Heat Conduction in a 1-D Rod with an Oscillating Boundary

Heat Conduction in a 1-D Rod with an Oscillating Boundary | 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Download PDF Article Heat Conduction in a 1-D Rod with an Oscillating Boundary Aryan Pradhan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7713306/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 Classical studies explore the conduction of heat in uniform materials or boundaries of fixed boundaries - where equilibration proceeds monotonically toward a static steady state [ 9 ]. This paper explores the effect of oscillating boundaries on 1-dimensional rods for achieving equilibration during thermal conduction. Specifically, the rod’s length oscillates sinusoidally with time which fundamentally alters the diffusion process. By applying a coordinate transformation from the moving domain to a fixed reference domain, this paper derives a modified partial differential equation that includes an additional advective term reflecting the stretching and compression of the rod. Because the resulting problem is analytically intractable for general oscillations, this paper implements a finite difference method of lines combined with implicit time integration to compute numerical solutions. The simulations demonstrate that oscillatory boundary motion prevents convergence to a static equilibrium: instead, the system approaches a periodic steady state where the temperature distribution fluctuates in synchrony with the boundary oscillations. The amplitude and frequency of the oscillations determine the degree of modulation, with larger or faster oscillations producing more pronounced departures from the classical static case. Thus, our results show that introducing oscillatory geometry transforms the nature of equilibration in diffusion problems, replacing the standard monotonic approach to equilibrium with a dynamically sustained periodic state. These insights are relevant for microscale oscillating devices and thermally stressed structures where dynamic boundary conditions arise. Heat conduction moving boundary method of lines equilibration and oscillatory geometrics 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. 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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-7713306","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":529960902,"identity":"cd3f3d4d-d005-4b7a-85aa-bc17166bfdc1","order_by":0,"name":"Aryan 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