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Dr. Khalil Mohamed Khalil Mohamed :: Publications:

Generalized thermoelastic-diffusion model with higher-order fractional time-derivatives and four-phase-lags
Authors: Ahmed E. Abouelregal; Mohammed A Elhagary; Amr Soleiman; Khalil M KhalilAhmed E Abouelregal, Mohammed A. Elh
Year: 2020
Keywords: Thermoelasticity; fractional heat conduction fractional Fickian diffusion; four-phase-lags; higher-order
Journal: Mechanics Based Design of Structures and Machines
Volume: 48
Issue: Not Available
Pages: Not Available
Publisher: Taylor & Francis
Local/International: International
Paper Link:
Full paper Khalil Mohamed Khalil Mohamed_10.1080@15397734.2020.1730189.pdf
Supplementary materials Not Available

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 thermoelasticdiffusion problem for a half-space exposed to thermal and chemical shock with a permeable material in contact with the half-surface. We discussed the sensitivity of the different physical parameters in all studied fields in detail and the results are presented graphically as well as in tabular forms.

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