{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T09:41:00Z","timestamp":1773135660900,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2014,11,19]],"date-time":"2014-11-19T00:00:00Z","timestamp":1416355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The entropy generation based on the second law of thermodynamics is investigated for turbulent forced convection flow of ZrO2-water nanofluid through a square pipe with constant wall heat flux. Effects of different particle concentrations, inlet conditions and particle sizes on entropy generation of ZrO2-water nanofluid are studied. Contributions from frictional and thermal entropy generations are investigated, and the optimal working condition is analyzed. The results show that the optimal volume concentration of nanoparticles to minimize the entropy generation increases when the Reynolds number decreases. It was also found that the thermal entropy generation increases with the increase of nanoparticle size whereas the frictional entropy generation decreases. Finally, the entropy generation of ZrO2-water was compared with that from other nanofluids (including Al2O3, SiO2 and  CuO nanoparticles in water). The results showed that the SiO2 provided the highest  entropy generation.<\/jats:p>","DOI":"10.3390\/e16116116","type":"journal-article","created":{"date-parts":[[2014,11,19]],"date-time":"2014-11-19T10:56:41Z","timestamp":1416394601000},"page":"6116-6132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":61,"title":["Entropy Generation during Turbulent Flow of Zirconia-water and Other Nanofluids in a Square Cross Section Tube with a Constant Heat Flux"],"prefix":"10.3390","volume":"16","author":[{"given":"Hooman","family":"Yarmand","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,  Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5277-7960","authenticated-orcid":false,"given":"Goodarz","family":"Ahmadi","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam,  NY 13699, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samira","family":"Gharehkhani","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,  Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Salim","family":"Kazi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,  Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Safaei","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,  Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maryam","family":"Alehashem","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abu","family":"Mahat","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, University of Malaya,  Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,11,19]]},"reference":[{"key":"ref_1","unstructured":"Maxwell, J.C. 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