ИСТИНА

As classical and continuum theories reach their limits, phenomena that may be insignificant at larger length scales (such as interfacial and nanosized effects) can become dominant [1-7]. We analyze the nanoscale effects on heat conduction across a nanosized system using discrete variable model (DVM) [1-5]. In contrast to the continuum-based description, the DVM assumes that the time and space are discrete variables, and models heat conduction by periodic thermal lattice consisting of interacting discrete elements of a characteristic size h. The discrete size h represents a minimum size of a zone to which the local temperature can still be assigned. The DVM takes into account the fundamental role of the physical scales of space and time, which are comparable to the mean-free path and the mean-free time of the energy carriers, respectively, and inherently includes both diffusive and ballistic components of energy transport [1-5]. Using the DVM, we study such non-Fourier effects in nano scale systems as boundary temperature jumps, size- and distance-dependent local thermal conductivity [3-5]. We also introduce the effective thermal extrapolation length, which eliminates the temperature jump at the boundaries by shifting the "apparent" boundary positions [5]. The effective thermal conductivities and the extrapolation length depend on the Knudsen number, which controls the transition from diffusion to ballistic regime. Moreover, the local (distance-dependent) thermal conductivity at the boundary is only half of the bulk value when Knudsen number is small due to the nanoscale effects. We demonstrate that the two effective thermal conductivities in nanosized systems can be introduce depending on how the corresponding temperature gradient (between the thermal reservoirs, inside the system, or near the boundary) is chosen [3-5]. The model may be easily implemented for practical experimental conditions and can help make molecular dynamic [6] and Monte Carlo [7] simulations more effective.