{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T02:43:05Z","timestamp":1780368185963,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,3]],"date-time":"2017-03-03T00:00:00Z","timestamp":1488499200000},"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":["11572056"],"award-info":[{"award-number":["11572056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51406015"],"award-info":[{"award-number":["51406015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Laboratory of Renewable Energy Electric-Technology of Hunan Province, China","award":["2011KFJ005"],"award-info":[{"award-number":["2011KFJ005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy generation for a paramagnetic fluid in a square enclosure with thermomagnetic convection is numerically investigated under the influence of a magnetic quadrupole field. The magnetic field is calculated using the scalar magnetic potential approach. The finite-volume method is applied to solve the coupled equation for flow, energy, and entropy generation. Simulations are conducted to obtain streamlines, isotherms, Nusselt numbers, entropy generation, and the Bejan number for various magnetic forces (1 \u2264 \u03b3 \u2264 100) and Rayleigh numbers (104 \u2264 Ra \u2264 106). In the absence of gravity, the total entropy generation increases with the increasing magnetic field number, but the average Bejan number decreases. In the gravitational field, the total entropy generation respects the insensitive trend to the change of the magnetic force for low Rayleigh numbers, while it changes significantly for high Rayleigh numbers. When the magnetic field enhances, the share of viscous dissipation in energy losses keeps growing.<\/jats:p>","DOI":"10.3390\/e19030096","type":"journal-article","created":{"date-parts":[[2017,3,3]],"date-time":"2017-03-03T11:30:04Z","timestamp":1488540604000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Effect of a Magnetic Quadrupole Field on Entropy Generation in Thermomagnetic Convection of Paramagnetic Fluid with and without a Gravitational Field"],"prefix":"10.3390","volume":"19","author":[{"given":"Er","family":"Shi","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"Key Laboratory of Renewable Energy Eletric-Technology of Hunan Province, Changsha 410114, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoqin","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"Key Laboratory of Renewable Energy Eletric-Technology of Hunan Province, Changsha 410114, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yecong","family":"He","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"Key Laboratory of Renewable Energy Eletric-Technology of Hunan Province, Changsha 410114, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changwei","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"Key Laboratory of Renewable Energy Eletric-Technology of Hunan Province, Changsha 410114, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1143\/JJAP.39.L262","article-title":"Magnetic acceleration of inhaled and exhaled flows in breathing","volume":"39","author":"Wakayama","year":"2000","journal-title":"Jpn. 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