Nonlocal heat conduction in silicon nanowires and carbon nanotubes

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

“…As it has been mentioned above, the G-K equation, Equation (16), and the Jeffreys type equation, Equation (18), are of the parabolic type and give rise to an infinite speed of propagation of the temperature wave. To eliminate this disadvantage, we can modify the corresponding constitutive equation for heat fluxes, keeping in mind that the left-hand side of Equations ( 15) and ( 17) are the first order approximations of the "time lag equation" for the heat flux q(t + τ i ).…”

“…where τ is the relaxation time to the local equilibrium. Equation (1) has been obtained from both macroscopic and microscopic approaches (see [12,[16][17][18]22,25,26,[29][30][31] and references therein). The values of the relaxation time τ range from tens of seconds in systems with heterogeneous inner structure and biosystems [49][50][51][52][53][54][55][56][57][58] to picoseconds in metals and dielectric solids [4][5][6]12,[32][33][34]38,39,46,47].…”

“…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].…”