Solids, thermal conductivity temperature dependence

Foam Insulation Since foams are not homogeneous materials, their apparent thermal conductivity is dependent upon the bulk density of tne insulation, the gas used to foam the insulation, and the mean temperature of the insulation. Heat conduction through a foam is determined by convection and radiation within the cells and by conduction in the solid structure. Evacuation of a foam is effective in reducing its thermal conductivity, indicating a partially open cellular structure, but the resulting values are stiU considerably higher than either multilayer or evacuated powder insulations. 

In Solids, heal conduction is due to two effects the lattice vibrational waves induced by the vibrational motions of the molecules po.sitioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid (Fig. 1—28). The Ihermal conductivity of a solid is obtained by adding the lattice and electronic components. The relatively high thermal conductivities of pure metals arc primarily due to the electronic component. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, diamond, which is a liighly ordered crystalline solid, has the highest known thermal conductivity at room temperature. 

The thermal conductivity of a-alumina single crystals as a function of temperature is given in Table 16 (from [2, 23]). Heat is conducted through a nonmetallic solid by lattice vibrations or phonons. The mean free path of the phonons determines the thermal conductivity and depends on the temperature, phonon-phonon interactions, and scattering from lattice defects in the solid. At temperatures below the low temperature maximum (below about 40°K), the mean free path is mainly determined by the sample size because of phonon scattering from the sample surfaces. Above the maximum, the... 

It is appropriate here to make some remarks on the physical foundations of thermal conductivity. The dependence of thermal conductivity on temperature has been experimentally recognized. However, there is no universal theory explaining this dependence. Gases, liquids, conducting and insulating solids can each be explained with somewhat different microscopic considerations. Although the text is on the continuum aspects of heat transfer, the following remarks are made for some appreciation of the microscopic aspects of thermal conductivity. 

Mfn = 549.5 g/mol (Fa)2PF6.) Solid curves calculated temperature dependence for thermally-activated paramagnetism (t.a.p.) and for the paramagnetism of the conduction electrons with an effective energy gap of 2Aeff(T) in the quasi-metallic state for T> Tp, according to the Lee-Rice-Anderson model (L-R-A). From [29]. 

Wlien a temperature difference exists in or across a body, an energy transfer occurs from the high-tem-perature region to the low-temperature region. This heat transfer, q, which can occur in gases, liquids, and solids, depends on a change m temperature, AT, over a distance. Ax (i.e., AT/z)ix) and a positive constant, k, which is called the thermal conductivity of the material. In equation form, the rate of conductive heat transfer per unit area is written as... 

The temperature dependence of electrical conductivity has been used [365] to distinguish between the possible structural modifications of the Mn02 yielded by the thermal decomposition of KMn04. In studies involving additives, it is possible to investigate solid-solution formation, since plots of electrical conductivity against concentration of additive have a characteristic V-shape [366]. 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

Fig. 3.15. Temperature dependence of the thermal conductivity of some dielectric solids.

At a given (low) temperature and pressure a crystalline phase of some substance is thermodynamically stable vis a vis the corresponding amorphous solid. Furthermore, because of its inherent metastability, the properties of the amorphous solid depend, to some extent, on the method by which it is prepared. Just as in the cases of other substances, H20(as) is prepared by deposition of vapor on a cold substrate. In general, the temperature of the substrate must be far below the ordinary freezing point and below any possible amorphous crystal transition point. In addition, conditions for deposition must be such that the heat of condensation is removed rapidly enough that local crystallization of the deposited material is prevented. Under practical conditions this means that, since the thermal conductivity of an amorphous solid is small at low temperature, the rate of deposition must be small. 

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