Time-nonlocal six-phase-lag generalized theory of thermoelastic diffusion with two-temperature

Abstract

A mathematical model for time-nonlocal six-phase-lag generalized thermoelastic diffusion with two-temperature is proposed for a linear, isotropic and homogeneous thermoelastic diffusive continuum by considering modified Fourier's law of heat conduction together with modified Fick's law of mass diffusion. The modified Fourier's law includes temperature gradient and thermal displacement gradient among the constitutive variables whereas the modified Fick's law includes chemical potential gradient and the chemical potential displacement gradient among the constitutive variables. The Fourier's law of heat conduction is replaced by a fractional-order approximation to a modification of the Fourier's law with three different phase lags for the heat flux vector, the temperature gradient and the thermal displacement gradient whereas the Fick's law of mass diffusion is replaced by a fractional-order approximation to a modification of the Fick's law with three different phase lags for the mass flux vector, the chemical potential gradient and the chemical potential displacement gradient. The proposed model includes some of the existing thermoelastic diffusion models as special cases. A variational principle is derived and a uniqueness theorem is proved. Finally, a dynamic reciprocity theorem is established for the proposed generalized thermoelastic diffusion model.