Temperature state of polymer dielectric layer, bounded by curvilinear surfaces, at constant voltage

Temperature state of polymer dielectric layer, bounded by curvilinear surfaces, at constant voltage | 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 Temperature state of polymer dielectric layer, bounded by curvilinear surfaces, at constant voltage Vladimir Zarubin, Georgy Kuvyrkin, Inga Savelyeva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3939031/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Oct, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted 7 You are reading this latest preprint version Abstract The solution of one-dimensional nonlinear problem of stationary heat conduction in a dielectric layer with volumetric energy release at a constant difference in electric potentials on the curvilinear heat transfer surfaces, bounding the layer, is presented in a closed analytical form. The analytical form of the solution, being a set of integral relations, allows to conduct a quantitative analysis of the influence of governing parameters on temperature state of the layer, including the one preceding the occurrence of thermal dielectric breakdown. Such form of solution can be used to test the results of numerical solution of this problem. An example of quantitative analysis of the presented integral relations is given. Approximate formulas that make it possible to find estimates of the parameters of temperature state of dielectric layer and the maximum difference in electrical potentials, preceding the thermal breakdown of the layer, are obtained. Mathematics Subject Classification (2010). Primary 80A19; Secondary 97M50. Layer with curvilinear heat transfer surfaces one-dimensional steady-state temperature distribution volumetric energy release thermal dielectric breakdown polytetrafluoroethylene Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 28 Oct, 2024 Read the published version in Zeitschrift für angewandte Mathematik und Physik → Version 1 posted Editorial decision: Accepted 07 Oct, 2024 Reviewers agreed at journal 14 Mar, 2024 Reviewers agreed at journal 12 Mar, 2024 Reviewers invited by journal 11 Feb, 2024 Editor assigned by journal 09 Feb, 2024 Submission checks completed at journal 08 Feb, 2024 First submitted to journal 08 Feb, 2024 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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The analytical form of the solution, being a set of integral relations, allows to conduct a quantitative analysis of the influence of governing parameters on temperature state of the layer, including the one preceding the occurrence of thermal dielectric breakdown. Such form of solution can be used to test the results of numerical solution of this problem. An example of quantitative analysis of the presented integral relations is given. Approximate formulas that make it possible to find estimates of the parameters of temperature state of dielectric layer and the maximum difference in electrical potentials, preceding the thermal breakdown of the layer, are obtained.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2010). 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