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Generalized thermoelastic-diffusion model with higher-order fractional time-derivatives and four-phase-lags

Author name : AMR SOLIMAN MAHMOUD HASSAN
Publication Date : 2019-02-24
Journal Name : Mechanics Based Design of Structures and Machines

Abstract

The present work is devoted to the derivation of fundamental equations in generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. The equations of the heat conduction and the mass diffusion have been modified by using Taylor’s series of time-fractional order. In this new model, the Fourier and the Fick laws have been modified to include a higher time-fractional order of the heat conduction vector, the gradient of temperature, the diffusing mass flux and the gradient of chemical potential. We adopted the definitions of Caputo and Jumarie; for time-fractional derivatives. The work of Nowacki; Sherief, Hamza, and Saleh; and Aouadi; are deduced as limit cases from the current investigation. Applying this formulation, we have discussed a thermoelastic-diffusion problem for a half-space exposed to thermal and chemical shock with a permeable material in contact with the half-surface

Keywords

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Publication Link

https://doi.org/10.1080/15397734.2020.1730189

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