TY - JOUR

T1 - The finite element method for fractional non-local thermal energy transfer in non-homogeneous rigid conductors

AU - Zingales, Massimiliano

AU - Failla, Giuseppe

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Applied Mathematics

KW - Finite element method

KW - Fractional calculus

KW - Long-range heat transport

KW - Modeling and Simulation

KW - Non-homogeneous conductors

KW - Numerical Analysis

KW - Applied Mathematics

KW - Finite element method

KW - Fractional calculus

KW - Long-range heat transport

KW - Modeling and Simulation

KW - Non-homogeneous conductors

KW - Numerical Analysis

UR - http://hdl.handle.net/10447/215535

M3 - Article

VL - 29

SP - 116

EP - 127

JO - COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION

JF - COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION

SN - 1007-5704

ER -