4.6 Article

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

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TAYLOR & FRANCIS INC
DOI: 10.1080/15397734.2020.1730189

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Thermoelasticity; fractional heat conduction fractional Fickian diffusion; four-phase-lags; higher-order

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This work focuses on deriving fundamental equations for generalized thermoelastic diffusion with four lags and higher-order time-fractional derivatives. It modified the equations of heat conduction and mass diffusion using Taylor's series of time-fractional order, and discussed sensitivity of physical parameters in different fields including a thermoelastic-diffusion problem for a half-space exposed to thermal and chemical shock. The results are presented graphically as well as in tabular forms.
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. 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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