Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions

Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions | 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 Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions Ilya Barmak, Subham Pal, Alexander Gelfgat, Neima Brauner This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6968009/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Mar, 2026 Read the published version in Theoretical and Computational Fluid Dynamics → Version 1 posted 10 You are reading this latest preprint version Abstract This study explores the effects of a non-conductive gas layer flowing concurrently with a conductive liquid on the two-phase flow characteristics in wide horizontal ducts under a constant vertical magnetic field. To this end, analytical solutions for the velocity profile and induced magnetic field are presented for laminar gas-liquid stratified magnetohydrodynamic (MHD) flow between two infinite plates of various conductivities. The contributions of the Lorentz force and wall shear stresses to the pressure gradient are examined. To the best of our knowledge, it is shown for the first time that, unlike the single-phase Hartmann flow, the velocity profiles in two-phase flow differ significantly depending on whether the bottom wall is conducting or insulating. In the case of an insulating bottom wall, the gas lubrication effect and potential pumping power savings are significantly greater, regardless of the magnetic Reynolds number. This conclusion also holds for gas-liquid MHD flows in rectangular ducts with finite width-to-height aspect ratios. To assess the applicability of the Two-Plate (TP) model to wide ducts, numerical solutions of the two-dimensional problem are used to investigate the influence of side walls on the two-phase flow characteristics, considering various combinations of bottom and side wall conductivities. In all cases, the results for high aspect ratios converge to the analytical solution obtained from the TP model with the same bottom wall conductivity. However, the influence of insulating side walls remains significant even at large aspect ratios when the bottom wall is conducting. Unexpectedly, in such cases, the change in the induced magnetic field due to the presence of side walls has a dramatic effect on the velocity profile, leading to a reduced pressure gradient compared to that predicted by the TP model. MHD flow Stratified flow Gas–liquid Wall conductivity Induced magnetic field Gas lubrication Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Mar, 2026 Read the published version in Theoretical and Computational Fluid Dynamics → Version 1 posted Editorial decision: Revision requested 18 Jan, 2026 Reviews received at journal 28 Dec, 2025 Reviews received at journal 16 Dec, 2025 Reviewers agreed at journal 11 Dec, 2025 Reviewers agreed at journal 06 Dec, 2025 Reviewers agreed at journal 09 Sep, 2025 Reviewers invited by journal 09 Sep, 2025 Editor assigned by journal 25 Jun, 2025 Submission checks completed at journal 25 Jun, 2025 First submitted to journal 24 Jun, 2025 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-6968009","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":512452579,"identity":"aaece081-2533-4209-b4cb-9c62e9debfd5","order_by":0,"name":"Ilya Barmak","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYBACNnYGBmaGCjTRAw/waWEGaTljAFUK05KAzxqQFsY2NC0M+LTwMfMYfi6c90fe4HiPAfOHmsMM/O0HGPHawsbMYyw9c5uB4YYzxxIYDhw7zCBxJgG/w4BaDKR5txkwbriRfIDhANthBoYbBPwCsuU37xwD+w33HzYwHPh3mEGeCC1m0rwNBokbbjAfYDjYdpjBgLAWtjLrGceMk2eeSUs4cLYvncfwTGIDXi3y7c2bbxfUyNn2HT9j+KDim7Wc3PHDhz98wKOFgYHDAM48AMQ8DAyMDXg1MDCwPyCgYBSMglEwCkY8AAD1Mk2UcrgTZgAAAABJRU5ErkJggg==","orcid":"","institution":"Soreq NRC","correspondingAuthor":true,"prefix":"","firstName":"Ilya","middleName":"","lastName":"Barmak","suffix":""},{"id":512452580,"identity":"f7ec2e2c-3742-4617-9444-f7ad4508c152","order_by":1,"name":"Subham Pal","email":"","orcid":"","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Subham","middleName":"","lastName":"Pal","suffix":""},{"id":512452581,"identity":"2abd0e15-d4a7-4f18-8e8f-11412a6c2424","order_by":2,"name":"Alexander Gelfgat","email":"","orcid":"","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Alexander","middleName":"","lastName":"Gelfgat","suffix":""},{"id":512452582,"identity":"6863caef-d22f-46e3-8fe8-fa9bf82ab481","order_by":3,"name":"Neima Brauner","email":"","orcid":"","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Neima","middleName":"","lastName":"Brauner","suffix":""}],"badges":[],"createdAt":"2025-06-24 17:23:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6968009/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6968009/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00162-026-00780-6","type":"published","date":"2026-03-24T16:10:38+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":105755085,"identity":"84270e3e-5b12-45cc-84fb-40f9f8cbac0f","added_by":"auto","created_at":"2026-03-30 16:25:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":22715393,"visible":true,"origin":"","legend":"","description":"","filename":"BarmakTCFDsubmission062025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6968009/v1_covered_bd9bf346-1248-47ff-bb29-99f436edef7e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Two-phase stratified MHD flows in wide rectangular ducts: analytical and numerical solutions","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"theoretical-and-computational-fluid-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tcfd","sideBox":"Learn more about [Theoretical and Computational Fluid Dynamics](http://link.springer.com/journal/162)","snPcode":"162","submissionUrl":"https://submission.nature.com/new-submission/162/3","title":"Theoretical and Computational Fluid Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"MHD flow, Stratified flow, Gas–liquid, Wall conductivity, Induced magnetic field, Gas lubrication","lastPublishedDoi":"10.21203/rs.3.rs-6968009/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6968009/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study explores the effects of a non-conductive gas layer flowing concurrently with a conductive liquid on the two-phase flow characteristics in wide horizontal ducts under a constant vertical magnetic field. 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