Mathematical modeling of anisotropic thermal protective coatings with respect to spatial nonlocal effects

Mathematical modeling of anisotropic thermal protective coatings with respect to spatial nonlocal effects | 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 Mathematical modeling of anisotropic thermal protective coatings with respect to spatial nonlocal effects Inga Savelyeva, Yury Safronov, Vladimir Zarubin, Victor Leonov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8249780/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 8 You are reading this latest preprint version Abstract This paper considers a nonlocal mathematical model of thermal conductivity of layered anisotropic coatings. Such coatings are widely used in various fields of engineering, for example, for the protection of spacecraft or aircraft engines. The use of anisotropic materials in combination with isotropic materials allows to reach acceptable temperature threshold values, which do not exceed the critical value. This opens up space for the study of various configurations of layered media. Consideration of spatial nonlocality in modeling allows us to analyze new configurations of layered anisotropic coatings, as it opens up opportunities for the use of nanostructured materials, for which classical models give unsatisfactory results. Mathematics Subject Classification (2010). Primary 80A19; Secondary 97M50. Nonlocal mathematical model of thermal conductivity thermal protective coatings thermal protection multilayered media anisotropic materials nanostructured materials Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 13 Feb, 2026 Reviews received at journal 13 Feb, 2026 Reviewers agreed at journal 13 Feb, 2026 Reviewers agreed at journal 07 Dec, 2025 Reviewers invited by journal 07 Dec, 2025 Editor assigned by journal 06 Dec, 2025 Submission checks completed at journal 02 Dec, 2025 First submitted to journal 01 Dec, 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. 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