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Global stability analysis of a Curzon–Ahlborn heat engine using the Lyapunov method

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  • Reyes-Ramírez, Israel
  • Barranco-Jiménez, Marco A.
  • Rojas-Pacheco, A.
  • Guzmán-Vargas, Lev

Abstract

In the present work, we analyze the global stability of a heat engine working at maximum power regime. We use the Lyapunov stability theory to construct the Lyapunov function to prove the asymptotic stability behavior about the steady-state of intermediate temperatures in the engine model. Our analysis is focused on the characterization of the global stability by considering internal irreversibilities and a linear heat transfer law in the thermal couplings. Besides, numerical integrations were performed to corroborate the findings of the global asymptotic stability of the system.

Suggested Citation

  • Reyes-Ramírez, Israel & Barranco-Jiménez, Marco A. & Rojas-Pacheco, A. & Guzmán-Vargas, Lev, 2014. "Global stability analysis of a Curzon–Ahlborn heat engine using the Lyapunov method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 98-105.
    • Handle: RePEc:eee:phsmap:v:399:y:2014:i:c:p:98-105
    DOI: 10.1016/j.physa.2013.12.044
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    References listed on IDEAS

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    1. Wu, Chih & Kiang, Robert L., 1992. "Finite-time thermodynamic analysis of a Carnot engine with internal irreversibility," Energy, Elsevier, vol. 17(12), pages 1173-1178.
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    Cited by:

    1. Valencia-Ortega, G. & Levario-Medina, S. & Barranco-Jiménez, M.A., 2021. "Local and global stability analysis of a Curzon–Ahlborn model applied to power plants working at maximum k-efficient power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    2. Zhang, Lei & Chen, Lingen & Sun, Fengrui, 2016. "Power optimization of chemically driven heat engine based on first and second order reaction kinetic theory and probability theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 221-230.
    3. Pengchao Zang & Lingen Chen & Yanlin Ge, 2022. "Maximizing Efficient Power for an Irreversible Porous Medium Cycle with Nonlinear Variation of Working Fluid’s Specific Heat," Energies, MDPI, vol. 15(19), pages 1-12, September.
    4. Ramírez-Moreno, M.A. & González-Hernández, S. & Angulo-Brown, F., 2016. "The role of the Stefan–Boltzmann law in the thermodynamic optimization of an n-Müser engine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 914-921.

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