Salta al contenuto principale
Passa alla visualizzazione normale.

MASSIMILIANO ZINGALES

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

  • Autori: Zingales, M.; Failla, G.
  • Anno di pubblicazione: 2015
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • Parole Chiave: Finite element method; Fractional calculus; Long-range heat transport; Non-homogeneous conductors; Modeling and Simulation; Numerical Analysis; Applied Mathematics
  • OA Link: http://hdl.handle.net/10447/215535

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.