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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All the variables are functions of a material point at at time. In differential form the Clausius—Duhem inequality can be written as.

## Continuum mechanics/Clausius-Duhem inequality for thermoelasticity

Now, using index notation with respect to a Cartesian coordinate system. In differential form the Clausius—Duhem inequality can be written as. Now, the material time derivatives of and are given by.

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

Views Read Edit View history. Rheology Viscoelasticity Rheometry Rheometer. Using the divergence theoremwe get. The inequality can be expressed in terms of the internal energy as. Assume that is an arbitrary fixed control volume.

Surface tension Capillary action. This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality.

Since is arbitrary, we must have.

Retrieved from ” https: This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable. Laws Conservations Energy Mass Momentum.

From Wikipedia, the free encyclopedia. This page was last edited on 9 Augustat Using the divergence theoremwe get. Clauwius Clausius—Duhem xlausius can be expressed in integral form as. From the balance of energy.

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. Rheology Viscoelasticity Rheometry Rheometer.

## Clausius–Duhem inequality

In a real material, the dissipation is always greater than zero. From the balance of energy. In this equation is the time, represents a body and cllausius integration is over the volume of the body, represents the surface of the body, is 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 claksius source per unit mass, and is the absolute temperature.

This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved.

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

Hence the Clausius—Duhem inequality is also called the dissipation inequality. Clauwius 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. Laws Conservations Energy Mass Momentum. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

Surface tension Capillary action. The inequality can be expressed in terms of the internal energy as. This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics. By using this site, you agree to the Terms of Use and Privacy Policy.