Search results for "Anomalous heat transfer"
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Fractional-order constitutive equations in mechanics and thermodynamics
2019
This chapter is devoted to the application of fractional calculus in mechanics of materials and thermodynamics. The use of fractional calculus in mechanics is related to the definition of fractional-order constitutive equations leading to the class of fractional hereditariness. In this regard, a brief description of the classical rheological models of material hereditariness and a comparison with the fractional elements are reported. It is shown that a rheological hierarchy corresponding to the fractional order stress-strain relation may be defined. Such a model provides a multi-scale mechanical picture of the power-law hereditariness and it leads toward an unique definition of material fre…
Fractional-Order Theory of Thermoelasticity. II: Quasi-Static Behavior of Bars
2018
This work aims to shed light on the thermally-anomalous coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo's fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the anomaly mentioned previously. The interp…