Machine Learning Investigation of Marangoni Convection in Hybrid Nanofluids with Darcy-Forchheimer

Machine Learning Investigation of Marangoni Convection in Hybrid Nanofluids with Darcy-Forchheimer | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Machine Learning Investigation of Marangoni Convection in Hybrid Nanofluids with Darcy-Forchheimer Hamid QURESHI, Sebastian ALTMEYER, Muhammad ZUBAIR This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7348640/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted 12 You are reading this latest preprint version Abstract This research utilizes machine learning to investigate Marangoni convection in a hybrid nanofluid (MnZnFe 2 O 4 +NiZnFe 2 O 4 ⁄H 2 O) within a Darcy-Forchheimer porous framework. We conduct both qualitative and quantitative assessments of heat transfer, mass transfer, and viscous dissipation irreversibility during the flow. Numerical results are obtained using a Python finite difference algorithm, after which MATLAB is employed for AI-based analysis. Additionally, the Levenberg-Marquardt neural network algorithm is trained and utilized. Our findings show that fluid velocity diminishes as the inverse Darcy parameter, Marangoni ratio, and Forchheimer parameter increase. Moreover, the temperature rises with the Eckert number and Prandtl ratio. As concentration increases, activation energy and Schmidt parameter also grow. Mean Square Error (MSE) for the results reaches up to 10 -11 across various impacts. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Nanoscience and technology Physical sciences/Physics Artificial intelligence Machine Learning Levenberg Marquardt Neural-Network Algorithm hybrid nanofluid Darcy Forchheimer Marangoni ratio convection Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 12 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 10 Sep, 2025 Reviews received at journal 10 Sep, 2025 Reviews received at journal 06 Sep, 2025 Reviews received at journal 04 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers invited by journal 03 Sep, 2025 Editor assigned by journal 20 Aug, 2025 Editor invited by journal 14 Aug, 2025 Submission checks completed at journal 13 Aug, 2025 First submitted to journal 13 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7348640","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":511717052,"identity":"b07d7884-fa3b-409b-97cd-47805e213bf1","order_by":0,"name":"Hamid QURESHI","email":"","orcid":"","institution":"Mohi-Ud-Din Islamic University","correspondingAuthor":false,"prefix":"","firstName":"Hamid","middleName":"","lastName":"QURESHI","suffix":""},{"id":511717054,"identity":"4eacb2a0-657e-42b4-bba8-7d200fbb1f62","order_by":1,"name":"Sebastian ALTMEYER","email":"data:image/png;base64,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","orcid":"","institution":"Universitat Politecnica de Catalunya EETAC - School of Telecom and Aerospace Engineering","correspondingAuthor":true,"prefix":"","firstName":"Sebastian","middleName":"","lastName":"ALTMEYER","suffix":""},{"id":511717056,"identity":"f4f2fe82-0bf0-4b88-92ba-6654b63b129d","order_by":2,"name":"Muhammad ZUBAIR","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"ZUBAIR","suffix":""}],"badges":[],"createdAt":"2025-08-11 17:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7348640/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7348640/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-23362-8","type":"published","date":"2025-11-12T15:58:20+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":96106213,"identity":"1760238e-e13f-4a63-a6a9-31f71994ade8","added_by":"auto","created_at":"2025-11-17 16:12:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2292804,"visible":true,"origin":"","legend":"","description":"","filename":"paper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7348640/v1_covered_c4b5b791-44e0-4213-a48f-1d37aa81893b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine Learning Investigation of Marangoni Convection in Hybrid Nanofluids with Darcy-Forchheimer","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Artificial intelligence, Machine Learning, Levenberg Marquardt Neural-Network Algorithm, hybrid nanofluid, Darcy Forchheimer, Marangoni ratio, convection","lastPublishedDoi":"10.21203/rs.3.rs-7348640/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7348640/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research utilizes machine learning to investigate Marangoni convection in a hybrid nanofluid (MnZnFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e +NiZnFe\u003csub\u003e2\u003c/sub\u003e O\u003csub\u003e4\u003c/sub\u003e⁄H\u003csub\u003e2\u003c/sub\u003e O) within a Darcy-Forchheimer porous framework. We conduct both qualitative and quantitative assessments of heat transfer, mass transfer, and viscous dissipation irreversibility during the flow. Numerical results are obtained using a Python finite difference algorithm, after which MATLAB is employed for AI-based analysis. Additionally, the Levenberg-Marquardt neural network algorithm is trained and utilized. Our findings show that fluid velocity diminishes as the inverse Darcy parameter, Marangoni ratio, and Forchheimer parameter increase. Moreover, the temperature rises with the Eckert number and Prandtl ratio. As concentration increases, activation energy and Schmidt parameter also grow. 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