{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T06:31:25Z","timestamp":1769149885781,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11405032"],"award-info":[{"award-number":["11405032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Thermally driven heat pump systems play important roles in the utilization of low-grade thermal energy. In order to evaluate and compare the performances of three different constructions of thermally driven heat pump and heat transformer, the low-dissipation assumption has been adopted to establish the irreversible thermodynamic models of them in the present paper. By means of the proposed models, the heating loads, the coefficients of performance (COPs) and the optimal relations between them for various constructions are derived and discussed. The performances of different constructions are numerically assessed. More importantly, according to the results obtained, the upper and lower bounds of the COP at maximum heating load for different constructions are generated and compared by the introduction of a parameter measuring the deviation from the reversible limit of the system. Accordingly, the optimal constructions for the low-dissipation three-terminal heat pump and heat transformer are determined within the frame of low-dissipation assumption, respectively. The optimal constructions in accord with previous research and engineering practices for various three-terminal devices are obtained, which confirms the compatibility between the low-dissipation model and endoreversible model and highlights the validity of the application of low-dissipation model for multi-terminal thermodynamic devices. The proposed models and the significant results obtained enrich the theoretical thermodynamic model of thermally driven heat pump systems and may provide some useful guidelines for the design and operation of realistic thermally driven heat pump systems.<\/jats:p>","DOI":"10.3390\/e23050513","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T12:08:30Z","timestamp":1619179710000},"page":"513","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Comparative Assessment of Various Low-Dissipation Combined Models for Three-Terminal Heat Pump Systems"],"prefix":"10.3390","volume":"23","author":[{"given":"Zhexu","family":"Li","sequence":"first","affiliation":[{"name":"College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China"}]},{"given":"Haibo","family":"Cao","sequence":"additional","affiliation":[{"name":"College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China"}]},{"given":"Hanxin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China"}]},{"given":"Juncheng","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"220601","DOI":"10.1103\/PhysRevLett.116.220601","article-title":"Power-efficiency-dissipation relations in linear thermodynamics","volume":"116","author":"Proesmans","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012152","DOI":"10.1103\/PhysRevE.96.012152","article-title":"Endoreversible quantum heat engines in the linear response regime","volume":"96","author":"Wang","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1119\/1.10023","article-title":"Efficiency of a Carnot engine at maximum power output","volume":"43","author":"Curzon","year":"1975","journal-title":"Am. J. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ge, Y., Chen, L., and Sun, F. (2016). Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy, 18.","DOI":"10.3390\/e18040139"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gonzalez-Ayala, J., Roco, J.M.M., Medina, A., and Hernandez, A.C. (2020). Optimization, stability, and entropy in endoreversible heat engines. Entropy, 22.","DOI":"10.3390\/e22111323"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3740","DOI":"10.1063\/1.455832","article-title":"The effect of heat-transfer law on performance of a two-heat-source endoreversible cycle","volume":"90","author":"Chen","year":"1989","journal-title":"J. Chem. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"150603","DOI":"10.1103\/PhysRevLett.105.150603","article-title":"Efficiency at maximum power of low-dissipation Carnot engines","volume":"105","author":"Esposito","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20003","DOI":"10.1209\/0295-5075\/81\/20003","article-title":"Efficiency at maximum power: An analytically solvable model for stochastic heat engines","volume":"81","author":"Schmiedl","year":"2008","journal-title":"Europhys. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"022130","DOI":"10.1103\/PhysRevE.98.022130","article-title":"Ecological efficiency of finite-time thermodynamics: A molecular dynamics study","volume":"98","author":"Rodriguez","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"042120","DOI":"10.1103\/PhysRevE.97.042120","article-title":"Efficiency at maximum power of a laser quantum heat engine enhanced by noise-induced coherence","volume":"97","author":"Dorfman","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"011127","DOI":"10.1103\/PhysRevE.86.011127","article-title":"Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators","volume":"86","author":"Wang","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"012133","DOI":"10.1103\/PhysRevE.87.012133","article-title":"Universal efficiency bounds of weak-dissipative thermodynamic cycles at the maximum power output","volume":"87","author":"Guo","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"110606","DOI":"10.1103\/PhysRevLett.124.110606","article-title":"Optimal cycles for low-dissipation heat engines","volume":"124","author":"Abiuso","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"042119","DOI":"10.1103\/PhysRevE.87.042119","article-title":"Efficiency at maximum power of a heat engine working with a two-level atomic system","volume":"87","author":"Wang","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"103504","DOI":"10.1063\/1.4765725","article-title":"General performance characteristics and parametric optimum bounds of irreversible chemical engines","volume":"112","author":"Guo","year":"2012","journal-title":"J. Appl. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"052101","DOI":"10.1103\/PhysRevE.100.052101","article-title":"Performance optimization of low-dissipation thermal machines revisited","volume":"100","author":"Johal","year":"2019","journal-title":"Phys. Rev. E"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"075011","DOI":"10.1088\/1367-2630\/17\/7\/075011","article-title":"Time, entropy generation, and optimization in low-dissipation heat devices","volume":"17","author":"Medina","year":"2015","journal-title":"New J. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"042112","DOI":"10.1103\/PhysRevE.98.042112","article-title":"Universal constraint for efficiency and power of a low-dissipation heat engine","volume":"98","author":"Ma","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"062132","DOI":"10.1103\/PhysRevE.98.062132","article-title":"Low-dissipation Carnot-like heat engines at maximum efficient power","volume":"98","author":"Singh","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"032142","DOI":"10.1103\/PhysRevE.98.032142","article-title":"Link between optimization and local stability of a low-dissipation heat engine: Dynamic and energetic behaviors","volume":"98","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gonzalez-Ayala, J., Santillan, M., Santos, M.J., Hernandez, A.C., and Roco, J.M.M. (2018). Optimization and stability of heat engines: The role of entropy evolution. Entropy, 20.","DOI":"10.3390\/e20110865"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10004","DOI":"10.1209\/0295-5075\/97\/10004","article-title":"Efficiency at maximum power of minimally nonlinear irreversible heat engines","volume":"97","author":"Izumida","year":"2012","journal-title":"Europhys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"052140","DOI":"10.1103\/PhysRevE.91.052140","article-title":"Heat devices in nonlinear irreversible thermodynamics","volume":"91","author":"Izumida","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"022139","DOI":"10.1103\/PhysRevE.97.022139","article-title":"Entropy generation and unified optimization of Carnot-like and low-dissipation refrigerators","volume":"97","author":"Medina","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"012151","DOI":"10.1103\/PhysRevE.96.012151","article-title":"Heat engines at optimal power: Low-dissipation versus endoreversible model","volume":"96","author":"Johal","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Gonzalez-Ayala, J., Roco, J.M.M., Medina, A., and Hernandez, A.C. (2017). Carnot-like heat engines versus low-dissipation models. Entropy, 19.","DOI":"10.3390\/e19040182"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"119270","DOI":"10.1016\/j.energy.2020.119270","article-title":"Performance evaluation of a new hybrid system consisting of a photovoltaic module and an absorption heat transformer for electricity production and heat upgrading","volume":"216","author":"Zhao","year":"2021","journal-title":"Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"316","DOI":"10.3390\/e6030316","article-title":"Optimal cooling load and COP relationship of a four-heat reservoir endoreversible absorption refrigeration cycle","volume":"6","author":"Chen","year":"2004","journal-title":"Entropy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.apm.2009.03.034","article-title":"Optimal performance of an endoreversible three-mass-reservoir chemical pump with diffusive mass transfer law","volume":"34","author":"Xia","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4492","DOI":"10.1016\/j.energy.2011.03.069","article-title":"Comparative assessment of alternative cycles for waste heat recovery and upgrade","volume":"36","author":"Little","year":"2011","journal-title":"Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"045433","DOI":"10.1103\/PhysRevB.98.045433","article-title":"Absorption refrigerators based on Coulomb-coupled single-electron systems","volume":"98","author":"Erdman","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.energy.2015.12.025","article-title":"Thermoelectric performance and optimization of three-terminal quantum dot nano-devices","volume":"95","author":"Zhang","year":"2016","journal-title":"Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"111917","DOI":"10.1016\/j.enconman.2019.111917","article-title":"Thermally driven refrigerators: Equivalent low-dissipation three-heat-source model and comparison with experimental and simulated results","volume":"198","author":"Guo","year":"2019","journal-title":"Energy Convers. Manage."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"113100","DOI":"10.1016\/j.enconman.2020.113100","article-title":"The equivalent low-dissipation combined cycle system and optimal analyses of a class of thermally driven heat pumps","volume":"220","author":"Guo","year":"2020","journal-title":"Energy Convers. Manage."},{"key":"ref_35","unstructured":"Huang, F.F. (1976). Engineering Thermodynamics Fundamental and Applications, Macmillan Publishing Co."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4951","DOI":"10.1063\/1.456594","article-title":"Equivalent combined systems of three-heat-source heat pumps","volume":"90","author":"Chen","year":"1989","journal-title":"J. Chem. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/01430750.2002.9674875","article-title":"The equivalent combined cycle of an irreversible chemical pump and its performance analysis","volume":"23","author":"Lin","year":"2002","journal-title":"Int. J. Ambient Energy"},{"key":"ref_38","first-page":"119","article-title":"The equivalent combined cycle of an irreversible chemical potential transformer and its optimal performance","volume":"2","author":"Lin","year":"2002","journal-title":"Int. J. Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/j.enconman.2010.09.037","article-title":"A model for analysis and design of H2O-LiBr absorption heat pumps","volume":"52","author":"Bakhtiari","year":"2011","journal-title":"Energy Convers. Manage."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1016\/j.applthermaleng.2010.07.032","article-title":"A mathematical model with experiments of single effect absorption heat pump using LiBr-H2O","volume":"30","author":"Sun","year":"2010","journal-title":"Appl. Therm. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1016\/j.energy.2018.10.052","article-title":"Waste heat recovery of power plant with large scale serial absorption heat pumps","volume":"165","author":"Xu","year":"2018","journal-title":"Energy"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1016\/j.energy.2017.10.002","article-title":"Performance of a vapour absorption heat transformer operating with ionic liquids and ammonia","volume":"141","author":"Sujatha","year":"2017","journal-title":"Energy"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/j.applthermaleng.2018.08.104","article-title":"Analysis of single stage steam generating absorption heat transformer","volume":"144","author":"Hong","year":"2018","journal-title":"Appl. Therm. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"073202","DOI":"10.1088\/1742-5468\/2016\/07\/073202","article-title":"Irreversible and endoreversible behaviors of the LD-model for heat devices: The role of the time constraints and symmetries on the performance at maximum \u03c7 figure of merit","volume":"2016","author":"Hernandez","year":"2016","journal-title":"J. Stat. Mech."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/5\/513\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:51:57Z","timestamp":1760161917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/5\/513"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":44,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["e23050513"],"URL":"https:\/\/doi.org\/10.3390\/e23050513","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,23]]}}}