Abstract
The correct analysis of heat transport at nanoscale is one of the main reasons of new developments in physics and nonequilibrium thermodynamic theories beyond the classical Fourier law. In this paper, we provide a two-temperature model which allows to describe the different regimes which electrons and phonons can undergo in the heat transfer phenomenon. The physical admissibility of that model is showed in view of second law of thermodynamics. The above model is applied to study the propagation of heat waves in order to point out the special role played by nonlocal and nonlinear effects.
Highlights
Modern ultrafast laser-assisted manufacturing technology is empowering the fabrication of miniaturized nano/microscale devices for electronics, optics, medicine and energy applications [1,2]
According with the above observations, by regarding the electrons and the phonons as a mixture of heat carriers flowing through the crystal lattice, and assuming that they are endowed with their own temperatures [19,20], here we propose a theoretical model based on the following equations which allow to take into account memory, nonlocal and nonlinear effects: 7 Page 2 of 15
Vp = Vp0 φ2p + 1 + ψp − φp wherein we have introduced the following speeds λe cev τ1e λp cpv τ1p and the following nondimensional scalar-valued functions φe qj0nj cev θ0 Ve0 ψe 2 e cev τ2eλe φp ψp Throughout the present paper, we use the appellation electronic heat (EH-) wave for the A-wave whose speed is given by Eq (18a) and the appellation phononic heat (PH-) wave for the A-wave whose speed is given by Eq (18b)
Summary
Modern ultrafast laser-assisted manufacturing technology is empowering the fabrication of miniaturized nano/microscale devices for electronics, optics, medicine and energy applications [1,2]. With a different importance, in common materials used at nanoscale both the electrons and the lattice vibrations (i.e., the phonons) are the heat carriers [11,12,13,14]. Both heat carriers are not in an equilibrium state during the heat transfer; ii. According with the above observations, by regarding the electrons and the phonons as a mixture of heat carriers flowing through the crystal lattice, and assuming that they are endowed with their own temperatures [19,20], here we propose a theoretical model based on the following equations which allow to take into account memory, nonlocal and nonlinear effects:
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