{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T00:08:57Z","timestamp":1784333337263,"version":"3.55.0"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T00:00:00Z","timestamp":1661212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSRF","award":["B05F640092"],"award-info":[{"award-number":["B05F640092"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The energy and mass transition through Newtonian hybrid nanofluid flow comprised of copper Cu and aluminum oxide (Al2O3) nanoparticles (nps) over an extended surface has been reported. The thermal and velocity slip conditions are also considered. Such a type of physical problems mostly occurs in symmetrical phenomena and are applicable in physics, engineering, applied mathematics, and computer science. For desired outputs, the fluid flow has been studied under the consequences of the Darcy effect, thermophoresis diffusion and Brownian motion, heat absorption, viscous dissipation, and thermal radiation. An inclined magnetic field is applied to fluid flow to regulate the flow stream. Hybrid nanofluid is created by the dispensation of Cu and Al2O3 nps in the base fluid (water). For this purpose, the flow dynamics have been designed as a system of nonlinear PDEs, which are simplified to a system of dimensionless ODEs through resemblance substitution. The parametric continuation method is used to resolve the obtained set of dimensionless differential equations. It has been noticed that the consequences of heat absorption and thermal radiation boost the energy transmission rate; however, the effect of suction constraint and Darcy\u2013Forchhemier significantly diminished the heat transference rate of hybrid nanofluids. Furthermore, the dispersion of Cu and Al2O3 nps in the base fluid remarkably magnifies the velocity and energy transmission rate.<\/jats:p>","DOI":"10.3390\/sym14091759","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T02:55:34Z","timestamp":1661309734000},"page":"1759","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Computational Study of MHD Darcy\u2013Forchheimer Hybrid Nanofluid Flow under the Influence of Chemical Reaction and Activation Energy over a Stretching Surface"],"prefix":"10.3390","volume":"14","author":[{"given":"Izharul","family":"Haq","sequence":"first","affiliation":[{"name":"College of Sciences and Human Studies (CSHS), Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3952-4341","authenticated-orcid":false,"given":"Mansour F.","family":"Yassen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0335-4686","authenticated-orcid":false,"given":"Mohamed E.","family":"Ghoneim","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7773-4844","authenticated-orcid":false,"given":"Muhammad","family":"Bilal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Science and Technology, Peshawar 25000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0792-337X","authenticated-orcid":false,"given":"Aatif","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9595-6096","authenticated-orcid":false,"given":"Wajaree","family":"Weera","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.rser.2014.11.023","article-title":"A review on hybrid nanofluids: Recent research, development and applications","volume":"43","author":"Sarkar","year":"2015","journal-title":"Renew. 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