Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers

Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers | 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 Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers I. Bochicchio ID, F. Giannetti ID, A. Sellitto ID This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4168453/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 Owing to the heat propagation, in nano-systems the phonons always undergo to different scattering mechanisms. The particular regime of heat transfer, instead, strictly depends on the ratio between the phonon mean-free path and the characteristic size of the system, i.e., the so-called Knudsen number. At nano-scale, wherein several conceptual questions still remain unanswered, the analysis of the role played by the phonon-boundary scatterings, for different values of the Knudsen number, in particular is an interesting research playground. We therefore here propose an enhanced model of boundary conditions in order to suitably address the problem of the correct tackling of the phonon-boundary scatterings when heat is flowing in a thin layer. Nano-scale Heat Transfer Phonon-Wall Interactions Non-local Effects Second-Order Boundary Conditions 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-4168453","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":285930594,"identity":"7f0829ee-e06c-43dd-8973-15109e4b4cd3","order_by":0,"name":"I. Bochicchio ID","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBACNgkGBmYGAwYGfiDnABDzEK9FsgGqhbAesBYgMDgAFSCohU+6+eDnggI7eeMbuQcP/qhhkLEn6DCZY8nSMwySDbfdyEs4zHOMCIexSeSYMfMYHEgwu5FjcJiBjRQtxjNyDA7++EeKFgOJHIMDvG3EaAH5hQfolxln3hgc5u2T4OE5QECL/GxgiPH8sZPnb88x/vjjm409ewMha9CABInqR8EoGAWjYBRgBQAe0zMsAywFbgAAAABJRU5ErkJggg==","orcid":"","institution":"University of Salerno","correspondingAuthor":true,"prefix":"","firstName":"I.","middleName":"Bochicchio","lastName":"ID","suffix":""},{"id":285930595,"identity":"50f9dc7b-727a-4b6c-ae57-d6b170e35b85","order_by":1,"name":"F. Giannetti ID","email":"","orcid":"","institution":"University of Salerno","correspondingAuthor":false,"prefix":"","firstName":"F.","middleName":"Giannetti","lastName":"ID","suffix":""},{"id":285930597,"identity":"dc9cac33-d3cc-47e0-b098-bbe29720668f","order_by":2,"name":"A. Sellitto ID","email":"","orcid":"","institution":"University of Salerno","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"Sellitto","lastName":"ID","suffix":""}],"badges":[],"createdAt":"2024-03-26 08:57:28","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4168453/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4168453/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59059561,"identity":"f45d66a7-86d0-49af-acce-1b68e1d630ee","added_by":"auto","created_at":"2024-06-26 00:00:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":472768,"visible":true,"origin":"","legend":"","description":"","filename":"SOBCs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4168453/v1_covered_4d2f2240-7101-4ccb-8238-496462e0ddf9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers","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":"Nano-scale Heat Transfer, Phonon-Wall Interactions, Non-local Effects, Second-Order Boundary Conditions","lastPublishedDoi":"10.21203/rs.3.rs-4168453/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4168453/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Owing to the heat propagation, in nano-systems the phonons always undergo to different scattering mechanisms. The particular regime of heat transfer, instead, strictly depends on the ratio between the phonon mean-free path and the characteristic size of the system, i.e., the so-called Knudsen number. At nano-scale, wherein several conceptual questions still remain unanswered, the analysis of the role played by the phonon-boundary scatterings, for different values of the Knudsen number, in particular is an interesting research playground. We therefore here propose an enhanced model of boundary conditions in order to suitably address the problem of the correct tackling of the phonon-boundary scatterings when heat is flowing in a thin layer.","manuscriptTitle":"Phonon-boundary scatterings and second-order boundary conditions: Application to the heat transfer in thin layers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-01 17:03:35","doi":"10.21203/rs.3.rs-4168453/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":"d2b79822-aa0d-469f-ac39-8e480f1c9a38","owner":[],"postedDate":"April 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-25T23:52:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-01 17:03:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4168453","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4168453","identity":"rs-4168453","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}