Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
Garcia-Bernabé, Abel (Universitat Politècnica de Valencia. Departament de Termodinàmica Aplicada)
Hernández, Saul Iván (Universidad Nacional Autónoma de México. Facultad de Ciencias)
del Castillo, L. F. (Universidad Nacional Autónoma de México. Instituto de Investigaciones en Materiales)
Jou i Mirabent, David, 1953- (Universitat Autònoma de Barcelona. Departament de Física)

Data:	2016
Resum:	The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy production, and using the time fractional derivative, we have derived a space-time generalized telegrapher's equation with a fractional nested hierarchy which can be used in separate developments for the mass transport, for the heat conduction and for the flux of ions. We have obtained a new formalism which includes the contribution of fast of higher-order fluxes in the mesoscopic and inhomogeneous media. The results take the form of continued fraction expansions. The balance equations are used in a scheme of continued fractions, and they appear as a closure condition. In this way the transport equation and its corresponding wave number-frequency relation are obtained, both of them in the mathematical structure of the continued fraction scheme. Numerical examples are included to show the dispersive nature of the solutions, and the generalized fractional transport equation in the same mathematical form, which can be applied to the mass transport, the heat conduction and the flux of ions.
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Transport phenomena ; Anomalous transport ; Continued fraction ; Extended Irreversible ; Thermodynamics
Publicat a:	Mathematics, Vol. 4 Núm. 4 (2016) , p. 1-10, ISSN 2227-7390

DOI: 10.3390/math4040067

10 p, 1.7 MB

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