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Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory

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  • Xia, Shaojun
  • Chen, Lingen
  • Sun, Fengrui

Abstract

A multistage irreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝(ΔT)m] and the irreversibility of heat resistance and internal dissipation is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine optimal fluid temperature configurations for maximum power output under the conditions of fixed duration and fixed initial temperature of the driving fluid. Based on general optimization results, the analytical solution for the case with Newtonian heat transfer law (m=1) is further obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming (DP) algorithm is adopted to obtain complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail.

Suggested Citation

  • Xia, Shaojun & Chen, Lingen & Sun, Fengrui, 2011. "Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory," Energy, Elsevier, vol. 36(1), pages 633-646.
  • Handle: RePEc:eee:energy:v:36:y:2011:i:1:p:633-646
    DOI: 10.1016/j.energy.2010.09.052
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    References listed on IDEAS

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    1. Lucia, Umberto, 2007. "Irreversible entropy variation and the problem of the trend to equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 289-292.
    2. Zhou, Shengbing & Chen, Lingen & Sun, Fengrui & Wu, Chih, 2005. "Optimal performance of a generalized irreversible Carnot-engine," Applied Energy, Elsevier, vol. 81(4), pages 376-387, August.
    3. Sieniutycz, Stanislaw, 2009. "Dynamic bounds for power and efficiency of non-ideal energy converters under nonlinear transfer laws," Energy, Elsevier, vol. 34(3), pages 334-340.
    4. Chen, Lingen & Zhu, Xiaoqin & Sun, Fengrui & Wu, Chih, 2006. "Effect of mixed heat-resistances on the optimal configuration and performance of a heat-engine cycle," Applied Energy, Elsevier, vol. 83(6), pages 537-544, June.
    5. Chen, Lingen & Zeng, Fanming & Sun, Fengrui & Wu, Chih, 1996. "Heat-transfer effects on net work and/or power as functions of efficiency for air-standard diesel cycles," Energy, Elsevier, vol. 21(12), pages 1201-1205.
    6. 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.
    7. Salamon, P. & Nulton, J.D. & Siragusa, G. & Andersen, T.R. & Limon, A., 2001. "Principles of control thermodynamics," Energy, Elsevier, vol. 26(3), pages 307-319.
    8. Chen, Lingen & Zhu, Xiaoqin & Sun, Fengrui & Wu, Chih, 2004. "Optimal configuration and performance for a generalized Carnot cycle assuming the heat-transfer law Q[is proportional to]([Delta]T)m," Applied Energy, Elsevier, vol. 78(3), pages 305-313, July.
    9. Johannessen, Eivind & Kjelstrup, Signe, 2004. "Minimum entropy production rate in plug flow reactors: An optimal control problem solved for SO2 oxidation," Energy, Elsevier, vol. 29(12), pages 2403-2423.
    10. Chen, Lingen & Sun, Fengrui & Chen, Wenzhen, 1995. "Optimization of the specific rate of refrigeration in combined refrigeration cycles," Energy, Elsevier, vol. 20(10), pages 1049-1053.
    11. Bonjour, J. & Bejan, A., 2006. "Optimal distribution of cooling during gas compression," Energy, Elsevier, vol. 31(4), pages 409-424.
    12. Kolenda, Z. & Donizak, J. & Hubert, J., 2004. "On the minimum entropy production in steady state heat conduction processes," Energy, Elsevier, vol. 29(12), pages 2441-2460.
    13. de Koeijer, Gelein & Røsjorde, Audun & Kjelstrup, Signe, 2004. "Distribution of heat exchange in optimum diabatic distillation columns," Energy, Elsevier, vol. 29(12), pages 2425-2440.
    14. Göktun, S. & Özkaynak, S. & Yavuz, H., 1993. "Design parameters of a radiative heat engine," Energy, Elsevier, vol. 18(6), pages 651-655.
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    Citations

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    Cited by:

    1. Ahmadi, Mohammad H. & Ahmadi, Mohammad Ali & Sadatsakkak, Seyed Abbas, 2015. "Thermodynamic analysis and performance optimization of irreversible Carnot refrigerator by using multi-objective evolutionary algorithms (MOEAs)," Renewable and Sustainable Energy Reviews, Elsevier, vol. 51(C), pages 1055-1070.
    2. Açıkkalp, Emin, 2015. "Exergetic sustainability evaluation of irreversible Carnot refrigerator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 311-320.
    3. Chen, Lingen & Ding, Zemin & Sun, Fengrui, 2011. "Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics," Energy, Elsevier, vol. 36(7), pages 4011-4018.
    4. Chen, Lingen & Xia, Shaojun, 2022. "Maximizing power of irreversible multistage chemical engine with linear mass transfer law using HJB theory," Energy, Elsevier, vol. 261(PB).
    5. Meng, Fankai & Chen, Lingen & Sun, Fengrui, 2011. "A numerical model and comparative investigation of a thermoelectric generator with multi-irreversibilities," Energy, Elsevier, vol. 36(5), pages 3513-3522.
    6. Zhou, Junle & Chen, Lingen & Ding, Zemin & Sun, Fengrui, 2016. "Analysis and optimization with ecological objective function of irreversible single resonance energy selective electron heat engines," Energy, Elsevier, vol. 111(C), pages 306-312.

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