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RESEARCH PRODUCT
The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors
Massimiliano ZingalesGiuseppe Faillasubject
PhysicsFinite element methodNumerical Analysisbusiness.industryApplied MathematicsMathematical analysisFinite differenceFinite element method; Fractional calculus; Long-range heat transport; Non-homogeneous conductors; Modeling and Simulation; Numerical Analysis; Applied MathematicsMixed finite element methodFractional calculuFinite element methodFractional calculussymbols.namesakeLong-range heat transportFourier transformModeling and SimulationsymbolsHeat equationNon-homogeneous conductorbusinessSettore ICAR/08 - Scienza Delle CostruzioniNumerical AnalysiThermal energyExtended finite element methoddescription
Abstract In a non-local fractional-order model of thermal energy transport recently introduced by the authors, it is assumed that local and non-local contributions coexist at a given observation scale: while the first is described by the classical Fourier transport law, the second involves couples of adjacent and non-adjacent elementary volumes, and is taken as proportional to the product of the masses of the interacting volumes and their relative temperature, through a material-dependent, distance-decaying power-law function. As a result, a fractional-order heat conduction equation is derived. This paper presents a pertinent finite element method for the solution of the proposed fractional-order heat conduction equation. Homogenous and non-homogeneous rigid bodies are considered. Numerical applications are carried out on 1D and 2D bodies, including a standard finite difference solution for validation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-12-01 |