Total thermal conductivity

The following separation of the total heat transfer into its component parts, even if not completely rigorous, proves valuable to understanding the total thermal conductivity, k, of foams ... 

The variation in total thermal conductivity with density has the same general nature for ah. cellular polymers (143,189). The increase in at low densities is owing to an increased radiant heat transfer the rise at high densities to an increasing contribution of k. ... 

Properties of peroxide cross-linked polyethylene foams manufactured by a nitrogen solution process, were examined for thermal conductivity, cellular structure and matrix polymer morphology. Theoretical models were used to determine the relative contributions of each heat transfer mechanism to the total thermal conductivity. Thermal radiation was found to contribute some 22-34% of the total and this was related to the foam s mean cell structure and the presence of any carbon black filler. There was no clear trend of thermal conductivity with density, but mainly by cell size. 27 refs. 

ZT Y r A A A A A AC dimensionless thermoelectric figure of merit electronic coefficient of heat capacity (1+ZT)F2 crystal field singlet non-Kramers doublet (crystal field state) crystal field triplet crystal field triplet hybridization gap jump in heat capacity at Tc K KL -min P 6>d X JCO total thermal conductivity of solid thermal conductivity of electrons or holes thermal conductivity of lattice minimum lattice thermal conductivity electrical resistivity Debye temperature magnetic susceptibility magnetic susceptibility at T = 0... 

The thermal conductivity of a metal or alloy consists of two components, a phonon contribution (a phonon is a quantum of acoustic energy, which possesses wave-particle duality), Kph, and an electronic contribution (free electrons moving through the crystal also carry thermal energy), k i- In pure metals, Xei is the dominant contribution to the total thermal conduction. This free electron contribution to the thermal conductivity is given by the gas-kinetic formula as ... 

Use the modihed Wiedemann-Franz-Lorenz law to estimate the phonon contribution to the thermal conductivity of a semiconductor at 298 K whose total thermal conductivity is 2.2 W m if the electrical conductivity is 0.4 x 10 S m ... 

Experimentally, "kcont can be determined when the total thermal conductivity of the system is determined in vacuum as a function of the temperature. 

Total thermal conductivity (k In practice, the radiation and conduction contributions to the heat flux (Q) are interactive, and the interpretation of the combined conductive-radiative heat transfer is complex. Various models have therefore been proposed to simpify the theory of the heat transfer process. One widely-used model is the diffusion approximation which assumes that the heat flux (Q) is given by Equation 2, where k is the effective thermal conductivity and is defined by Equation 3 where x is the distance. Garden has pointed out that this model only applies strictly when (i) k is small and (ii) ad > 8. ... 

This raw data, when used in equation 1, gives total thermal conductivity, which is shown in figure 4. The total thermal conductivity data represent essentially five thermal resistances. 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

Figure 3 Total thermal conductivity X of various RF aerogels versus gas pressure Pg p = 82 kg/m3 (circles) p = 157 kg/m (triangles) p = 303 kg/m3 (squares). The data were measured with the hot-wire method at room temperature.

Euken , also using the first approximation. The total thermal conductivity is considered to be the sum of these three contributions x = + x + Xj ,. The... 

Fig. 13. Translational (electrons and heavy species), reactional, internal and total thermal conductivity of a nitrogen plasma at one atm. Reprinted from...

We now assume that the electron and the lattice contribution to A are additive, giving the following result for the total thermal conductivity ... 

There are several contributions to the thermal conductivity of low-density, closed-cell foams thermal conductivity of the polymeric cell walls and the cell gas, plus convection and radiation in the cells. The thermal conductivity of most solid polymers is within a factor of 2 of 0.3 W m K . For foams of density 30kgm , the cell wall contribution, which is proportional to the foam relative density, is small. The contribution from convection inside the cells is negligible for cell diameters smaller than 10 mm. The radiation contribution is linearly proportional to the cell size, because infrared radiation is absorbed at each cell face then re-radiated. Figure 11.19 shows the effect of reducing the cell size of polyurethane foams on the total thermal conductivity. In polystyrene foams, the cells are rarely larger than 0.5 mm, so the radiation contribution to the foam conductivity is minimal. 

Thermal energy is transported by two mechanisms in solids—electronic conduction and lattice or phonon conduction. An electrical analog for thermal conduction is shown in Fig. 2 [% The total thermal conductivity. A, is the sum of the electronic term and the lattice term. For pure metals and dilute alloys, thermal conduction is dominated by the electronic term, while for heavily alloyed metals, the phonon contribution is appreciable. 

Ar = temperature difference between thermometer stations A = total thermal conductivity Ag = electronic component of thermal conductivity Ag = lattice or phonon component of thermal conductivity Ah = total thermal conductivity at magnetic field H p = electrical resistivity Ph = electrical resistivity at magnetic field H... 

Fig. 5. Temperature dependence of some electrical properties of CrSi2 a) thermoelectric power b) electrical conductivity c) total thermal conductivity d) lattice thermal conductivity H) parallel to the c axis i.) perpendicular to the c axis.

The influence of the structure of the alloys on their physical properties was determined by measuring the room-temperature values of the electrical conductivity (Hall coefficient, the thermoelectric power (a), and the total thermal conductivity (>t). The carrier density (p), the carrier mobility (/i), and the thermoelectric figure of merit (z) were calculated. The samples used in these measurements were cut from the middle parts of the ingots and their compositions were checked by x-ray diffraction analysis. The results of the measurements are presented in Table 1. 

Typically the total thermal conductivity of a solid, k, can be considered to be the sum of the electronic, kg and phonon, kph, contributions that is ... 

Total thermal conductivity is a sum of the lattice and electronic parts, K = Ki + Ke- The lattice part of the thermal conductivity describes the scattering of phonons on the vibrations of atoms, whereas the electronic part describes thermal conductivity appearing due to conduction electrons and is related to the electrical conductivity Wiedemann-Franz equation, = a T Lo, where T is the absolute temperature and Lq is the ideal Lorenz number, 2.45 X 10 Wf2K [64]. The electronic part of the thermal conductivity is typically low for low-gap semiconductors. For the tin-based cationic clathrates it was calculated to contribute less than 1% to the total thermal conductivity. The lattice part of the thermal conductivity can be estimated based on the Debye equation /Cl = 1 /3(CvAvj), where C is the volumetric heat capacity, X is the mean free path of phonons and is the velocity of sound [64]. The latter is related to the Debye characteristic temperature 6 as Vs = [67t (7V/F)] . Extracting the... 

A different picture is observed for the silicon-based cationic clathrates. The values of the total thermal conductivity are greater than those for the tin-based clathrates. Typical room-temperature values for these compounds lie between 3 and 5 W m [13, 52]. This is explained by two facts. First, the silicon-based... 

The thermal conductivity of Siso.sPis.eTee.eSei shows additional features and deserves more discussion. It was shown [14] that the total thermal conductivity of this clathrate is much lower than for other Si-based compounds. At room temperature it reaches only 2.0 W m Moreover, the temperature dependence of the thermal conductivity is typical for glasses. It increases sharply from 2 to 50 K, then slowly reaches 2.0 W m at about 130 K and remains constant up to room temperature (Fig. 5.9). The glass-like behavior of this semimetallic compound is associated with the mass alteration of two types of the guest atoms, tellurium and selenium, coupled to a slight disorder in distribution of silicon and phosphorus atoms within the cationic framework. 

In theory, heat in crystalline solids is transferred by three mechanisms (i) electrons (ii) lattice vibrations and (iii) radiation [44], Since zirconia is an electronic insulator (electrical conductivity occurring at high temperatures by oxygen ion diffusion), electrons play no part in the total thermal conductivity of the system. Hence, thermal conduction in zirconia-based ceramics is mainly by lattice vibrations (phonons) or by radiation (photons). 

Where a o is referred to as the electrical power factor, with a, the Seebeck coefficient, a the electrical conductivity and X. is the total thermal conductivity. The figure-of-merit is often expressed in its dimensionless form ZT wWe T is absolute tenperature. 

Figure 23.6. Total thermal conductivity of a resorcinol-formaldehyde aerogel (density = 330 kg m , porosity = 0.78, average pore size 0.6 pm) as a function of argon gas pressure at 21°C. The solid line is the calculated thermal conductivity according to (23.10) without taking a coupling effect into account.

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