{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:42:00Z","timestamp":1760244120629,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2003,12,31]],"date-time":"2003-12-31T00:00:00Z","timestamp":1072828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Heat transfer between a thermoacoustic engine and its surrounding heat reservoirs can be out of phase with oscillating working gas temperature. The paper presents a generalized heat transfer model using a complex heat transfer exponent. Both the real part and the imaginary part of the heat transfer exponent change the power versus efficiency relationship quantitatively. When the real part of the heat transfer exponent is fixed, the power output P decreases and the efficiency \u03b7 increases along with increasing of the imaginary part. The Optimization zone on the performance of the thermoacoustic heat engine is obtained. The results obtained will be helpful for the further understanding and the selection of the optimal operating mode of the thermoacoustic heat engine.<\/jats:p>","DOI":"10.3390\/e5050444","type":"journal-article","created":{"date-parts":[[2008,10,25]],"date-time":"2008-10-25T13:44:42Z","timestamp":1224942282000},"page":"444-451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimization of a Thermoacoustic Engine with a Complex Heat Transfer Exponent"],"prefix":"10.3390","volume":"5","author":[{"given":"Feng","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Physics, Wuhan Institute of Chemical Technology, Wuhan, 430073, China"}]},{"given":"Chih","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, U.S. Naval Academy, Annapolis, MD 21402, USA"}]},{"given":"Fangzhong","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Energy, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"Technical Institute of Physics and Chemistry, Chinese Academy of Science, BeiJing 100080, China"}]},{"given":"Lingen","family":"Chen","sequence":"additional","affiliation":[{"name":"Faculty 306, Naval academy of Engineering, Wuhan 430033, China"}]}],"member":"1968","published-online":{"date-parts":[[2003,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1121\/1.396617","article-title":"Thermoacoustic engines","volume":"84","author":"Swift","year":"1988","journal-title":"J. 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[Investigation on modeling and optimization of thermoacoustic engine systems, Huazhong University of Science and Technology]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/5\/5\/444\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:26:43Z","timestamp":1760221603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/5\/5\/444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12,31]]},"references-count":15,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2003,12]]}},"alternative-id":["e5050444"],"URL":"https:\/\/doi.org\/10.3390\/e5050444","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2003,12,31]]}}}