A heat conduction equation for heterogeneous media and its connections to various known equations. (June 2021) - Wang, Linjuan
Abstract: We derive the governing equation of the macroscopically average temperature field in a heterogeneous medium. Although the constituents of the heterogeneous medium obey Fourier's law, the average temperature field is governed by a spatiotemporally nonlocal integro-differential formulation. Then, we find that the average fluctuation of the temperature in the matrix region of the heterogeneous medium plays a key role in determining the various degenerate forms of the governing equation. Depending on the value of this average fluctuation, the governing equation can degenerate into the well-known equations in the literature, including the Jeffreys-type equation, Nunziato equation, Gurtin and Pipkin equation, peridynamic formulation, and dual-phase-lag (DPL) equation. These connections establish the relations between the coefficients in these equations with the properties of the constituents of a heterogeneous medium, and provide guidelines for their applications to the prediction of heat conduction in heterogeneous media.