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 2Dbodies, including a standard finite difference solution for validation

The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors / Zingales, M; Failla, Giuseppe. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 29:1-3(2015), pp. 116-127. [10.1016/j.cnsns.2015.04.023]

The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors

FAILLA, Giuseppe
2015-01-01

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 2Dbodies, including a standard finite difference solution for validation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/1587
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