{"paper_id":"3cbc8581-2467-4fe3-8387-e0aca49ff5b1","body_text":"Theoretical investigation on heat transfer rate of hydromagnetic transformer oil based multiphase fluid: Comprehensive modeling and computational study | 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 Theoretical investigation on heat transfer rate of hydromagnetic transformer oil based multiphase fluid: Comprehensive modeling and computational study Mubbashar Nazeer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5809689/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 Motivation and objective: The main objective of this research is to investigate the thermal analysis of the magneto two-phase flow of Prandtl fluid with the suspension of silver and hafnium nanoparticles through inclined walls of the channel. The momentum equations are modified under the addition of body forces to consider the impact of magnetic and gravitational forces. The heat equation is also updated with the addition of the heat flux term to capture the thermal radiation effects. Methodology: The two-phase model is developed in terms of continuity, momentum, and heat equations of fluid and particle phases and uses dimensionless variables to simplify the system of equations. The dimensionless form of equations is solved by using the regular perturbation method in which the second Prandtl fluid parameter is taken as a perturbation parameter and produces the analytical solution. The graphical results revealed many physical aspects under the physical parameters in which the first and second Prandtl fluid parameters diminish the fluid and particle phase velocity distribution. Outcomes: The suspension of hafnium particles in the base fluid provides more heat to the system as compared to silver nanoparticles. The particle phase velocity distribution is much greater than the fluid phase against all parameters of the study. The magnetic force has an inverse relation with the velocity and thermal profiles of both phases. The two-phase Prandtl fluid model provides 55 % more heat transfer as compared to the single-phase Prandtl fluid model. The two-phase Prandtl fluid model gives 29% greater heat transfer to the system as compared to the phase Newtonian fluid model. Significance of the study: The current study will help to optimize the industrial thermal management process and to design efficient cooling systems in electronic devices, and in polymer and food processing. Originality: The topic discussed in this study is new and has not been deliberated before. Prandtl fluid magneto two-phase flow OT-4 transformer oil silver and hafnium nanoparticles inclined walls 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-5809689\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":401918852,\"identity\":\"f23ded6e-f6f1-4cb0-938b-4eea066d3b2c\",\"order_by\":0,\"name\":\"Mubbashar Nazeer\",\"email\":\"data:image/png;base64,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\",\"orcid\":\"\",\"institution\":\"Government College University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Mubbashar\",\"middleName\":\"\",\"lastName\":\"Nazeer\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-01-11 13:38:07\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-5809689/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-5809689/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":73928235,\"identity\":\"b239d784-8fe1-48dc-9a2a-6e8407b2114d\",\"added_by\":\"auto\",\"created_at\":\"2025-01-16 05:25:13\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1442005,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5809689/v1_covered_7f9b3165-e862-4826-97c7-02462b09b4bd.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Theoretical investigation on heat transfer rate of hydromagnetic transformer oil based multiphase fluid: Comprehensive modeling and computational study\",\"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\":\"info@researchsquare.com\",\"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\":\"Prandtl fluid, magneto two-phase flow, OT-4 transformer oil, silver and hafnium nanoparticles, inclined walls\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5809689/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5809689/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003e\\u003cstrong\\u003eMotivation and objective: \\u003c/strong\\u003eThe main objective of this research is to investigate the thermal analysis of the magneto two-phase flow of Prandtl fluid with the suspension of silver and hafnium nanoparticles through inclined walls of the channel. The momentum equations are modified under the addition of body forces to consider the impact of magnetic and gravitational forces. The heat equation is also updated with the addition of the heat flux term to capture the thermal radiation effects.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eMethodology: \\u003c/strong\\u003eThe two-phase model is developed in terms of continuity, momentum, and heat equations of fluid and particle phases and uses dimensionless variables to simplify the system of equations. The dimensionless form of equations is solved by using the regular perturbation method in which the second Prandtl fluid parameter \\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;\\u0026nbsp;is taken as a perturbation parameter and produces the analytical solution. The graphical results revealed many physical aspects under the physical parameters in which the first and second Prandtl fluid parameters diminish the fluid and particle phase velocity distribution.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eOutcomes: \\u003c/strong\\u003eThe suspension of hafnium particles in the base fluid provides more heat to the system as compared to silver nanoparticles. The particle phase velocity distribution is much greater than the fluid phase against all parameters of the study. The magnetic force has an inverse relation with the velocity and thermal profiles of both phases. The two-phase Prandtl fluid model provides \\u003cstrong\\u003e55 %\\u003c/strong\\u003emore heat transfer as compared to the single-phase Prandtl fluid model. 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