In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.

Borino, G., Di Paola, M., Zingales, M. (2011). A non-local model of fractional heat conduction in rigid bodies. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS, 193, 173-184 [10.1140/epjst/e2011-01389-y].

A non-local model of fractional heat conduction in rigid bodies

BORINO, Guido;DI PAOLA, Mario;ZINGALES, Massimiliano
2011-01-01

Abstract

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.
Settore ICAR/08 - Scienza Delle Costruzioni
Borino, G., Di Paola, M., Zingales, M. (2011). A non-local model of fractional heat conduction in rigid bodies. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS, 193, 173-184 [10.1140/epjst/e2011-01389-y].
File in questo prodotto:
File Dimensione Formato  
Borino-DiPaola-Zingales-EPJ-2011.pdf

Solo gestori archvio

Dimensione 3.87 MB
Formato Adobe PDF
3.87 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/63778
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 25
social impact