Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation

Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation | 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 Research Article Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation P. D. Selvi, Annuri Shobha, K. Venkatadri, K Sudarmozhi, J. O. Akanni This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9131455/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This research presents a numerical investigation of free convection of a ternary hybrid nanofluid in a permeable enclosure under the impact of an inclined magnetic field, thermal radiation, and internal heat generation. The ternary hybrid nanofluid consists of a base fluid with dispersed nanoparticles of aluminum oxide, copper ( Cu ), and multi-walled carbon nanotubes to increase thermal conductivity. The governing equations for mass, momentum, and energy are formulated in nondimensional form and solved via the Marker-And-Cell (MAC) method on a staggered grid with a finite difference discretization scheme. The effects of key dimensionless parameters including Rayleigh number ( Ra ), Hartmann number ( Ha ), radiation ( Rd ), Darcy number ( Da ), and heat generation/absorption parameter ( Q ) on heat transfer characteristics are analyzed. The results show that increasing Ra from \({10}^{3}to{10}^{6}\) enhances convective heat transfer, leading to a 192% increase in the average Nusselt number ( \(N{u}_{a}\) ), whereas decreasing Da from 0.1 to 0.0001 suppresses convection and results in a 53% drop in \(N{u}_{a}\) . The application of an external magnetic field ( Ha = 50) reduces energy transfer efficiency by 41%, confirming the suppressive effect of Lorentz forces. Conversely, increasing Rd from 0 to 5 significantly enhances radiative energy transfer, leading to a 229% rise in \(N{u}_{a}\) . Internal heat generation ( Q = 5) weakens convective motion, reducing \(N{u}_{a}\) ​ by 12%, while heat absorption enhances convection and increases heat transfer. These findings highlight the strong interplay between buoyancy, magnetic field suppression, porous medium resistance, radiative heat transfer, and internal heat generation, demonstrating that ternary hybrid nanofluids can be optimized for various thermal management applications, including nuclear reactor cooling, MHD power generation, industrial heat exchangers, and electronic cooling systems. Ternary hybrid nanofluid Magnetohydrodynamic (MHD) Square enclosure heat transfer Porous medium Finite difference Method Free convection Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9131455","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":607732082,"identity":"b18c6302-9635-4960-97df-9b584de211c3","order_by":0,"name":"P. D. Selvi","email":"","orcid":"","institution":"Sri Padmavathi Mahila Visva Vidyalyam","correspondingAuthor":false,"prefix":"","firstName":"P.","middleName":"D.","lastName":"Selvi","suffix":""},{"id":607732083,"identity":"34d676dc-22f6-4128-b3bd-387cda6e96d4","order_by":1,"name":"Annuri Shobha","email":"","orcid":"","institution":"Sri Padmavathi Mahila Visva Vidyalyam","correspondingAuthor":false,"prefix":"","firstName":"Annuri","middleName":"","lastName":"Shobha","suffix":""},{"id":607732084,"identity":"d1665b6f-f8af-4f5d-b8ef-67ad8f49adcc","order_by":2,"name":"K. Venkatadri","email":"","orcid":"","institution":"Mohan Babu University (Erstwhile Sree Vidyanikethan Engineering College)","correspondingAuthor":false,"prefix":"","firstName":"K.","middleName":"","lastName":"Venkatadri","suffix":""},{"id":607732085,"identity":"5d1ac22c-85de-420b-912c-e65057f7d5ab","order_by":3,"name":"K Sudarmozhi","email":"","orcid":"","institution":"Saveetha School of Engineering, SIMATS","correspondingAuthor":false,"prefix":"","firstName":"K","middleName":"","lastName":"Sudarmozhi","suffix":""},{"id":607732086,"identity":"258b31f1-38bf-4c86-98a1-ae5fb825984d","order_by":4,"name":"J. O. Akanni","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYBACxmYGA4YPFTYgZuMBorUwzjiTBmI2EKcFCAyYedsOg1nEaWFuZ974gOfMebu17YeBttTYRBPhMLZiA4mK28nbziQCtRxLy20grIXHTMLgzO1kswNALYwNh4nSYv4jse1cstn5h8RrMWM42HbAzuwG8bawFUs2nElOMLsBtCWBGL8Y9h/e+PlPhZ292fn0hw8+1NgQoQWqIhFMJxBSDgLyUNqeGMWjYBSMglEwQgEAeH5JGOAfFO0AAAAASUVORK5CYII=","orcid":"","institution":"Saveetha School of Engineering, SIMATS","correspondingAuthor":true,"prefix":"","firstName":"J.","middleName":"O.","lastName":"Akanni","suffix":""}],"badges":[],"createdAt":"2026-03-15 23:23:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9131455/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9131455/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107487602,"identity":"6fb546cc-195f-4551-8b71-c3639bd8c693","added_by":"auto","created_at":"2026-04-22 02:42:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2122446,"visible":true,"origin":"","legend":"","description":"","filename":"NumericalAnalysisofFreeConvectionina.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9131455/v1_covered_7ebef69f-c2e8-4176-956b-e7d596c1b520.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ternary hybrid nanofluid, Magnetohydrodynamic (MHD), Square enclosure, heat transfer, Porous medium, Finite difference Method, Free convection","lastPublishedDoi":"10.21203/rs.3.rs-9131455/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9131455/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research presents a numerical investigation of free convection of a ternary hybrid nanofluid in a permeable enclosure under the impact of an inclined magnetic field, thermal radiation, and internal heat generation. The ternary hybrid nanofluid consists of a base fluid with dispersed nanoparticles of aluminum oxide, copper (\u003cem\u003eCu\u003c/em\u003e), and multi-walled carbon nanotubes to increase thermal conductivity. The governing equations for mass, momentum, and energy are formulated in nondimensional form and solved via the Marker-And-Cell (MAC) method on a staggered grid with a finite difference discretization scheme. The effects of key dimensionless parameters including Rayleigh number (\u003cem\u003eRa\u003c/em\u003e), Hartmann number (\u003cem\u003eHa\u003c/em\u003e), radiation (\u003cem\u003eRd\u003c/em\u003e), Darcy number (\u003cem\u003eDa\u003c/em\u003e), and heat generation/absorption parameter (\u003cem\u003eQ\u003c/em\u003e) on heat transfer characteristics are analyzed. The results show that increasing \u003cem\u003eRa\u003c/em\u003e from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({10}^{3}to{10}^{6}\\)\u003c/span\u003e\u003c/span\u003e enhances convective heat transfer, leading to a 192% increase in the average Nusselt number (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N{u}_{a}\\)\u003c/span\u003e\u003c/span\u003e), whereas decreasing \u003cem\u003eDa\u003c/em\u003e from 0.1 to 0.0001 suppresses convection and results in a 53% drop in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N{u}_{a}\\)\u003c/span\u003e\u003c/span\u003e. The application of an external magnetic field (\u003cem\u003eHa\u003c/em\u003e\u0026thinsp;=\u0026thinsp;50) reduces energy transfer efficiency by 41%, confirming the suppressive effect of Lorentz forces. Conversely, increasing \u003cem\u003eRd\u003c/em\u003e from 0 to 5 significantly enhances radiative energy transfer, leading to a 229% rise in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N{u}_{a}\\)\u003c/span\u003e\u003c/span\u003e. Internal heat generation (\u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5) weakens convective motion, reducing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N{u}_{a}\\)\u003c/span\u003e\u003c/span\u003e​ by 12%, while heat absorption enhances convection and increases heat transfer. These findings highlight the strong interplay between buoyancy, magnetic field suppression, porous medium resistance, radiative heat transfer, and internal heat generation, demonstrating that ternary hybrid nanofluids can be optimized for various thermal management applications, including nuclear reactor cooling, MHD power generation, industrial heat exchangers, and electronic cooling systems.\u003c/p\u003e","manuscriptTitle":"Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-20 19:58:42","doi":"10.21203/rs.3.rs-9131455/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8933fa18-8db1-4502-874a-1c776378f4ce","owner":[],"postedDate":"March 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-21T15:26:42+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-20 19:58:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9131455","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9131455","identity":"rs-9131455","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}