On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind | 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 On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind I. L. Ferreira, G. E.M. Santos Júnior, A. L.S. Moreira This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3906701/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 Solidification and fusion are important processes applied in several fields of science and technology. Recently, far beyond the realms of materials science and metallurgy, many applications have risen in latent heat thermal energy storage and melting and growth of ice plates. Due to the relative difficulty in obtaining numerical solutions for moving boundary problems for a wide range of space and time scales. In this work, four closed-form solutions for the transient solidification of pure and eutectic materials are proposed for one- and three-dimensional semi-infinite slabs considering convective boundary conditions and melting superheating. The analytical results are plotted against the numerical simulation results. Physical sciences/Engineering/Mechanical engineering Physical sciences/Materials science/Theory and computation Physical sciences/Energy science and technology/Energy storage/Batteries Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Similarity solution Convective boundary condition Transient analytical solution One-phase and two-phase moving boundary problem domains Cartesian one- and three-dimensional problem Semi-infinite slab 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-3906701","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":271165533,"identity":"7c325842-56a4-43b7-8d18-3ddb849db97a","order_by":0,"name":"I. L. Ferreira","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVRIiWNgGAWjYBACNnYQWcHAD2ITqYUZRJ5hkGwgWgsDSAtjGyla+JiZD374OO+whDn7AbbHFcQ5jC1Zcua2wxKWPQnshmeI08JjIM277XCdwYEENpDriNHC//k375zDEgbnHxCthYdNmrcBqOUG8bawmVnOOJYuYTnjYbshUVrk25sf3/hQYy1hzp987CFRWuDAgIGRNA0gLaNgFIyCUTAKcAAAFgcqPcHLNioAAAAASUVORK5CYII=","orcid":"","institution":"Federal University of Pará, UFPA","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"I.","middleName":"L.","lastName":"Ferreira","suffix":""},{"id":271165534,"identity":"dd67adeb-691f-44cd-87c9-2cf89a8edfd0","order_by":1,"name":"G. E.M. Santos Júnior","email":"","orcid":"","institution":"Federal University of Pará, UFPA","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"G.","middleName":"E.M. Santos","lastName":"Júnior","suffix":""},{"id":271165535,"identity":"1cca07cf-1558-400d-869c-d2e29c37345b","order_by":2,"name":"A. L.S. Moreira","email":"","orcid":"","institution":"Federal University of Pará, UFPA","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"A.","middleName":"L.S.","lastName":"Moreira","suffix":""}],"badges":[],"createdAt":"2024-01-28 19:44:34","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3906701/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3906701/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52896569,"identity":"298af2f0-2c8d-48f5-9ea4-d4cf271bd8ed","added_by":"auto","created_at":"2024-03-18 13:01:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2248781,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptformattedRevTechCheckReq.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3906701/v1_covered_80b289f2-c924-4eca-a3ff-b0632257fee8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind","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":true,"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":"Similarity solution, Convective boundary condition, Transient analytical solution, One-phase and two-phase moving boundary problem domains, Cartesian one- and three-dimensional problem, Semi-infinite slab","lastPublishedDoi":"10.21203/rs.3.rs-3906701/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3906701/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSolidification and fusion are important processes applied in several fields of science and technology. Recently, far beyond the realms of materials science and metallurgy, many applications have risen in latent heat thermal energy storage and melting and growth of ice plates. Due to the relative difficulty in obtaining numerical solutions for moving boundary problems for a wide range of space and time scales. In this work, four closed-form solutions for the transient solidification of pure and eutectic materials are proposed for one- and three-dimensional semi-infinite slabs considering convective boundary conditions and melting superheating. The analytical results are plotted against the numerical simulation results.\u003c/p\u003e","manuscriptTitle":"On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-07 02:14:51","doi":"10.21203/rs.3.rs-3906701/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":"134605ce-65d8-49cc-8a1d-9541af27556e","owner":[],"postedDate":"February 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":28580607,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":28580608,"name":"Physical sciences/Materials science/Theory and computation"},{"id":28580609,"name":"Physical sciences/Energy science and technology/Energy storage/Batteries"},{"id":28580610,"name":"Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2024-03-18T12:53:36+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-07 02:14:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3906701","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3906701","identity":"rs-3906701","version":["v1"]},"buildId":"-HB7Z8yhvgn0wM9Nzuekk","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}