Analytical solution of the heat conduction equation in one-dimensional spherical coordinates at nanoscale

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dc.contributor.authorMohammadi-Fakhar, V.
dc.contributor.authorMomeni-Masuleh, S. H.
dc.date.accessioned2024-07-12T20:50:24Z
dc.date.available2024-07-12T20:50:24Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractHeat conduction equation at microscale has been widely applied to thermal analysis of thin metal films. The microscopic heat flux equation developed from physical and mathematical reasoning is different from the traditional heat equation. Here a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time will appear in the heat equation. An approximate analytical solution to the non-Fourier heat conduction equation in one-dimensional spherical coordinates based on the dual-phase-lag framework is obtained by employing the Adomian decomposition method (ADM). The application of ADM to partial differential equations, when the exact solution is not reached or existed, demands the use of truncated series. The major reduction in computational effort associated with the ADM is the main factor behind their popularity while other numerical methods require extensive computation. The ADM does not discretize variables and gives an analytical solution in the form of truncated series. If there are nonlinear factors in an equation, ADM gives the analytical solution without any need for linearization. In this presentation, the reliability and efficiency of the solution were verified using the ADM.en_US
dc.identifier.citationMohammadi-Fakhar, V. ve Momeni-Masuleh, S. H. (2009).Analytical solution of the heat conduction equation in one-dimensional spherical coordinates at nanoscale. Maltepe Üniversitesi. s. 375.en_US
dc.identifier.endpage376en_US
dc.identifier.isbn9.78605E+12
dc.identifier.startpage375en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2334
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07699
dc.subjectAdomian decompositionen_US
dc.subjectHeat conduction equationen_US
dc.subjectNanoscaleen_US
dc.subjectSpherical coordinatesen_US
dc.titleAnalytical solution of the heat conduction equation in one-dimensional spherical coordinates at nanoscaleen_US
dc.typeConference Object
dspace.entity.typePublication

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