Kirchhoff’s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator

Kirchhoff’s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator | 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 Kirchhoff’s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator Jun Jiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8389819/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 We unveil a long-unrecognized fundamental principle that governs thermoelectric generator performance. Thermoelectric generator is traditionally treated as voltage-producing device whose output current is determined by the external load. Here, we demonstrate that under a parallel temperature-gradient field, Kirchhoff’s Current Law imposes a decisive constraint: the operating current is dictated exclusively by the ‘weaker’ leg, which refers to the P- or N-type thermoelement with the smaller intrinsic short-circuit current. This physical insight leads directly to a universal design rule based on their individual short-circuit currents: I_"sc" ^P=I_"sc" ^N. By applying this principle to PbTe-based module, we achieved a conversion efficiency of 15.2%, significantly surpassing the previous record, which had remained below 11%. This discovery reframes the intrinsic operating mechanism of thermoelectric generator and establishes a practical design methodology for achieving breakthrough performance. Physical sciences/Energy science and technology/Thermoelectric devices and materials Physical sciences/Materials science/Materials for devices/Electronic devices thermoelectric generator Kirchhoff’s Current Law short-circuit current Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx Kirchhoff’s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator 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. 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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-8389819","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":563175924,"identity":"eee66186-5fb5-4dbe-9107-72c2f7870702","order_by":0,"name":"Jun Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArUlEQVRIiWNgGAWjYBACxoYDDAwfGCRI1MI4A6iFhySbmEHKidfC3HjG7LHtDotoe/YGxg8/GOzyiHDYGXPj3DMSuT08B5glexiSi4nRYiad2wbUIpHAIM3AcCCxgSgtliAt8g+YfxOvhRFsCwMbsbYcK5PsBWk5k9hm2WOQTFiL4YzD2yR+ttXltrcfPnzjR4UdMVoOICxkYDAgpB4I5PkJmjoKRsEoGAUjHgAAioE5eQryBv8AAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-8365-0812","institution":"Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Jun","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2025-12-18 01:15:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8389819/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8389819/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107488106,"identity":"45d9a6e2-f079-4445-bd8d-fdb7d84a7c55","added_by":"auto","created_at":"2026-04-22 02:43:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":965571,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8389819/v1_covered_d938b5c2-3230-4a7b-a281-6f37a9ec6551.pdf"},{"id":98875615,"identity":"96bdd292-c33e-48f9-848d-0d745213c7d5","added_by":"auto","created_at":"2025-12-23 12:48:51","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":42272604,"visible":true,"origin":"","legend":"Kirchhoff\u0026#x2019;s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-8389819/v1/8b5fa7b6336c7c7b43c8d653.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Kirchhoff’s Current Law Under Parallel Temperature Gradient: The Fundamental Principle Governing Thermoelectric Generator","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"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":"thermoelectric generator, Kirchhoff’s Current Law, short-circuit current","lastPublishedDoi":"10.21203/rs.3.rs-8389819/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8389819/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We unveil a long-unrecognized fundamental principle that governs thermoelectric generator performance. 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