On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation

Year 2019, Volume: 22 Issue: 1, 19 - 24, 02.03.2019

Federico Zullo , Enrico Sciubba

https://doi.org/10.5541/ijot.515606

Cited By: 1

Abstract

This paper is a follow-up of previous work aimed at the identification
and quantification of the exergy of macroscopic non-equilibrium systems.
Assuming that both energy and exergy are a priori concepts, it is
possible to show that a system in an initial non-equilibrium state relaxes to
equilibrium releasing (or absorbing) an additional amount of exergy, called non-equilibrium
exergy, which is fundamentally different from Gibbs’ Available Energy and
depends on both the initial state and the imposed boundary conditions. The
existence of such a quantity implies that all iso-energetic non-equilibrium
states can be ranked in terms of their non-equilibrium exergy content, any
point of the Gibbs plane corresponding therefore to a possible initial
distribution, each one with its own exergy-decay history. The non-equilibrium
exergy is always larger than its equilibrium counterpart and constitutes the
“real” total exergy content of the system, i.e., the real maximum work
extractable (or absorbable) from the system. The application of the method to
heat conduction problems led to the calculation of a “relaxation curve”, i.e.,
to the determination of the time-history of the relaxation towards equilibrium
that takes place in finite rather than infinite time interval. In our previous
works, use was made of the Fourier heat diffusion equation. In this study, the
Cattaneo heat transfer equation is used instead, in an attempt to extend the
validation range of the procedure. Cattaneo introduced in 1948 a second time
derivative term that renders the diffusion equation hyperbolic and avoids an
infinite speed of propagation. A finite propagation velocity of thermal
disturbances affects the value of the non-equilibrium exergy: this paper
presents the new results and offers a discussion of the implications.

Keywords

non-equilibrium thermodynamics, Cattaneo equation, exergy, heat diffusion

References

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