Mathematical Modeling of Hydromagnetic Flow of Hybrid Nanofluid in a Parabolic Thermal Solar Collector

Mathematical Modeling of Hydromagnetic Flow of Hybrid Nanofluid in a Parabolic Thermal Solar Collector | 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 Mathematical Modeling of Hydromagnetic Flow of Hybrid Nanofluid in a Parabolic Thermal Solar Collector Charles Otieno Ndede, Jeconia Okelo Abonyo, Viona Ojiambo, Joel Ngesa Ochola This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6873143/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 The exploration of nanofluids in thermal systems is growing day by daywhich is linked to the ever-growing global demand for energy which is pri-marily due to population explosion, technological advancements, and eco-nomic development. Efficient thermal solar collectors offer a promising so-lution to meet these growing demands. A novel computational model is pre-sented for the unsteady flow of copper and titanium dioxide (Cu−TiO2)/waterhybrid nanofluid in a parabolic thermal solar collector with variable fluidproperties such as thermal conductivity and dynamic viscosity in the pres-ence of a variable magnetic field. The governing equations, comprising asystem of nonlinear partial differential equations, are transformed into or-dinary differential equations using similarity transformation. The resultingsystem of ordinary differential equations is solved numerically using thecollocation method utilizing the bvp4c solver. Some of the assumptionsand approximations considered in this study include the following: the flowis axisymmetric and laminar, the dynamic viscosity and thermal conduc-tivity of the hybrid nanofluid vary linearly with fluid temperature, and thechemical reaction between the hybrid nanofluid and the nanoparticles isnegligible. The impact of various flow parameters on flow variables is in-vestigated. The key findings reveal that increasing the Reynolds numberfrom 3.5 to 4.5 led to a decrease in both the velocity and nanoparticle con-centration profiles and an increase in temperature and magnetic inductionprofiles. In addition, increasing the Brownian diffusion parameter from 20to 30 led to an increase in nanoparticle velocity, temperature, and nanopar-ticle profiles. Moreover, an increase in the Reynolds number (Re) causesa reduction in the skin friction coefficient, Nusselt number, and Sherwood1number. This is due to the relationship between the thickness of the wallboundary layer and the flow gradient.The findings of this study have impor-tant implications for the design and optimization of parabolic thermal solarcollectors for enhanced efficiency. By understanding the effects of differentflow parameters on the performance of hybrid nanofluids, researchers andengineers can develop more efficient and effective solar energy systems. Hybrid nanofluid Solar collector Similarity transformation bvp4c Mathematical modeling 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. 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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-6873143","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":470480139,"identity":"9426d916-f822-4be5-8585-16edc4adeac7","order_by":0,"name":"Charles Otieno Ndede","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYDACCSB+AGIcYDBg+ACk2diJ0ZIA1cI4A6SFmRQtzDwgBiEt/LObn31IqKjL4zvevPGxza9t8nzMDIwfPubgseTOMeMZCWcOF0ueOVZsnNt327CNmYFZcuY23FoMJBKMGRLbDiRuuJFjJp3bc5sRqIWNmRevlvTPDIn/6hI33H9j/tuy57Y9EVpygLY0MANt4TFjZvhxO5GgFokbOcUMCccOJ848k1Ys2dtwO7mNmbEZr1/4Z6RvZvhQU5fYd/zwxg8//ty2nd/efPDDRzxaUAFjG5hsIFY9CPwhRfEoGAWjYBSMFAAAYJFVVasGvPgAAAAASUVORK5CYII=","orcid":"","institution":"Jomo Kenyatta University of Agriculture and Technology (JKUAT)","correspondingAuthor":true,"prefix":"","firstName":"Charles","middleName":"Otieno","lastName":"Ndede","suffix":""},{"id":470480140,"identity":"fa8a9076-26e2-4975-9bdf-6cf940d69a10","order_by":1,"name":"Jeconia Okelo Abonyo","email":"","orcid":"","institution":"Jomo Kenyatta University of Agriculture and Technology (JKUAT)","correspondingAuthor":false,"prefix":"","firstName":"Jeconia","middleName":"Okelo","lastName":"Abonyo","suffix":""},{"id":470480141,"identity":"679f09b5-2b22-4721-b59e-d6018da68179","order_by":2,"name":"Viona Ojiambo","email":"","orcid":"","institution":"Jomo Kenyatta University of Agriculture and Technology (JKUAT)","correspondingAuthor":false,"prefix":"","firstName":"Viona","middleName":"","lastName":"Ojiambo","suffix":""},{"id":470480142,"identity":"efaf929b-0d21-4190-ae77-4a781e59c129","order_by":3,"name":"Joel Ngesa Ochola","email":"","orcid":"","institution":"South Eastern Kenya University","correspondingAuthor":false,"prefix":"","firstName":"Joel","middleName":"Ngesa","lastName":"Ochola","suffix":""}],"badges":[],"createdAt":"2025-06-11 15:08:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6873143/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6873143/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84521491,"identity":"f4eecc8c-0eb9-49f4-bc44-c1521c68606c","added_by":"auto","created_at":"2025-06-13 03:39:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1345768,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript01.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6873143/v1_covered_c00f959e-a556-4356-87cc-6f3afacc57b3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Modeling of Hydromagnetic Flow of Hybrid Nanofluid in a Parabolic Thermal Solar Collector","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Hybrid nanofluid, Solar collector, Similarity transformation, bvp4c, Mathematical modeling","lastPublishedDoi":"10.21203/rs.3.rs-6873143/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6873143/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe exploration of nanofluids in thermal systems is growing day by daywhich is linked to the ever-growing global demand for energy which is pri-marily due to population explosion, technological advancements, and eco-nomic development. Efficient thermal solar collectors offer a promising so-lution to meet these growing demands. A novel computational model is pre-sented for the unsteady flow of copper and titanium dioxide (Cu−TiO2)/waterhybrid nanofluid in a parabolic thermal solar collector with variable fluidproperties such as thermal conductivity and dynamic viscosity in the pres-ence of a variable magnetic field. The governing equations, comprising asystem of nonlinear partial differential equations, are transformed into or-dinary differential equations using similarity transformation. The resultingsystem of ordinary differential equations is solved numerically using thecollocation method utilizing the bvp4c solver. Some of the assumptionsand approximations considered in this study include the following: the flowis axisymmetric and laminar, the dynamic viscosity and thermal conduc-tivity of the hybrid nanofluid vary linearly with fluid temperature, and thechemical reaction between the hybrid nanofluid and the nanoparticles isnegligible. The impact of various flow parameters on flow variables is in-vestigated. The key findings reveal that increasing the Reynolds numberfrom 3.5 to 4.5 led to a decrease in both the velocity and nanoparticle con-centration profiles and an increase in temperature and magnetic inductionprofiles. In addition, increasing the Brownian diffusion parameter from 20to 30 led to an increase in nanoparticle velocity, temperature, and nanopar-ticle profiles. Moreover, an increase in the Reynolds number (Re) causesa reduction in the skin friction coefficient, Nusselt number, and Sherwood1number. This is due to the relationship between the thickness of the wallboundary layer and the flow gradient.The findings of this study have impor-tant implications for the design and optimization of parabolic thermal solarcollectors for enhanced efficiency. By understanding the effects of differentflow parameters on the performance of hybrid nanofluids, researchers andengineers can develop more efficient and effective solar energy systems.\u003c/p\u003e","manuscriptTitle":"Mathematical Modeling of Hydromagnetic Flow of Hybrid Nanofluid in a Parabolic Thermal Solar Collector","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-13 03:15:14","doi":"10.21203/rs.3.rs-6873143/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":"885e86a7-f27a-4a4f-bec2-406168f13af4","owner":[],"postedDate":"June 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-13T03:15:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-13 03:15:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6873143","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6873143","identity":"rs-6873143","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}