Heat Conduction Equation at Micro and Nano Scale: Approximation Methods

Sayed Masuleh

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=65
Date :  2009/08/04
Publish in :    International Conferences of Mathematical Sciences


Keywords :Conduction, Micro, Scale, Approximation

Abstract :

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In the classical theory of di®usion, Fourier law of heat conduction, it is assumed that the heat °ux vector and temperature gradient across a material volume occur at the same instant of time. It has shown that if the scale in one direction is at the microscale (of order 0:1¹m), then the heat °ux and temperature gradient occur in this direction at di®erent times. In the so-called non-Fourier heat conduction equation 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. Among the frameworks to study the non-Fourier heat conduction equation, the dual-phase-lag framework is employed. In this talk, some numerical approaches for solving the heat conduction equation in various domains are presented.