{"paper_id":"3b3e3e93-d10a-4cd9-aa95-d62c8c952360","body_text":"Instability of Hydromagnetic Hybrid Flow Fe2O3-Fe3O4 /H2O of Thermocapillary Layers of Shear-Thinning Nanofluids | 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 Instability of Hydromagnetic Hybrid Flow Fe2O3-Fe3O4 /H2O of Thermocapillary Layers of Shear-Thinning Nanofluids Mehboob Ali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-125249/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 Nanofluids have inordinate uses in industries due to their high rate of heat transformation. The enhancement of heat transfer rates, an advanced type of nanofluids called “Hybrid nanofluid” is discovered. Hybrid nanofluids are created by the suspension of two or more type of nano sized atoms in base fluid such as water, oil etc. In current work, the instability of Hydromagnetic Poiseuille flow of thermocapillary layers of liquid of shear thinning hybrid nanofluid of Fe2O3-Fe3O4 in water based fluid is investigated. The transverse magnetic field is imposed on the flow. The solution of obtained ODEs for current problem is found using a numerical method called “cheybeshev collocation method”. The eigenvalue problem from generalized Orr-sommerfeld equations is solved using the algorithm of “QZ” abbreviated as (Qualitat and Zuverlassigkeit). The instability of water based hybrid nanofluids for variation of different parameters are analyzed and discussed through graphs. It has been found that Reynolds number and prandtl number has destabilizing effect on the flow while wave number and magnetic parameter has stabilizing impact on the fluid flow Nanoscience Hybrid nanofluid Heat transfer Hydromagnetic Poiseuille flow Thermocapillary layers Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Full Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the latest manuscript can be downloaded and accessed as a PDF. 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-125249\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":6196345,\"identity\":\"e3bf163b-5a38-47bd-94c8-c78444a5b199\",\"order_by\":0,\"name\":\"Mehboob Ali\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIiWNgGAWjYFACHjYgcQDEAjIqwAwDIE4gRgszkHGGZC2MbURo0W3vPfbgQ8UdIOP8sYc/591JbGBv3ibBuCMNpxazM+fSDWeceQZkJLMb8257ltjAc6xMgvFMDm4tN3LMpHnbDjOYHUhmk2bcdjixQSLHTIKxrQK3lvtvoFrOP2aT/DkHqEX+DQEtN3igWm4ks0nwNoBs4QFpweOwMznmEL/ceGwmzXPssHEbT1qxReIZPN4/fsYMHGJm5xOfSf6oOSzbz354442PO5JxaoGB+gYYCxRNDIkNuBTiBIykaxkFo2AUjILhCwAculpcxr9kDAAAAABJRU5ErkJggg==\",\"orcid\":\"\",\"institution\":\"Hazara University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Mehboob\",\"middleName\":\"\",\"lastName\":\"Ali\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2020-12-09 18:14:08\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-125249/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-125249/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":4306772,\"identity\":\"55cffdb5-85f9-45a2-8794-b2e613d25b7a\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":38540,\"visible\":true,\"origin\":\"\",\"legend\":\"Geometrical configuration of the problem \",\"description\":\"\",\"filename\":\"fig1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/d3d1ac7a545fc905233af3c2.png\"},{\"id\":4306773,\"identity\":\"fee1c61d-5f35-48ee-b00e-aa79b51745e1\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":102682,\"visible\":true,\"origin\":\"\",\"legend\":\"Curves for velocity distribution for third problem (Poiseuille Flow). \",\"description\":\"\",\"filename\":\"fig2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/ed940429b824df8f35c4771d.png\"},{\"id\":4306774,\"identity\":\"20804a3e-b93f-43b9-a8e5-c8e61d762a3b\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":150740,\"visible\":true,\"origin\":\"\",\"legend\":\" Graphs for growth rate ω vs. (a). Ha (b). Pr and (c). R for variation of wave number k\",\"description\":\"\",\"filename\":\"fig3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/abe41b5bfb84366a39f6814d.png\"},{\"id\":4306775,\"identity\":\"e6a534c4-0499-4ab5-bb45-71e3e99b1c34\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":143206,\"visible\":true,\"origin\":\"\",\"legend\":\"Graphs for growth rate ω vs. (a). k (b). Pr and (c). R for variation of magnetic parameter Ha \",\"description\":\"\",\"filename\":\"fig4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/3b5909782dda3f81485365ea.png\"},{\"id\":4306776,\"identity\":\"f5a4ded7-0feb-4f36-a5db-d9766a38c36f\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":97656,\"visible\":true,\"origin\":\"\",\"legend\":\"Graphs for growth rate ω vs. (a). Ha (b). k and (c). Pr for variation of Reynolds number R \",\"description\":\"\",\"filename\":\"fig5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/96b1e95fd901f29c67bf363d.png\"},{\"id\":4306777,\"identity\":\"32d7e68e-7e56-4af8-9198-ef894e9442b8\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:40\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":156734,\"visible\":true,\"origin\":\"\",\"legend\":\"Graphs for growth rate ω vs. (a). Ha (b). k and (c). R for variation of Prandtl number Pr \",\"description\":\"\",\"filename\":\"fig6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/3c17fdac428de53cca9c75c6.png\"},{\"id\":4306778,\"identity\":\"19196377-3b15-422c-ba78-59013314f3f6\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:41\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":174557,\"visible\":true,\"origin\":\"\",\"legend\":\"Graphs for growth rate ω vs. (a). Ha (b). k (c). Pr and (d). R for variation of ϕ1 \",\"description\":\"\",\"filename\":\"fig7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/53dcc6a68ac18c3ee1fa0381.png\"},{\"id\":4306779,\"identity\":\"ae18f08f-292c-4991-9d01-a1384813e2ac\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:41\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":175292,\"visible\":true,\"origin\":\"\",\"legend\":\" Graphs for growth rate ω vs. (a). Ha (b). k (c). Pr and (d). R for variation of ϕ2 \",\"description\":\"\",\"filename\":\"fig8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/367b0f299d0e3dd645f48754.png\"},{\"id\":4306780,\"identity\":\"a26c43c7-5e0d-43f1-97a1-f778043feda2\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:41\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":126569,\"visible\":true,\"origin\":\"\",\"legend\":\" Curves for neutral stability (a). Ha-Pr (b). R-Ha and (c). 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R-Pr for variation of Ha \",\"description\":\"\",\"filename\":\"fig10.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/c2be46e11c536f5457410a7c.png\"},{\"id\":4306782,\"identity\":\"3e97d382-ef1a-46df-99c1-63fac807521b\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:41\",\"extension\":\"png\",\"order_by\":11,\"title\":\"Figure 11\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":194373,\"visible\":true,\"origin\":\"\",\"legend\":\"Curves for neutral stability (a). Ha-k (b). Ha-Pr and (c). Pr-k for variation of R \",\"description\":\"\",\"filename\":\"fig11.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-125249/v1/7679a6322694424390318339.png\"},{\"id\":4306783,\"identity\":\"93a97b2c-2add-413e-9865-9df7fd5c8b6f\",\"added_by\":\"auto\",\"created_at\":\"2020-12-16 16:57:41\",\"extension\":\"png\",\"order_by\":12,\"title\":\"Figure 12\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":131117,\"visible\":true,\"origin\":\"\",\"legend\":\"Curves for neutral stability (a). Ha-k (b). R-Ha and (c). 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The enhancement of heat transfer rates, an advanced type of nanofluids called “Hybrid nanofluid” is discovered. Hybrid nanofluids are created by the suspension of two or more type of nano sized atoms in base fluid such as water, oil etc. In current work, the instability of Hydromagnetic Poiseuille flow of thermocapillary layers of liquid of shear thinning hybrid nanofluid of Fe2O3-Fe3O4 in water based fluid is investigated. The transverse magnetic field is imposed on the flow. The solution of obtained ODEs for current problem is found using a numerical method called “cheybeshev collocation method”. The eigenvalue problem from generalized Orr-sommerfeld equations is solved using the algorithm of “QZ” abbreviated as (Qualitat and Zuverlassigkeit). The instability of water based hybrid nanofluids for variation of different parameters are analyzed and discussed through graphs. It has been found that Reynolds number and prandtl number has destabilizing effect on the flow while wave number and magnetic parameter has stabilizing impact on the fluid flow\",\"manuscriptTitle\":\"Instability of Hydromagnetic Hybrid Flow Fe2O3-Fe3O4 /H2O of Thermocapillary Layers of Shear-Thinning Nanofluids\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2020-12-16 16:57:38\",\"doi\":\"10.21203/rs.3.rs-125249/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"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}}],\"origin\":\"\",\"ownerIdentity\":\"0e7b5cc5-77a4-4653-a894-6fbcbd4d2bf5\",\"owner\":[],\"postedDate\":\"December 16th, 2020\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":1473402,\"name\":\"Nanoscience\"}],\"tags\":[],\"updatedAt\":\"2021-03-05T08:29:07+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2020-12-16 16:57:38\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-125249\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-125249\",\"identity\":\"rs-125249\",\"version\":[\"v1\"]},\"buildId\":\"_2-kVJe1T_tPrBINL-cwx\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}