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EnglishIn this work, we compare different constitutive models of heat flux in a rigid heat conductor. In particular, we investigate the relation between the solutions of the Green-Naghdi type III equation and those of the classical Fourier heat equation. The latter is often referred to as a limit case of the former one, as (formally) obtained by letting certain small positive parameter (p) vanish. In presence of steady heat sources, we prove that the type III equation may be considered as a perturbation of the Fourier one only if the solutions are compared on a finite time interval of order 1/p, whereas significant differences occur in the longterm. Moreover, for a bar with finite length and prescribed heat flux at its ends, the solutions to the type III equation do not converge asymptotically in time to the steady solutions to the corresponding Fourier model. This suggests that the Green-Naghdi type III theory is not to be viewed as comprehensive of the Fourier theory, at least when either asymptotic or stationary phenomena are involved.
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| Data di pubblicazione: | 2014 | |
| Titolo: | On the Green-Naghdi type III heat conduction model | |
| Autori: | Giorgi C.; Grandi D.; Pata V. | |
| Rivista: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. | |
| Parole Chiave: | Heat conduction; Green-Naghdi theory; Fourier law; Singular limit | |
| Abstract in inglese: | In this work, we compare different constitutive models of heat flux in a rigid heat conductor. In particular, we investigate the relation between the solutions of the Green-Naghdi type III equation and those of the classical Fourier heat equation. The latter is often referred to as a limit case of the former one, as (formally) obtained by letting certain small positive parameter (p) vanish. In presence of steady heat sources, we prove that the type III equation may be considered as a perturbation of the Fourier one only if the solutions are compared on a finite time interval of order 1/p, whereas significant differences occur in the longterm. Moreover, for a bar with finite length and prescribed heat flux at its ends, the solutions to the type III equation do not converge asymptotically in time to the steady solutions to the corresponding Fourier model. This suggests that the Green-Naghdi type III theory is not to be viewed as comprehensive of the Fourier theory, at least when either asymptotic or stationary phenomena are involved. | |
| Digital Object Identifier (DOI): | 10.3934/dcdsb.2014.19.2133 | |
| Handle: | http://hdl.handle.net/11392/2362492 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
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