Analytical Solution of the Heat Conduction Equation in One-dimensionalSpherical Coordinates at Nanos

Sayed Masuleh | Vahid Mohammadi Fakhar

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=64
Date :  2009/08/04
Publish in :    International Conferences of Mathematical Sciences


Keywords :Analytical, Conduction

Abstract :

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Heat conduction equation at microscale has been widely applied to thermal analysis of thin metal ¯lms. The microscopic heat °ux equation developed from physical and mathematical reasoning is di®erent 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 re- spect 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 di®erential equations, when the exact solution is not reached or existed, demands the use of truncated series. The major reduction in computa- tional e®ort 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 lineatization. In this presentation, the reliability and e±ciency of the solution were veri¯ed using the ADM.