## Continuum ThermomechanicsThe 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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### Contents

Lagrangian Coordinates | 13 |

Chemical Reactions in a Stirred Tank | 16 |

The Principle of Material FrameIndifference | 27 |

Isotropy | 37 |

Equations in Lagrangian Coordinates | 43 |

8 | 46 |

9 | 57 |

10 | 70 |

Mixtures of ColemanNoll Fluids | 109 |

Chemical Equilibrium of a Reacting Mixture of Perfect Gases | 125 |

Flow of a Mixture of Reacting Perfect Gases | 135 |

The Method of Mixture Fractions | 145 |

Turbulent Flow of Reacting Mixtures of Perfect Gases | 152 |

A Vector and Tensor Algebra | 161 |

B Vector and Tensor Analysis | 172 |

Some Equations of Continuum Mechanics in Curvilinear Coordinates | 189 |

Quasistatic Thermoelasticity | 80 |

Perfect Gases | 93 |

Incompressible Fluids | 100 |

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### Common terms and phrases

called chain rule Chapter Coleman-Noll material compute conservative form constitutive class coordinates Corollary deduce deﬁned Deﬁnition density det(F div(pv diva Divu divv energy equation enthalpy entropy Eulerian field ﬁrst Firstly fluid ﬂuids following equality holds gases Gibbs free energy given gradh heat at constant Helmholtz free energy Hence incompressible isentropic isotropic Lagrangian Lagrangian Coordinates Lemma Let us assume Let us consider Let us denote Lin+ linear mapping mass conservation mass conservation equation material body mechanical equilibrium Moreover motion equation Newtonian Fluids obtain order tensor partial derivatives partial differential equations perfect gas pgcg pgii pressure Proof Proposition recall replacing this equality response function satisﬁes scalar ﬁeld solved species speciﬁc enthalpy speciﬁc entropy speciﬁc Gibbs free speciﬁc heat strain tensor stress tensor symmetric temperature tensor ﬁeld thermodynamic process turbulent vector ﬁeld velocity viscosity