Determination of one thermal coefficient through an overspecified Stefan problem with temperature-dependent thermal conductivity, considering flux and convective boundary conditions

Determination of one thermal coefficient through an overspecified Stefan problem with temperature-dependent thermal conductivity, considering flux and convective boundary conditions | 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 Determination of one thermal coefficient through an overspecified Stefan problem with temperature-dependent thermal conductivity, considering flux and convective boundary conditions N. N. Salva, M. Rossani, D. A. Tarzia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7621863/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Formulae are obtained for the determination of one unknown thermal coefficient of a semi-infinite material with temperature-dependent thermal conductivity through a phase-change process with an overspecified condition on the fixed face (flux and convective boundary conditions) through a free boundary problem (Ste-fan problem with 5 cases). A new error function is introduced as part of the similarity-type solution, which depends on a parameter related to thermal conductivity. For the special case in which the parameter assumes values close to zero (positive or negative), we show that the new error function presents some characteristic features of the classical error function, such as monotony, concavity, and boundedness. We also study the sensitivity of the solution depending on different thermal parameters applied to aluminum and uranium. Phase-change processes unknown thermal coefficient free boundary problem convective boundary conditions error function nonlinear second order ordinary differential equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 20 Dec, 2025 Reviews received at journal 16 Dec, 2025 Reviewers agreed at journal 09 Dec, 2025 Reviews received at journal 06 Oct, 2025 Reviewers agreed at journal 30 Sep, 2025 Reviewers agreed at journal 23 Sep, 2025 Reviewers invited by journal 22 Sep, 2025 Editor assigned by journal 17 Sep, 2025 Submission checks completed at journal 17 Sep, 2025 First submitted to journal 15 Sep, 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. 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-7621863","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":523733897,"identity":"df8b531d-617a-4ae4-bf5a-36f423331e70","order_by":0,"name":"N. N. 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