Pages 61-79
Linearized Models for Fluids, Acoustics….Pages 81-91
Perfect Gases….Pages 93-99
Incompressible Fluids….Pages 101-104
Turbulent Flow of Incompressible Newtonian Fluids….Pages 105-107
Mixtures of Coleman-Noll Fluids….Pages 109-117
Chemical Reactions in a Stirred Tank….Pages 119-124
Chemical Equilibrium of a Reacting Mixture of Perfect Gases in a Stirred Tank….Pages 125-134
Flow of a Mixture of Reacting Perfect Gases….Pages 135-143
The Method of Mixture Fractions….Pages 145-151
Turbulent Flow of Reacting Mixtures of Perfect Gases, The PDF Method….Pages 153-159