Search results for "Temperature evolution"

showing 3 items of 3 documents

An exact thermodynamical model of power-law temperature time scaling

2016

In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t)∝tβ with β∈R shows a different evolution of the temperature time rate T(t) with respect to the temperature time-dependence T(t). Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the therm…

PhysicsAnomalous conductionDiffusion equationField (physics)business.industryPower-lawTime evolutionTemperature evolutionGeneral Physics and AstronomyAnomalous conduction; Fractional derivative; Fractional Transport; Power-law; Temperature evolution;Function (mathematics)Fractional derivative01 natural sciencesPower law010305 fluids & plasmasFractional Transport010101 applied mathematics0103 physical sciencesStatistical physics0101 mathematicsDiffusion (business)businessSettore ICAR/08 - Scienza Delle CostruzioniScalingThermal energy
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A physical description of fractional-order Fourier diffusion

2014

In this paper the authors introduce a physical picture of anomalous heat transfer in rigid conductor. The analysis shows that a fractional-order Fourier transport is obtained by the analysis of the heat transport in a functionally graded conductor. The order of the fractional-type operator obtained is related to the grading of the physical properties of the conductor.

Materials scienceDifferential equationMathematics::Number TheoryOperator (physics)Mathematical analysisCondensed Matter::Mesoscopic Systems and Quantum Hall EffectConductorsymbols.namesakeFourier transformFourier numberThermal diffusion Fourier Equations Fractional-order calculus Temperature evolutionHeat transfersymbolsDiffusion (business)Settore ICAR/08 - Scienza Delle CostruzioniElectrical conductorICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014
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Fractional-order theory of thermoelasticicty. I: Generalization of the Fourier equation

2018

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 r…

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 function
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