FRACTIONAL HEAT CONDUCTION EQUATION AND ASSOCIATED THERMAL STRESS

A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory in...

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Bibliographic Details
Published in:Journal of thermal stresses 2004-12, Vol.28 (1), p.83-102
Main Author: Povstenko, Y. Z.
Format: Article
Language:English
Subjects:
fractional calculus
heat wave equation
non-Fourier heat conduction
thermal stresses
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Summary:A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.
ISSN:0149-5739
1521-074X
DOI:10.1080/014957390523741