Heat Transport by Phonons and Electrons

Abstract

Efficient heat transport requires a sufficient number of collisions among energy carriers to take place. Mean free path can be thought of as the averaged distance traveled by the energy carrier per collision over a sufficient number of collisions. Mean free time, on the other hand, is the averaged time traveled by the energy carrier per collision over a sufficient number of collisions. The mean free path for the lattice is of the order of 10 1 -10 2 nm. The mean free time for electron-electron, electron-phonon (for metals), and phonon-phonon (semiconductors, dielectric crystals, and insulators) collisions is of the order of 10 0 femtoseconds, 10 0 ps, and 10 1 ps, respectively. As the physical scale of a device shrinks to the order of the mean free path of the energy carriers (microscale effect in space), or the process time shortens into the range of their mean free time (microscale effect in time), individual and yet statistically meaningful behavior of the energy carriers becomes pronounced. The resulting behavior of heat transport in microscale will be very different from macroscale heat transfer based on the averages taken over hundreds of thousands of grains (in space) and collisions (in time). Different physical bases have been used in describing different types of energy carriers in microscale heat transfer. This chapter reviews most representative phonon-electron interaction (for metals) and phonon scattering (for semiconductors, dielectric crystals, and insulators) models in microscale heat transfer to exemplify the differences resulting from the development made on different physical bases. Special effort then follows to extract the commonalities among the differences, paving the way for the generalized dual-phase-lag model that will be deployed through the rest of the book.From a microscopic point of view, the process of heat transport is governed by phonon-electron interaction in metallic films and by phonon scattering in dielectric films, insulators, and semiconductors. Conventional theories established on the macroscopic level, such as heat diffusion assuming Fourier's law, are not expected to be informative for microscale conditions because they describe macroscopic behavior averaged over many grains. This holds even more true should the transient behavior at extremely short times, say, of the order of picoseconds to femtoseconds, become major concerns. A typical example is the ultrafast 1 laser heating in thermal processing of materials. The quasiequilibrium concept implemented in Fourier's law further breaks down in this case, along with the termination of macroscopic behavior in heat transport.This chapter provides a brief summary of existing microscale heat-transfer models, including the microscopic two-step model (phonon-electron interaction model), phonon-scattering model, phonon radiative transfer model, and the thermal wave model. The first three models emphasize microscale effects in space, while the fourth, the thermal wave model, describes microscale effects in time. Rather than a detai...

A Review on Heat Transfer of Nanofluids by Applied Electric Field or Magnetic Field

“…Recently, Tzou et al [53] and the team of Wang Liqiu et al [54,55] used a two-phase hysteresis model to investigate the heat transfer of nanofluids. By analyzing and measuring the heat flux vector and time lag ratio of different nanofluids, the existing conditions of the thermal wave were obtained, and the thermal wave theory of heat transfer of nanofluids was established.…”

“…By analyzing and measuring the heat flux vector and time lag ratio of different nanofluids, the existing conditions of the thermal wave were obtained, and the thermal wave theory of heat transfer of nanofluids was established. Contrary to the practice of Tzou et al [53], Dolatabadi et al [56] tried to clarify the energy transfer mechanism at the micro/nanoscale by analyzing the structure of the solid-liquid interface and established a model of macroscopic thermal conductivity. However, the inner mechanism of heat conduction of nanofluids is not clear, the temperature is discontinuous in the microscale heat transfer, and the heat flow vector and temperature gradient are separated.…”