Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects

Abstract

In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.

Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux

“…Some of these variables are polar vectors, such as the specific polarizations , or axial vectors such as the specific magnetizations ( i = 1, 2, …, n ) (see [ 73 , 74 ] and also [ 75 , 76 ]), partial heat fluxes ( i = 0, 1, 2, …, n ), contributions of the total heat flux [ 42 ], others are tensorial variables such as the partial inelastic strain tensors ( i = 1, 2, …, n ; (with and spatial coordinates) contributions of the total strain tensor in a medium [ 77 , 78 , 79 , 80 ], the dislocation core tensor , with i , j = 1, 2, 3 spatial coordinates, á la Maruszewski [ 81 ] or the dislocation tensor introduced by the authors [ 82 ] (see also [ 83 , 84 ]), analogous to the tensor defined to describe the quantized vortices in turbulent superfluid Helium II [ 85 ], the porosity tensor á la Kubik [ 86 ] (see also [ 87 , 88 , 89 ]), the inhomogeneity-grain density and the anisotropy-grain tensor both defined by Maruszewski [ 90 ] (see also [ 91 ]). Furthermore, the trace of the dislocation tensor is an internal scalar variable and describes the density of local dislocation lines at a point of the medium.…”

“…. , n; α, β = 1, 2, 3), (with α and β spatial coordinates) contributions of the total strain tensor in a medium [77][78][79][80], the dislocation core tensor a ij , with i, j = 1, 2, 3 spatial coordinates, á la Maruszewski [81] or the dislocation tensor introduced by the authors [82] (see also [83,84]), analogous to the tensor defined to describe the quantized vortices in turbulent superfluid Helium II [85], the porosity tensor r ij á la Kubik [86] (see also [87][88][89]), the inhomogeneitygrain density and the anisotropy-grain tensor both defined by Maruszewski [90] (see also [91]). Furthermore, the trace of the dislocation tensor is an internal scalar variable and describes the density of local dislocation lines at a point of the medium.…”