CLAUSIUS DUHEM INEQUALITY PDF

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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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Views Read Edit View history. Hence the Clausius—Duhem inequality is also called the dissipation inequality. All the variables are functions of a material point at at time. Now, the material time derivatives of and are given by. Laws Conservations Energy Mass Momentum. From the conservation of mass.

Continuum mechanics/Clausius-Duhem inequality for thermoelasticity – Wikiversity

Using the divergence theoremwe get. This inequality is particularly useful in determining whether the constitutive infquality of a material is thermodynamically allowable.

From the balance of energy. In a real material, the dissipation is always greater than zero. This page was last edited on 9 Augustat Rheology Viscoelasticity Rheometry Rheometer. 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. This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius—Duhem inequality.

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In this equation is the time, represents a body and the integration ruhem 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 energy source per unit mass, and is the absolute temperature.

Since is arbitrary, we must have. Surface tension Capillary action. Rheology Viscoelasticity Rheometry Rheometer.

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By using this site, you agree to the Terms of Use and Privacy Policy. This inequality incorporates the balance of energy and the balance of linear and clxusius momentum into the expression for the Clausius—Duhem inequality. Surface tension Capillary action. 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.

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

Using the divergence theoremwe get. Clausius—Duhem inequality Continuum mechanics. Hence the Clausius—Duhem inequality is also called the dissipation inequality. Now, using index notation with respect to a Cartesian coordinate system. This inequality is a statement concerning the irreversibility of natural clausous, especially when energy inquality is involved. Retrieved from ” https: In differential form the Clausius—Duhem inequality can be written as.

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The inequality can be expressed in terms of the internal energy as. In a real material, the dissipation is always greater than zero. The Clausius—Duhem inequality [1] [2] is a way of expressing the second law of thermodynamics that is used in continuum mechanics.

Clausius–Duhem inequality

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. The inequality can be expressed in terms of the internal energy as. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.

Laws Conservations Energy Mass Momentum. Assume that is an arbitrary fixed control volume. The Clausius—Duhem inequality can be expressed in integral form as. The Clausius—Duhem inequality can be expressed in integral form as.