{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T22:12:19Z","timestamp":1774822339195,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2022R59"],"award-info":[{"award-number":["PNURSP2022R59"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Due to their capacity to create better thermal conductivity than standard nanofluids, hybrid nano-fluids and modified nanofluids have notable applications in aerospace, energy materials, thermal sensors, antifouling, etc. This study aims to the modified and hybrid nanofluid flow with the Carreau fluid over a sloped shrinking sheet. The Cattaneo\u2013Christov heat flux also takes into account. To determine the thermal efficiency of the heat, three different kinds of nanomaterials, copper oxide (CuO), copper (Cu), and alumina (Al2O3), are used. The similarity alteration commutes the insolubility of the model into ODEs. The conclusions are attained by program writing in MATLAB software and dealing with them through the bvp4c solver with the shooting method. The skin-friction amount decreases with the inclined sheet and local Weissenberg parameter for both modified and hybrid nanofluid. An upsurge thermal relaxation parameter declines the skin-friction coefficient for modified nanofluid flow and increases the skin-friction coefficient for hybrid nanofluid flow. The heat transfer rate is upsurged with modified and hybrid nanofluid for thermal relaxation parameter. Furthermore, the presentation includes the development of skin friction coefficient and Nusselt number values for specific parameters. Through benchmarking, numerical solutions are validated using certain limiting situations that were previously published findings, and typically solid correlation is shown.<\/jats:p>","DOI":"10.3390\/sym14122605","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T02:20:31Z","timestamp":1670552431000},"page":"2605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Numerical Study of Cattaneo\u2013Christov Heat Flux on Water-Based Carreau Fluid Flow over an Inclined Shrinking Sheet with Ternary Nanoparticles"],"prefix":"10.3390","volume":"14","author":[{"given":"Sanju","family":"Jangid","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3283-4870","authenticated-orcid":false,"given":"Nazek","family":"Alessa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruchika","family":"Mehta","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3979-3549","authenticated-orcid":false,"given":"N.","family":"Thamaraikannan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Erode Arts and Science College, Erode 638009, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2462-8068","authenticated-orcid":false,"given":"Shilpa","family":"Shilpa","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0169-7722(98)00066-7","article-title":"Effect of hysteresis on water flow in a sand column with a fluctuating capillary fringe","volume":"33","author":"Lehmann","year":"1998","journal-title":"J. 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