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

• Ahmed E. Abouelregala ^[1] ; Mohammed A. Elhagary ^[2] ; Amr Soleiman ^[2] ; Khalil M. Khalil ^[2]
  1. [1] Mansoura University

     Mansoura University

     Egipto

     
  2. [2] Jouf University
• Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 50, Nº. 3, 2022, págs. 897-914
• Idioma: inglés
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• Resumen

  • 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.