6533b7d4fe1ef96bd1261ebc
RESEARCH PRODUCT
Fractional-order theory of heat transport in rigid bodies
Massimiliano Zingalessubject
PhysicsNumerical AnalysisField (physics)business.industryApplied MathematicsFractional derivatives; Fractional-order calculus; Fractional-order derivatives; Generalized entropies; Molecular dynamics simulations; Nonlocal; Relative temperatures; Thermal energy transportThermodynamicsContext (language use)Fractional derivativeFractional-order calculuFractional calculusRelative temperatureHeat fluxModeling and SimulationHeat transferGeneralized entropieMolecular dynamics simulationFractional-order derivativeBoundary value problembusinessConvection–diffusion equationNonlocalSettore ICAR/08 - Scienza Delle CostruzioniThermal energyThermal energy transportdescription
Abstract The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53] , Mongiovi and Zingales, 2013 [54] ) that thermal energy transport is due to two phenomena: ( i ) A short-range heat flux ruled by a local transport equation; ( ii ) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law decay of the distance yielding a novel temperature equation in terms of α -order Marchaud fractional-order derivative ( 0 ⩽ α ⩽ 1 ) . Thermodynamical consistency of the model is provided in the context of Clausius–Plank inequality. The effects induced by the boundary conditions on the temperature field are investigated for diffusive as well as ballistic local heat flux. Deviations of the temperature field from the linear distributions in the neighborhood of the thermostated zones of small-scale conductors are qualitatively predicted by the used fractional-order heat transport model, as shown by means of molecular dynamics simulations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-11-01 |