On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation
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.
References
- [1] E.Sciubba, F.Zullo: Exergy Dynamics of Systems in Thermal or Concentration Non-Equilibrium, Entropy, v.19 n.6, 263, 2017
- [2] E.Sciubba, F.Zullo: A Novel Derivation of the Time Evolution of the Entropy for Macroscopic systems in Thermal Non-Equilibrium, Entropy, v.19, S.I., 584-600, 2017
- [3] Lebon G., Jou D.: Understanding Non-Equilibrium Thermodynamics, Springer Verlag, Berlin, Heidelberg, 2008.
- [4] C. Cattaneo: On a form of heat equation which eliminates the paradox of instantaneous propagation, C. R. Acad. Sci. Paris, 431-433, July 1958
- [5] G. B. Nagy, O. E. Ortiz, and O. A. Reula, The behavior of hyperbolic heat equations solutions near their parabolic limits, J. of Mathematical Physics 35, 4334, 1994; doi: http://dx.doi.org/10.1063/1.530856
- [6] J. Bright, Z. M. Zhang: Common Misperceptions of the Hyperbolic Heat Equation, J. of Thermophysics and Heat Transfer, v. 23, n. 3, July–September 2009
- [7] F. P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, Hoboken, NJ, 2002
- [8] M. Fabrizio, C. Giorgi, A. Morro: Modeling of heat conduction via fractional derivatives, Heat Mass Transfer (2017) 53:2785-2797 DOI 10.1007/s00231-017-1985-8
Abstract
References
- [1] E.Sciubba, F.Zullo: Exergy Dynamics of Systems in Thermal or Concentration Non-Equilibrium, Entropy, v.19 n.6, 263, 2017
- [2] E.Sciubba, F.Zullo: A Novel Derivation of the Time Evolution of the Entropy for Macroscopic systems in Thermal Non-Equilibrium, Entropy, v.19, S.I., 584-600, 2017
- [3] Lebon G., Jou D.: Understanding Non-Equilibrium Thermodynamics, Springer Verlag, Berlin, Heidelberg, 2008.
- [4] C. Cattaneo: On a form of heat equation which eliminates the paradox of instantaneous propagation, C. R. Acad. Sci. Paris, 431-433, July 1958
- [5] G. B. Nagy, O. E. Ortiz, and O. A. Reula, The behavior of hyperbolic heat equations solutions near their parabolic limits, J. of Mathematical Physics 35, 4334, 1994; doi: http://dx.doi.org/10.1063/1.530856
- [6] J. Bright, Z. M. Zhang: Common Misperceptions of the Hyperbolic Heat Equation, J. of Thermophysics and Heat Transfer, v. 23, n. 3, July–September 2009
- [7] F. P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, Hoboken, NJ, 2002
- [8] M. Fabrizio, C. Giorgi, A. Morro: Modeling of heat conduction via fractional derivatives, Heat Mass Transfer (2017) 53:2785-2797 DOI 10.1007/s00231-017-1985-8
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Regular Original Research Article |
| Authors | |
| Publication Date | March 2, 2019 |
| Published in Issue | Year 2019 Volume: 22 Issue: 1 |