Abstract
Compared with endoreversible heat engine with pure heat transfer and endoreversible isothermal chemical engine with pure mass transfer, endoreversible non-isothermal chemical engine (ENICE) is a more reasonable model of practical mass exchanger, solid device and chemo-electric systems. There exists heat and mass transfer (HMT) simultaneously between working fluid and chemical potential reservoir in ENICE. There is coupled HMT effect that in ENICE should be considered. There are two ways to consider this coupled effect. One is based on Onsager equations, and another is based on Lewis analogy. For the mathematical and physical description of the above HMT process, the model using Onsager equations are more appropriate in the linear HMT region not far from the equilibrium state, while that based on Lewis analogy is more appropriate in nonlinear HMT region far from the equilibrium state. Different from the previous research on the power optimization of ENICEs with Onsager equations, this paper optimizes power and efficiency of ENICE based on Lewis analogy. HMT processes are assumed to obey Newtonian heat transfer law (q ∝ ΔT, and T is temperature) and Fick’s diffusive mass transfer law (g ∝ Δc, and c is concentration), respectively. Analytical results of power output and corresponding vector efficiency (ηT and ημ) of ENICE are obtained, which provide important parallel results with those based on Onsager equations. They include special cases for endoreversible Carnot heat engine with q ∝ Δ T and endoreversible isothermal chemical engine with g ∝ Δ c. Adopting Lewis analogy in the modelling of ENICEs with simultaneous HMT is an important work. It provides important analytical and numerical results different from those with Onsager equations obtained previously and enriches the research contents of FTT. The research results in this paper have a certain guiding significance for the optimal designs of single irreversible NICEs, multistage NICE systems, practical mass exchangers, solid devices, chemo-electric systems, and so on.
Similar content being viewed by others
References
Curzon F L, Ahlborn B. Efficiency of a Carnot engine at maximum power output. Am J Phys, 1975, 43: 22–24
Andresen B. Finite-Time Thermodynamics. Dissertation for Doctoral Degree. Copenhagen: University of Copenhagen, 1983
Andresen B. Current trends in finite-time thermodynamics. Angew Chem Int Ed, 2011, 50: 2690–2704
Sieniutycz S. Complexity and Complex Chemo-Electric Systems. Elsevier, 2021
Chen L G, Wu C, Sun F R. Finite time thermodynamic optimization or entropy generation minimization of energy systems. J Non-Equilib Thermodyn, 1999, 24: 327–359
Chen L G, Xia S J. Progresses in generalized thermodynamic dynamic-optimization of irreversible processes (in Chinese). Sci Sin Tech, 2019, 49: 981–1022
Chen L G, Xia S J, Feng H J. Progress in generalized thermodynamic dynamic-optimization of irreversible cycles (in Chinese). Sci Sin Tech, 2019, 49: 1223–1267
Gyftopoulos E P. Fundamentals of analysis of processes. Energy Convers Manag, 1997, 38: 1525–1533
Sekulic D P. A fallacious argument in the finite time thermodynamics concept of endoreversibility. J Appl Phys, 1998, 83: 4561–4565
Moran M J. On second-law analysis and the failed promise of finite-time thermodynamics. Energy, 1998, 23: 517–519
Gyftopoulos E P. Infinite time (reversible) versus finite time (irreversible) thermodynamics: A misconceived distinction. Energy, 1999, 24: 1035–1039
Ishida M. The role and limitations of endoreversible thermodynamics. Energy, 1999, 24: 1009–1014
Gyftopoulos E P. On the Curzon-Ahlborn efficiency and its lack of connection to power producing processes. Energy Convers Manage, 2002, 43: 609–615
Salamon P. Physics versus engineering of finite-time thermodynamic models and optimizations. In: Thermodynamic Optimization of Complex Energy Systems. NATO Advanced Study Institute, Neptun, Romania, 1324, 1998. Bejan A, Mamut E, eds. Kluwer Academic Publishers, 1999. 421–424
Salamon P. A contrast between the physical and the engineering approaches to finite-time thermodynamic models and optimizations. In: Recent Advances in Finite Time Thermodynamics. Wu C, Chen L, Chen J, eds. New York: Nova Science Publisher, 1999. 541–552
Chen J, Yan Z, Lin G, Andresen B. On the Curzon-Ahlborn efficiency and its connection with the efficiencies of real heat engines. Energy Convers Manage, 2001, 42: 173–181
Salamon P, Nulton J D, Siragusa G, et al. Principles of control thermodynamics. Energy, 2001, 26: 307–319
Andresen B. Comment on “A fallacious argument in the finite time thermodynamic concept of endoreversibility” [J. Appl. Phys. 83, 4561 (1998)]. J Appl Phys, 2001, 90: 6557–6559
Gonca G, Sahin B. Performance analysis of a novel eco-friendly internal combustion engine cycle. Int J Energy Res, 2019, 43: 5897–5911
Gonca G, Hocaoglu M F. Performance analysis and simulation of a diesel-miller cycle (DiMC) engine. Arab J Sci Eng, 2019, 44: 5811–5824
Gonca G, Genc I. Thermoecology-based performance simulation of a Gas-Mercury-Steam power generation system (GMSPGS). Energy Convers Manage, 2019, 189: 91–104
Gonca G, Genc I. Performance simulation of a double-reheat Rankine cycle mercury turbine system based on exergy. Int J Exergy, 2019, 30: 392–403
Wu Z, Feng H, Chen L, et al. Constructal thermodynamic optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle. Energy Convers Manage, 2020, 210: 112727
Chen L G, Meng F K, Ge Y L, et al. Performance optimization of a class of combined thermoelectric heating devices. Sci China Tech Sci, 2020, 63: 2640–2648
Feng H, Wu Z, Chen L, et al. Constructal thermodynamic optimization for dual-pressure organic Rankine cycle in waste heat utilization system. Energy Convers Manage, 2021, 227: 113585
Zhang X, Yang G F, Yan M Q, et al. Design of an all-day electrical power generator based on thermoradiative devices. Sci China Tech Sci, 2021, 64: 2166–2173
Liu X W, Chen L G, Ge Y L, et al. Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with spin-1/2 systems. J Non-Equilib ThermoDyn, 2021, 46: 61–76
Chen L, Meng F, Ge Y, et al. Performance optimization for a multielement thermoelectric refrigerator with linear phenomenological heat transfer law. J Non-Equilibrium ThermoDyn, 2021, 46: 149–162
Qi C, Ding Z, Chen L, et al. Modeling of irreversible two-stage combined thermal brownian refrigerators and their optimal performance. J Non-Equilibrium ThermoDyn, 2021, 46: 175–189
Ding Z, Qiu S, Chen L, et al. Modeling and performance optimization of double-resonance electronic cooling device with three electron reservoirs. J Non-Equilibrium ThermoDyn, 2021, 46: 273–289
Valencia-Ortega G, Levario-Medina S, Barranco-Jiménez M A. The role of internal irreversibilities in the performance and stability of power plant models working at maximum ∊-ecological function. J Non-Equilibrium ThermoDyn, 2021, 46: 413–429
Qiu S S, Ding Z M, Chen L G, et al. Performance optimization of three-terminal energy selective electron generators. Sci China Tech Sci, 2021, 64: 1641–1652
Gonca G, Hocaoglu Fatih M. Exergy-based performance analysis and evaluation of a dual-diesel cycle engine. Therm Sci, 2021, 25: 3675–3685
Ge Y, Shi S, Chen L, et al. Power density analysis and multi-objective optimization for an irreversible dual cycle. J Non-Equilibrium Ther-moDyn, 2022, 47: 289–309
Lin J, Xie S, Jiang C X, et al. Maximum power and corresponding efficiency of an irreversible blue heat engine for harnessing waste heat and salinity gradient energy. Sci China Tech Sci, 2022, 65: 646–656
Chen L G, Li P L, Xia S J, et al. Multi-objective optimization for membrane reactor for steam methane reforming heated by molten salt. Sci China Tech Sci, 2022, 65: 1396–1414
Gonca G, Guzel B. Exergetic and exergo-economical analyses of a gas-steam combined cycle system. J Non-Equilibrium ThermoDyn, 2022, 47: 415–431
Chen L, Qi C, Ge Y, et al. Thermal Brownian heat engine with external and internal irreversibilities. Energy, 2022, 255: 124582
Gonca G, Sahin B, Genc I. Investigation of maximum performance characteristics of seven-process cycle engine. Int J Exergy, 2022, 37: 302–312
Xu H, Chen L, Ge Y, et al. Multi-objective optimization of Stirling heat engine with various heat and mechanical losses. Energy, 2022, 256: 124699
Gonca G, Sahin B. Performance investigation and evaluation of an engine operating on a modified dual cycle. Intl J Energy Res, 2022, 46: 2454–2466
Chen L, Shi S, Ge Y, et al. Performance optimization of diffusive mass transfer law irreversible isothermal chemical pump. Energy, 2023, 263: 125956
Jin Q, Xia S, Chen L. A modified recompression S-CO2 Brayton cycle and its thermodynamic optimization. Energy, 2023, 263: 126015
Chen L, Shi S, Feng H, et al. Maximum ecological function performance for a three-reservoir endoreversible chemical pump. J Non-Equilibrium ThermoDyn, 2023, 48: 179–194
Smith Z, Pal P S, Deffner S. Endoreversible Otto engines at maximal power. J Non-Equilibrium ThermoDyn, 2020, 45: 305–310
Chen L, Ma K, Feng H, et al. Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies, 2020, 13: 3229
Boykov S Y, Andresen B, Akhremenkov A A, et al. Evaluation of irreversibility and optimal organization of an integrated multi-stream heat exchange system. J Non-Equilibrium ThermoDyn, 2020, 45: 155–171
Chen L, Ma K, Ge Y, et al. Re-optimization of expansion work of a heated working fluid with generalized radiative heat transfer law. Entropy, 2020, 22: 720
Chen L, Feng H, Ge Y. Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs. Energy Convers Manage, 2020, 223: 113261
Badescu V. Self-driven reverse thermal engines under monotonous and oscillatory optimal operation. J Non-Equilibrium ThermoDyn, 2021, 46: 291–319
Badescu V. Maximum work rate extractable from energy fluxes. J Non-Equilibrium ThermoDyn, 2022, 47: 77–93
Paul R, Hoffmann K H. Optimizing the piston paths of stirling cycle cryocoolers. J Non-Equilibrium ThermoDyn, 2022, 47: 195–203
Li P L, Chen L G, Xia S J, et al. Total entropy generation rate minimization configuration of a membrane reactor of methanol synthesis via carbon dioxide hydrogenation. Sci China Tech Sci, 2022, 65: 657–678
Li J, Chen L. Optimal configuration of finite source heat engine cycle for maximum output work with complex heat transfer law. J Non-Equilibrium ThermoDyn, 2022, 47: 433–441
Chen L, Xia S. Heat engine cycle configurations for maximum work output with generalized models of reservoir thermal capacity and heat resistance. J Non-Equilibrium ThermoDyn, 2022, 47: 329–338
Chen L, Xia S. Minimizing entransy dissipation for heat transfer processes with q ∝Δ(Tn) and heat leakage. Case Studies Thermal Eng, 2022, 36: 102183
Chen L, Ma K, Feng H, et al. Optimal piston motion paths for a light-driven engine with generalized radiative law and maximum ecological function. Case Studies Thermal Eng, 2022, 40: 102505
Li P L, Chen L G, Xia S J, et al. Multi-objective optimal configurations of a membrane reactor for steam methane reforming. Energy Rep, 2022, 8: 527–538
Ge Y, Chen L, Feng H. Optimal piston motion configuration for irreversible Otto cycle heat engine with maximum ecological function objective. Energy Rep, 2022, 8: 2875–2887
Chen L, Xia S. Minimum power consumption of multistage irreversible Carnot heat pumps with heat transfer law of q ∝ (ΔT)m. J Non-Equilibrium ThermoDyn, 2023, 48: 107–118
Diskin D, Tartakovsky L. Finite-time energy conversion in a hybrid cycle combining electrochemical, combustion and thermochemical recuperation processes. Energy Convers Manage, 2022, 262: 115673
Tsirlin A M, Leskov E E, Kazakov V. Finite time thermodynamics: Limiting performance of diffusion engines and membrane systems. J Phys Chem A, 2005, 109: 9997–10003
Gordon J M, Orlov V N. Performance characteristics of endoreversible chemical engines. J Appl Phys, 1993, 74: 5303–5309
Lin G, Chen J, Brück E. Irreversible chemical-engines and their optimal performance analysis. Appl Energy, 2004, 78: 123–136
Hooyberghs H, Cleuren B, Salazar A, et al. Efficiency at maximum power of a chemical engine. J Chem Phys, 2013, 139: 134111
Diskin D, Tartakovsky L. Efficiency at maximum power of the low-dissipation hybrid electrochemical-Otto cycle. Energies, 2020, 13: 3961
Diskin D, Tartakovsky L. Power and efficiency characteristics of a hybrid electrochemical-ICE cycle. SAE Int J Adv Curr Pract Mobil, 2021, 3: 1487–1494
Chen L, Xia S. Maximizing power of irreversible multistage chemical engine with linear mass transfer law using HJB theory. Energy, 2022, 261: 125277
Chen L, Xia S. Maximum work output configuration of finite potential source irreversible isothermal chemical engines with bypass mass leakage and mass resistance. Energy Rep, 2022, 8: 11440–11445
De Vos A. Endoreversible thermodynamics and chemical reactions. J Phys Chem, 1991, 95: 4534–4540
De Vos A. Endoreversible Thermodynamics of Solar Energy Conversion. Oxford: Oxford University, 1992
Sieniutycz S. Optimal control framework for mutistage endoreversible engines with heat and mass transfer. J Non-Equibrium ThermoDyn, 1999, 24: 40–74
Sieniutycz S, Kubiak M. Dynamical energy limits in traditional and work-driven operations I. Heat-mechanical systems. Int J Heat Mass Transfer, 2002, 45: 2995–3012
Sieniutycz S. Thermodynamics of chemical power generators. Chem Process Eng, 2008, 29: 321–335
Sieniutycz S. Complex chemical systems with power production driven by heat and mass transfer. Int J Heat Mass Transfer, 2009, 52: 2453–2465
Cai Y, Su G Z, Chen J C. Influence of heat- and mass-transfer coupling on the optimal performance of a non-isothermal chemical engine. Rev Mex Fis, 2010, 56: 356–362
Guo J, Wang Y, Chen J. General performance characteristics and parametric optimum bounds of irreversible chemical engines. J Appl Phys, 2012, 112: 103504
Gordon J M, Hui T C. Thermodynamic perspective for the specific energy consumption of seawater desalination. Desalination, 2016, 386: 13–18
Chen L, Xia S. Maximizing power output of endoreversible non-isothermal chemical engine via linear irreversible thermodynamics. Energy, 2022, 255: 124526
Sieniutycz S. Analysis of power and entropy generation in a chemical engine. Int J Heat Mass Transfer, 2008, 51: 5859–5871
Chen L G, Xia S J. Power-optimization of multistage non-isothermal chemical engine system via Onsager equations, Hamilton-Jacobi-Bellman theory and dynamic programming. Sci China Tech Sci, 2023, 66: 841–852
Chen L, Xia S. Maximum work configuration of finite potential source endoreversible non-isothermal chemical engines. J Non-Equilibrium ThermoDyn, 2023, 48: 41–53
Berry R S, Kazakov V A, Sieniutycz S, et al. Thermodynamic Optimization of Finite Time Processes. Chichester: Wiley, 1999
Corless R M, Gonnet G H, Hare D E G, et al. Lambert’s W Function in Maple. Maple Technical Newsletter, 1993, 9: 12–22
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51976235 and 52171317).
Rights and permissions
About this article
Cite this article
Chen, L., Xia, S. Power output and efficiency optimization of endoreversible non-isothermal chemical engine via Lewis analogy. Sci. China Technol. Sci. 66, 2651–2659 (2023). https://doi.org/10.1007/s11431-022-2281-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-022-2281-8