{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T22:59:02Z","timestamp":1775602742828,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T00:00:00Z","timestamp":1647388800000},"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":["12132015"],"award-info":[{"award-number":["12132015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Pressure drop, heat transfer, and energy performance of ZnO\/water nanofluid with rodlike particles flowing through a curved pipe are studied in the range of Reynolds number 5000 \u2264 Re \u2264 30,000, particle volume concentration 0.1% \u2264 \u03a6 \u2264 5%, Schmidt number 104 \u2264 Sc \u2264 3 \u00d7 105, particle aspect ratio 2 \u2264 \u03bb \u2264 14, and Dean number 5 \u00d7 103 \u2264 De \u2264 1.5 \u00d7 104. The momentum and energy equations of nanofluid, together with the equation of particle number density for particles, are solved numerically. Some results are validated by comparing with the experimental results. The effect of Re, \u03a6, Sc, \u03bb, and De on the friction factor f and Nusselt number Nu is analyzed. The results showed that the values of f are increased with increases in \u03a6, Sc, and De, and with decreases in Re and \u03bb. The heat transfer performance is enhanced with increases in Re, \u03a6, \u03bb, and De, and with decreases in Sc. The ratio of energy PEC for nanofluid to base fluid is increased with increases in Re, \u03a6, \u03bb, and De, and with decreases in Sc. Finally, the formula of ratio of energy PEC for nanofluid to base fluid as a function of Re, \u03a6, Sc, \u03bb, and De is derived based on the numerical data.<\/jats:p>","DOI":"10.3390\/e24030416","type":"journal-article","created":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T22:09:58Z","timestamp":1647468598000},"page":"416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe"],"prefix":"10.3390","volume":"24","author":[{"given":"Wenqian","family":"Lin","sequence":"first","affiliation":[{"name":"School of Media and Design, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruifang","family":"Shi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8418-1176","authenticated-orcid":false,"given":"Jianzhong","family":"Lin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University, Hangzhou 310027, China"},{"name":"Faculty of Mechanical Engineering and & Mechanics, Ningbo University, Ningbo 315201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ijthermalsci.2011.12.017","article-title":"Numerical simulation of laminar forced convection heat transfer of Al2O3-water nanofluid in a pipe with return bend","volume":"55","author":"Choi","year":"2012","journal-title":"Int. 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