Non-Fourier heat conductions in nanomaterials

Abstract

We study the non-Fourier heat conductions in nanomaterials based on the thermomass theory. For the transient heat conduction in a one-dimensional nanomaterial with a low-temperature step at both ends, the temperature response predicted by the present model is consistent with those by the existing theoretical models for small temperature steps. However, if the step is large, the unphysical temperature distribution under zero predicted by the other models, when two low-temperature cooling waves meet, does not appear in the predictions by the present model. The steady-state non-Fourier heat conduction equation derived by the present model has been applied to predict the effective thermal conductivities of nanomaterials. The temperature and size dependences of effective thermal conductivities of nanofilms, nanotubes, and nanowires from the present predictions agree well with the available data from experiments in the literature and our molecular dynamics simulation results, which again proves the validity of the proposed heat conduction equations. The present analysis suggests that the inertial effect of high-rate heat and the interactions between heat and surface in confined nanostructures dominate the non-Fourier heat conduction in nanomaterials. V

Thermal rectification based on phonon hydrodynamics and thermomass theory

“…(9).The thermomass friction force, Eq. (13), is extended with the Laplacian term compared with the previous models [28][29][30]. It is a necessary extension for nanosystems regarding that the friction force of porous flow should also include the Laplacian of velocity when boundary effect is important, which is called the Brinkman extension to the Darcy's law.…”

“…Then such reduction can be explained by the boundary drag acting on the phonon gases [25][26][27]. The thermomass theory [28][29][30][31] derives the generalized heat conduction law from the approach of continuum mechanics. It regards the thermal energy as a continuum fluid with a certain amount of mass, which is the rest mass of energy in the relativity theory.…”

Thermal convection in a magnetized conducting fluid with the Cattaneo–Christov heat-flow model

“…Hyperbolic heat-flow effects have a range of practical applications that extend beyond their foundational significance. For example, thermal waves are important in the study of thermal transport in nanomaterials and nanofluids [6,13], and thermal shocks in solids [14], and for heat transport in biological tissue and surgical operations [8,[15][16][17]. Similarly, thermal relaxation has been shown to impact on flow velocity profiles in Jeffrey fluids [18], and a number of thermal convection problems in fluids and porous media [19][20][21][22] (including thermo-haline convection [23,24]), while type-II flux laws analogous to equation (1.1) have found utility in related contexts involving advection-diffusion systems [25][26][27].…”

Phonon transport effects in one-dimensional width-modulated graphene nanoribbons

“…Examples of these features include that: i) the thermal conductivity could deviate from Fourier's law [1][2][3][4][5], ii) a crossover is observed from ballistic into diffusive transport regimes [6,7], or from nanoto macro-scale behaviors [8,9], iii) the thermal conductivity could even increase under channel width confinement [10,11], iv) band mismatch under extreme confinement could result to phonon localization and 'effective transmission bandgaps' [12], v) heat transport could be below the Casimir or the amorphous limits, and many more [13,14]. Several interesting device concepts have also emerged recently in the area of phononics, which attempt to use heat to perform transistor action [15], create heat rectifiers [16], engineer the sound velocities and phonon dispersions, etc.…”