6533b855fe1ef96bd12b07ef
RESEARCH PRODUCT
Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation
Daniele ZontaMassimiliano ZingalesA. ChiappiniGianluca AlaimoMaurizio FerrariLuca DeseriValentina Piccolosubject
Uses of trigonometryGeneralization01 natural sciences010305 fluids & plasmasScreened Poisson equationsymbols.namesakeFractional operators0103 physical sciencesFractional Fourier equationMechanics of Material010306 general physicsFourier seriesMathematicsFourier transform on finite groupsEntropy functionsHill differential equationPartial differential equationMechanical EngineeringFourier inversion theoremMathematical analysisTemperature evolutionMechanics of MaterialssymbolsFractional operatorSettore ICAR/08 - Scienza Delle CostruzioniEntropy functiondescription
The paper deals with the generalization of Fourier-type relations in the context of fractional-order calculus. The instantaneous temperature-flux equation of the Fourier-type diffusion is generalized, introducing a self-similar, fractal-type mass clustering at the micro scale. In this setting, the resulting conduction equation at the macro scale yields a Caputo's fractional derivative with order [0,1] of temperature gradient that generalizes the Fourier conduction equation. The order of the fractional-derivative has been related to the fractal assembly of the microstructure and some preliminary observations about the thermodynamical restrictions of the coefficients and the state functions related to the fractional-order Fourier equation have been introduced. The distribution and temperature increase in simple rigid conductors have also been reported to investigate the influence of the derivation order in the temperature field. (C) 2017 American Society of Civil Engineers.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-02-01 |