Non-Fourier heat transport across 1D nano film between thermal reservoirs with different boundary resistances

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

“…The discontinuity propagates along subsystem 1 without interaction with subsystem 2 because τ 1,2 > τ 1 . Considering that 2 = k 1 τ 1,2 in the TTM, we obtain Equation (14). On the intermediate time scale t eq ∝ τ 1,2 > τ 1 , Equation (30) reduces to…”

“…However, when the deviation from equilibrium is strong, namely, when the characteristic time and space scales of the process are close to or even less than the MFT and MFP of energy carriers, respectively, the continuum hypothesis is not valid anymore. An example of a heat conduction approach, which is not based on the continuum hypophysis, is provided by the discrete variable model [14,15,26,31,38]. The model assumes that space and time are discrete variables, which allows one to study heat conduction in nanosized systems under strong deviation from the equilibrium, for example, heat conduction across a nano film [14,15], rapid phase transportation [37], and heat conduction in layered correlated materials [5,6].…”

“…The interest is largely motivated by technological needs such as thermal management in microelectronics and the ultra-fast laser processing of advanced metamaterials [1,4], i.e., artificial materials and media of designed properties, such as layered correlated materials [5,6]. Moreover, the heat transport at ultrashort space and time scales leads to unusual non-Fourier phenomena such as wavelike temperature propagation [4][5][6]12,13], size [14,15] and distance [15] dependent thermal conductivity, and boundary temperature jumps [1,14,15], which have raised an extensive body of literature concerning different conceptual questions of these phenomena [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The problem is that when the characteristic length of the process is of the order of the mean free path (MFP) of energy carriers and/or the characteristic time scale of the process is of the order of the mean free time (MFT) of energy carriers, the thermal dynamics occur under far from local equilibrium conductions and cannot be described by classical Fourier law based on the local equilibrium assumption [31].…”

“…However, the HHCE cannot be used to describe heat conduction in nanosized systems where the nonlocal space effects [14][15][16][17][18]21,22,[26][27][28]31] and ballistic component of heat transport [14][15][16][17]19,23,24] lead to non-Fourier phenomena such as size-dependent thermal conductivity [1,9,[14][15][16][17] and boundary temperature jumps [14][15][16][17]19], which can be observed even in the steady-state [14][15][16][17]. Note that the HHCE in the steady-state reduces to the classical heat conduction equation of the parabolic type, and consequently, cannot describe these effects.…”

“…The nonlocal space effects [1,7,26,31] have been extensively studied in the context of heat conduction in nanosized systems [10,11,[14][15][16][17][18][21][22][23][24]28], in metals under ultrashort (pico-and femtosecond) laser irradiation [4,[31][32][33][34][38][39][40][41][42][43][44][45][46][47], and in biological [48][49][50] and heterogeneous systems [51][52][53]. Comprehensive reviews of different nonlocal heat conduction theories are presented in [41,42].…”