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.

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Since is arbitrary, we must have. Now, the material time derivatives of and are given by. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in duhsm mechanics.

Surface tension Capillary action. In differential form the Clausius—Duhem inequality can be written as. In a real material, the dissipation is always greater than zero.

## Continuum mechanics/Clausius-Duhem inequality for thermoelasticity

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

All the variables are functions of a material point at at time. This page was last edited on 9 Augustat Hence the Clausius—Duhem inequality is also called the dissipation inequality.

Retrieved from ” https: From Wikipedia, the free encyclopedia. Assume that is an arbitrary fixed control volume.

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

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. The inequality can be expressed in terms of the internal energy as. Laws Conservations Energy Mass Momentum.

The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics. From the conservation of mass. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

In this equation is the time, represents a body and the integration is over the volume of the inequwlity, represents the surface of the body, is the mass density of the body, is the specific entropy c,ausius 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.

Hence the Clausius—Duhem inequality is also called the dissipation inequality. This inequality is a statement concerning clausihs irreversibility of natural processes, especially when energy dissipation is involved. Now, using index notation with respect to a Cartesian coordinate system. Views Read Edit View history.

Using the divergence theoremwe get. The Clausius—Duhem inequality can be expressed in integral form as. Using the divergence theoremwe get. From the clauwius of energy. Laws Conservations Energy Mass Momentum.

Surface tension Capillary action. In a real material, the dissipation is always greater than zero. By using this site, you agree to the Terms of Use and Privacy Policy. 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 duhfm, or, Now, the material time derivatives of and are given by Therefore, From the conservation of mass.

This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved. The inequality can be expressed in terms of the internal energy as.

The Clausius—Duhem inequality can be expressed in integral form as. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality. Clausius—Duhem inequality Continuum mechanics. From the balance of energy. Rheology Viscoelasticity Rheometry Rheometer. In differential form the Clausius—Duhem inequality can be written as.

Rheology Viscoelasticity Rheometry Rheometer.