{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T10:25:37Z","timestamp":1777026337240,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T00:00:00Z","timestamp":1623196800000},"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>Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag\/water) and a phase flow model (Cu\/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.<\/jats:p>","DOI":"10.3390\/e23060732","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T04:22:22Z","timestamp":1623212542000},"page":"732","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Entropy Analysis of the Peristaltic Flow of Hybrid Nanofluid Inside an Elliptic Duct with Sinusoidally Advancing Boundaries"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4079-3231","authenticated-orcid":false,"given":"Luthais B.","family":"McCash","sequence":"first","affiliation":[{"name":"School of Mathematics & Actuarial Science, University of Leicester, Leicester LE1 7RH, UK"}]},{"given":"Salman","family":"Akhtar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan"}]},{"given":"Sohail","family":"Nadeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan"}]},{"given":"Salman","family":"Saleem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1146\/annurev.fl.03.010171.000305","article-title":"Peristaltic pumping","volume":"3","author":"Jaffrin","year":"1971","journal-title":"Annu. 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