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A thermodynamic Approach to Rate Equations in Continuum Physics



Author(s)

Angelo Morro

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DOI:10.17265/2159-5348/2017.06.003

DIBRIS, University of Genoa, Genova 16145, Italy

The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose meaning is restricted to the invariance of the balance equations relative to Galilean frames. Objective time derivatives are defined to leave the tensor character of the appropriate field invariant within the set of Euclidean frames. Rate equations are required to involve objective time derivatives and to be consistent with the second law of thermodynamics. Here the general structure of objective time derivatives is established and the known derivatives of the physical literature are shown to be particular cases. Next, to fix ideas, a rate equation is considered for the model of heat conduction via a generalization of the Maxwell-Cattaneo equation with higher-order gradients as in the Guyer-Krumhansl equation. The thermodynamic restrictions are investigated and the expected effects, of the selected derivative of the heat flux, on the stress tensor are derived.

Objective derivatives, rate equations, thermodynamic consistency.