Theory of fractional-ordered thermoelastic diffusion

Abstract

In this note, the traditional theory of thermoelastic diffusion is replaced by fractional ordered thermoelasticity based on fractional conservation of mass, fractional Taylor series and fractional divergence theorem. We replace the integer-order Taylor series approximation for flux with the fractional-order Taylor series approximation which can remove the restriction that the flux has to be linear, or piece-wise linear and the restriction that the control volume must be infinitesimal. There are two important distinctions between the traditional thermoelastic diffusion, and its fractional equivalent. The first is that the divergence term in the heat conduction and mass diffusion equations are the fractional divergence, and the second is the appearance of strain tensor term in the fractional equation is in the form of “incomplete fractional-strain measures”.