Generalized mathematical novel model of thermoelastic diffusion with four phase lags and higher-order time derivative

In this work, taking into account the influences of thermal and diffusion, a new four-phase-lag model comprising the macroscopic and microscopic is constructed. The introduced model is an extension of the papers of Nowacki (Bull Acad Pol Sci Ser Sci Tech 22:55-64, 1974; Bull Acad Pol Sci Ser Sci Tech 22:129-135, 1974; Bull Acad Pol Sci Ser Sci Tech 22:257-266, 1974; Proc Vib Prob 15:105-128, 1974), Sherief et al. (Int J Eng Sci 42:591-608, 2004) and Aouadi (J Therm Stress 30:665-678, 2007). In this model, the Fourier's and the Fick's laws have been modified to include higher-order time derivatives of heat flow vector, the gradient of temperature, diffusing mass flux and gradient of chemical potential. Many models in the thermoelastic-diffusion field have been deduced as special cases from the current investigation. Using the resulting formulation, we have studied a thermoelastic-diffusion interaction in a half-space exposed to thermal and chemical shock. Also, the sensitivity of the studied field variables to the variation of the parameters of higher-order time derivative has been investigated.