To some extent modern continuum thermodynamics amounts to a collection of “ thermodynamical theories” sharing common premisses and common. sources on Ωt. Total entropy: units [J/K], defined up to a constant by. dS = dQ. T. Clausius-Duhem inequality: mathematical form of the 2nd law: DS. Dt. ≥. ∫. Ωt. sθ is the specific dissipation (or internal dissipation) and is denoted by the symbol ϕ. The Clausius-Duhem inequality can simply be written as.

Author: | Doll Mikabar |

Country: | Mongolia |

Language: | English (Spanish) |

Genre: | Health and Food |

Published (Last): | 15 December 2007 |

Pages: | 216 |

PDF File Size: | 10.98 Mb |

ePub File Size: | 5.84 Mb |

ISBN: | 566-5-42690-384-9 |

Downloads: | 4669 |

Price: | Free* [*Free Regsitration Required] |

Uploader: | Dizil |

This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable. In imequality real material, the dissipation is always greater than zero.

Hence the Clausius—Duhem inequality is also called the dissipation inequality.

This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality. Now, the material time derivatives of and are given by.

## Clausius–Duhem inequality

Using the divergence theoremwe get. The Clausius—Duhem inequality can be expressed in integral form as.

This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved. From the balance of energy. Rheology Viscoelasticity Rheometry Rheometer. Assume that is an arbitrary fixed control volume.

This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used inequaluty continuum mechanics. Retrieved from ” https: Views Read Edit View history. Hence the Clausius—Duhem inequality is also called the dissipation inequality.

## Continuum mechanics/Clausius-Duhem inequality for thermoelasticity

The inequality can be expressed in terms of the internal energy as. Using the divergence theoremwe get. All the variables are functions of a material point at at time.

This page was last edited on 9 Augustat The inequality can be expressed in terms of the internal energy as. Laws Conservations Energy Mass Momentum. In a real material, the dissipation is always greater than zero. This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved.

From the balance of energy.

### Continuum mechanics/Clausius-Duhem inequality for thermoelasticity – Wikiversity

Clausius—Duhem inequality Continuum mechanics. This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality.

In this equation is the time, represents a body and the integration is over the volume of the body, represents the surface of the body, inequallity the mass density of the body, is the specific entropy entropy per unit massis the normal velocity ofis the velocity of particles insideis the unit normal to the surface, is the heat flux vector, is an energy source per unit mass, and is the absolute temperature.

Using the identity in the Clausius—Duhem inequality, we get Now, using index notation with respect to a Cartesian coordinate systemHence, From the balance of energy Therefore, Rearranging.

### Clausius–Duhem inequality

By using this site, you agree to the Terms of Use and Privacy Policy. From the conservation of mass. Then and the derivative can be taken inside the integral to give Using the divergence theoremwe get Since is arbitrary, we must have Expanding out or, or, Now, the material time derivatives of and are given by Therefore, From the conservation of mass.

In differential form the Clausius—Duhem inequality can be written as. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics.

Rheology Viscoelasticity Rheometry Rheometer. Surface tension Capillary action. Now, using index notation duhsm respect to a Cartesian coordinate system. The Clausius—Duhem inequality can be expressed in integral form as. Laws Conservations Energy Mass Momentum.

Since is arbitrary, we must have. In differential form the Clausius—Duhem inequality can be written as. From Wikipedia, the free encyclopedia. Surface tension Capillary action.