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

Massimiliano Zingales, Giuseppe Failla

Risultato della ricerca: Articlepeer review

9 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)116-127
Numero di pagine12
RivistaCOMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION
Volume29
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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