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

Yıl 2019, Cilt 22, Sayı 1, 19 - 24, 02.03.2019
https://doi.org/10.5541/ijot.515606

Öz

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.


Kaynakça

  • [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

Yıl 2019, Cilt 22, Sayı 1, 19 - 24, 02.03.2019
https://doi.org/10.5541/ijot.515606

Öz

Kaynakça

  • [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

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Regular Original Research Article
Yazarlar

Federico ZULLO> (Sorumlu Yazar)
University of Brescia
Italy


Enrico SCİUBBA>

Yayımlanma Tarihi 2 Mart 2019
Yayınlandığı Sayı Yıl 2019, Cilt 22, Sayı 1

Kaynak Göster

Bibtex @araştırma makalesi { ijot515606, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {}, publisher = {Uluslararası Uygulamalı Termodinamik Derneği İktisadi İşletmesi}, year = {2019}, volume = {22}, number = {1}, pages = {19 - 24}, doi = {10.5541/ijot.515606}, title = {On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation}, key = {cite}, author = {Zullo, Federico and Sciubba, Enrico} }
APA Zullo, F. & Sciubba, E. (2019). On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation . International Journal of Thermodynamics , 22 (1) , 19-24 . DOI: 10.5541/ijot.515606
MLA Zullo, F. , Sciubba, E. "On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation" . International Journal of Thermodynamics 22 (2019 ): 19-24 <https://dergipark.org.tr/tr/pub/ijot/issue/43635/515606>
Chicago Zullo, F. , Sciubba, E. "On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation". International Journal of Thermodynamics 22 (2019 ): 19-24
RIS TY - JOUR T1 - On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation AU - FedericoZullo, EnricoSciubba Y1 - 2019 PY - 2019 N1 - doi: 10.5541/ijot.515606 DO - 10.5541/ijot.515606 T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 19 EP - 24 VL - 22 IS - 1 SN - 1301-9724-2146-1511 M3 - doi: 10.5541/ijot.515606 UR - https://doi.org/10.5541/ijot.515606 Y2 - 2019 ER -
EndNote %0 International Journal of Thermodynamics On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation %A Federico Zullo , Enrico Sciubba %T On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation %D 2019 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 22 %N 1 %R doi: 10.5541/ijot.515606 %U 10.5541/ijot.515606
ISNAD Zullo, Federico , Sciubba, Enrico . "On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation". International Journal of Thermodynamics 22 / 1 (Mart 2019): 19-24 . https://doi.org/10.5541/ijot.515606
AMA Zullo F. , Sciubba E. On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation. International Journal of Thermodynamics. 2019; 22(1): 19-24.
Vancouver Zullo F. , Sciubba E. On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation. International Journal of Thermodynamics. 2019; 22(1): 19-24.
IEEE F. Zullo ve E. Sciubba , "On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation", International Journal of Thermodynamics, c. 22, sayı. 1, ss. 19-24, Mar. 2019, doi:10.5541/ijot.515606