Modeling and Multiple Fractional Solutions for Two-Phase Blood Flow in a Slant Cylindrical Tube with Memory Effect

Modeling and Multiple Fractional Solutions for Two-Phase Blood Flow in a Slant Cylindrical Tube with Memory Effect | 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 Modeling and Multiple Fractional Solutions for Two-Phase Blood Flow in a Slant Cylindrical Tube with Memory Effect Maher Jebali, Muhammad Saqib, Zeineb Klai, Mohamed Bouzidi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7677402/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 α→1MPC(α,β, and γ)This work investigates the magnetohydrodynamic (MHD) flow of blood in an inclined cylindrical tube containing infused magnetic nanoparticles (MNPs). This system has significant implications for hyperthermia treatment and targeted drug administration. It is crucial for comprehending completely the interdependent effects of MNPs, tube inclination, and MHD. The Brinkman type fluid model is employed in the established two-phase flow. The Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional operators are used in succeeding fractionalization to account for memory effects and allow for a comparison analysis between various fractional frameworks. The joint Laplace-Hankel transforms are used to produce the exact solutions. When α→1 the classical results are restored. The results reveal that velocities caused by Lorentz forces decrease as the magnetic number (M) increases, with CF showing the fastest reaction. At the same time, because of stronger viscous and inertial effects, higher particle concentrations (PC) reduce velocities. The fractional orders (α,β, and γ), display dual time-dependent dynamics, speeding up flows over extended periods (after initially slowing them down. The most physically accurate predictions are produced by AB's Mittag-Leffler kernel, which combines short- and long-term memory effects. The results show the importance of fractional calculus in simulating complex biofluid dynamics, particularly in inclined tubes where gravity, magnetic, and viscous forces interact, and they offer a solid foundation for enhancing magnetic drug delivery devices. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Nanoscience and technology Physical sciences/Physics Blood flow Magnetic Particles Magnetohydrodynamic Fractional Calculus Integral Transforms 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-7677402","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":527228219,"identity":"8097e12e-68df-4805-b3e5-811c79667173","order_by":0,"name":"Maher Jebali","email":"","orcid":"","institution":"University of Ha'il","correspondingAuthor":false,"prefix":"","firstName":"Maher","middleName":"","lastName":"Jebali","suffix":""},{"id":527228220,"identity":"f966aa67-2123-4fa2-a48a-3ae8f2c2573e","order_by":1,"name":"Muhammad 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Effect","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":"Blood flow, Magnetic Particles, Magnetohydrodynamic, Fractional Calculus, Integral Transforms","lastPublishedDoi":"10.21203/rs.3.rs-7677402/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7677402/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"α→1MPC(α,β, and γ)This work investigates the magnetohydrodynamic (MHD) flow of blood in an inclined cylindrical tube containing infused magnetic nanoparticles (MNPs). This system has significant implications for hyperthermia treatment and targeted drug administration. It is crucial for comprehending completely the interdependent effects of MNPs, tube inclination, and MHD. The Brinkman type fluid model is employed in the established two-phase flow. The Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional operators are used in succeeding fractionalization to account for memory effects and allow for a comparison analysis between various fractional frameworks. The joint Laplace-Hankel transforms are used to produce the exact solutions. When α→1 the classical results are restored. The results reveal that velocities caused by Lorentz forces decrease as the magnetic number (M) increases, with CF showing the fastest reaction. At the same time, because of stronger viscous and inertial effects, higher particle concentrations (PC) reduce velocities. The fractional orders (α,β, and γ), display dual time-dependent dynamics, speeding up flows over extended periods (after initially slowing them down. The most physically accurate predictions are produced by AB's Mittag-Leffler kernel, which combines short- and long-term memory effects. The results show the importance of fractional calculus in simulating complex biofluid dynamics, particularly in inclined tubes where gravity, magnetic, and viscous forces interact, and they offer a solid foundation for enhancing magnetic drug delivery devices.","manuscriptTitle":"Modeling and Multiple Fractional Solutions for Two-Phase Blood Flow in a Slant Cylindrical Tube with Memory Effect","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-20 03:58:29","doi":"10.21203/rs.3.rs-7677402/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":"26035af6-1f94-4fd4-bb39-b55aa69f8a60","owner":[],"postedDate":"October 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":56043553,"name":"Physical sciences/Engineering"},{"id":56043554,"name":"Physical sciences/Mathematics and computing"},{"id":56043555,"name":"Physical sciences/Nanoscience and technology"},{"id":56043556,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-01-14T12:40:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-20 03:58:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7677402","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7677402","identity":"rs-7677402","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}