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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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    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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