Phonon heat transfer

Film conductances are also often defined for the impedance to thermal conduction when two solid conductors are placed in mechanical contact. A significant contact resistance is often observed when, on a microscopic scale, heat transfer involves an air-gap between the materials. Under such conditions, phonon propagation must be replaced by the kinetic interaction amongst gaseous atoms and then back to phonon heat transfer in the next solid. Fibrous and foam insulation axe effective thermal insulators because of the numerous contact resistances involved in the transfer of heat. 

At temperatures above ca. 1000 K, heat transfer via radiation becomes significant, that is, the heat transfer can occur by optical energy waves (photons) as well as conduction (phonons), with the heat transfer equation expressed by... 

The heat transfer in a solid is due both to lattice vibrations (phonons) and to conduction electrons. Experiments show that in reasonably pure metals, nearly all the heat is carried by the electrons. In impure metals, alloys and semiconductors, however, an appreciable... 

Thermal conduction through electrically insulating solids depends on the vibration of atoms in their lattice sites, which, as discussed in section 3.7, is the mechanism of thermal energy storage. These vibrations act as the conduit for heat transfer by the propagation of waves ( phonons ) superimposed on these vibrations (schematically depicted in Figure 8.1). An analogy... 

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. 

Chen, G., Phonon Wave Heat Conduction in Thin Films and Superlattices. Journal of Heat Transfer, 1999.121 p. 945-953. 

Mazumder, S., and Majumdar, A., Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization. ASME Journal of Heat Transfer, 2001.123 p. 749-759. 

Narumanchi, S.V.J., J.Y. Murthy, and C.H. Amon, Sub-micron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization. ASME J. Heat Transfer, 2004(in press). 

The phonons can interact amongst themselves or in reciprocal action with other particles, same as the gas molecules. Therefore, heat transfer is dependent on the structure of the solid matter. Since phonons are distributed with every disturbance of the crystal lattice, the value of Xsm drops as the number of ciystal lattice defects, impurities, grain boundaries or amorphous areas rises. 

The differences in the heat transfer processes for the glass, supercooled liquid and normal liquid phases of the three materials are attributed to the competition between the phonon transport and diffusive heat-transfer effects that are governed by dynamical processes taking place within the GHz-range. 

Acoustic (sound) waves are also transmitted by atomic vibrations. Atomic vibrations are often called phonons, i.e., "particles" of sound. Theories of heat transfer [13] in insulators usually attempt to relate X to other physical properties which are mainly determined by atomic vibrations, such as the velocity of sound and the heat capacity. 

The equation of radiative transfer will not be solved here since solutions to some approximations of the equation are well known. In photon radiation, it has served as the framework for photon radiative transfer. It is well known that in the optically thin or ballistic photon limit, one gets the heat flux as q = g T[ - T ) from this equation for radiation between two black surfaces [13]. For the case of phonons, this is known as the Casimir limit. In the optically thick or diffusive limit, the equation reduces to q = -kpVT where kp is the photon thermal conductivity. The same results can be derived for phonon radiative transfer [14,15]. 

PHONON PROCESSES Heat caused by conduction Heat caused by fiiction Heat transferred by flame... 

What is the thermal conductivity of silicon nanowires, n-alkane single molecules, carbon nanotubes, or thin films How does the conductivity depend on the nanowiie dimension, nanotube chirality, molecular length and temperature, or the film thickness and disorder More profoundly, what are the mechanisms of heat transfer at the nanoscale, in constrictions, at low tanperatures Recent experiments and theoretical studies have dononstrated that the thermal conductivity of nanolevel systems significantly differ from their macroscale analogs [1]. In macroscopic-continuum objects, heat flows diffusively, obeying the Fourier s law (1808) of heat conduction, J = -KVT, J is the current, K is the thermal conductivity and VT is the temperature gradient across the structure. It is however obvious that at small scales, when the phonon mean free path is of the order of the device dimension, distinct transport mechanisms dominate the dynamics. In this context, one would like to understand the violation of the Fourier s... 

The Landauer expression for heat transfer (Equation 12.13) assumes the absence of inelastic scattering processes in the system, and the two opposite phonon flows of different temperatures are out of equilibrium with each other. This leads to an anomalous transport of heat, where (classically) the energy flux is proportional to the temperature difference, Tl - T, rather than to the temperature gradient VT, as asserted by the Fourier s law of heat conductivity. 

Here is the normal life-time of the phonons for heat transfer to the bath it is increas by the factor (1 + b), the ratio of the combined heat capacity of spins -f phonons to that of the phonons alone. For large values of b the overall relaxation rate to the bath (the measured rate) should vary as cotanh (hco/lkT), instead of the first power that occurs in eq. (19). An experimental confirmation of this result is shown in fig. 5 at the lowest temperatures the rate is found to be slower for the higher concentration of magnetic spins, because of the greater value of the parameter b. 

The rate of heat transfer in a thermal gradient is lower than might be expected for transport of vibrational energy heat transport by conductivity is much slower than sound propagation. The accepted physical model for heat transfer is a process of diffusing phonons (wave packets in the vibrating lattice) heat conduction in solids and in fluids is observed to be diffusive. 

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