Thennal conductivity

Neglecting derivatives of the third order and higher, we obtain Fourier s law of thennal conduction... 

Fig. 49. Variation of thennal conductivity at 100 °K for various values of extrusion ratio >. ( ) small-diameter extrudates (O) specimens cut from laige-diameter extrudates...

Fig. 21. Thennal conductivity of titanium and graphite compacts and predicted combustion velocity, as a function of sample density (Adapted from Kottke et al 1990).

Pure metals have high thermal conductivities, and one would think that metal alloys should also have high conductivities. One would expect an alloy made of two metals of thennal conductivities and 2 to have a conductivity k between A , and ki. But this turns out not to be the case. TTie thermal conductivity of an alloy of two metals is usually much lower than that of either metal, a.s shown in Table 1-2. Even small amounts in a pure metal of foreign molecules that are good conductors themselves seriously disrupt the transfer of heat in that metal. For example, the thermal conductivity of steel containing just 1 percent of chrome is 62 W/m °C, while the thermal conductivities of irort and chromium are 83 and 95 W/m C, respectively. 

In heat transfer analysis, a material is normally assumed to be isotropic that is, to have unifonn properties in ail directions. This assumption is realistic for most materials, except those that exhibit different structural characteristics in different directions, such as laminated composite materials and wood. The thennal conductivity of wood across the grain, for example, is different than that parallel to the grain. 

The variation of thennal conductivity of a material with temperature can often be approximated as a linear function and expressed as... 

P " 47ny2/ 47r(Ouier radius)(Inner radius)(Thennal conductivity)... 

The thermal conductivity detector (TCD), which was one of the earliest detectors for gas chromatography, still finds wide application. This device consists of an electrically heated source whose temperature at constant electric power depends on the thermal conductivity of the surrounding gas. The heated element may be a fine platinum, gold, or tungsten wire (Figure 31 -9a) or, alternatively, a small thermistor. The electrical resistance of this element depends on the thermal conductivity of the gas. Twin detectors are ordinarily used, one located ahead of the sample injection chamber and the other immediately beyond the column alternatively, the gas stream can be split. The detectors are incorporated into two arms of a simple bridge circuit (see Figure 31 -9) such that the thennal conductivity of the carrier gas is... 

Figure 15.19. Thennal conductivity of polyethylene vs. volume content of carbon fiber. [Adapted, by permission, from Agari Y, Ueda A, Nagai S, J. Appl. Polym. Sci., 52, No.9, 1994, 1223-31.]...

The catalytic oxidation of ethane at 573-648 K was carried out at atmospheric pressure in a fixed bed flow reactor. Mbftures of ethane (4 mol%), oxygen (4-12 mol%), and helium (balance) were fed to the reactor with a residence time of 38 g. h/mol C2H6, using a catalyst load of 0.36 g, (particle size 0.25-0.42 mm) mixed with SiC bits (dilution 1 4 vA) to reduce the heat release per imit volume. Reactants and products were analysed by gas chromatography on a Vaiian 3400, equ ped with a thennal conductivity detector, using Porapak QS (3 m) and molecular sieve 13X (1 m) columns. In all reaction conditions, the mass and carbon balances were within 10012 %. 

The experimental set up has been described in details in an earlier study [10]. Tlie kinetic measurements were performed at 300 C in differential flow reactor conditions by recycling the outlet gas mixture. The reactants (NO, CO) and reaction products (Nj, NjO, COj) were analysed by means of a chromatograph HP5850 equipped with a thennal conductivity detector. Their separation was achieved on a column CTRl supplied by Alltech. 

For a given polymeric structure, the morphology (crystallinity and orientation), formulation (additives, fillers and impurities), humidity (especially for polar polymers), temperature, and pressure, are the most important factors which affect the thennal conductivity. References [1-8] review many of these factors. In addition, see Bigg [14] and Ross et al [15] for detailed treatments of the effects of fillers and of pressure, respectively, on thermal conductivity. 

The thennal conductivities of polymers at temperatures which are not extremely low will be discussed. See Hust [7] for the heat transfer properties of materials at cryogenic temperatures. 

A dataset of twenty X(exp) values, all measured at room temperature (298 5K), for amorphous polymers and for the amorphous phases of scmicrystalline polymers, was prepared by combining information provided in several sources [2,4,6]. This dataset was used to develop a direct correlation between the stmctural features of polymers, as encoded into the zeroth-order and first-order connectivity indices, and the thennal conductivity at room temperature. This correlation is a first step towards quantifying the relationships between the structures and thermal conductivities of amorphous polymers. Its value does not lie in its absolute accuracy but in the clues it provides on the stmctural factors determining thennal conductivity. 

In concluding this chapter, we must reemphasize that, while quantitative structure-property relationships for the thermal conductivities of amorphous polymers are useful indicators of the general trends as a function of the polymer stmcture, they must nonetheless be used with some caution in practical applications, since factors such as crystallinity, orientation, additives and/or impurities can modify the thermal conductivity by a very considerable amount, and differences among measurement methods introduce further uncertainties. The demand for and the limited availability of consistent thennal conductivity data for polymers were discussed in a concise review article [18] which is recommended as an indicator of the need for caution when utilizing either published experimental or predicted values of this property in practical applications. 

Ifie equation is most conveniently solved by the method of Laplace transforms, used for the solution of the unsteady state thennal conduction problem in Chapter 9. 

Thennal conductivity is an important topic, especially in thermal plasma. Details on the subject can be found in books by Boulos et al. (1994) or Eletsky, Palkina, and Smirnov... 

ANACON Thennal Conductivity Analyser. ANACON. Thame. Oxfordshire. 

Product/Supplier Type Viscosity cP (rpm) Cure Schedule Loss 300 °C by TGA Die-Shear Strei th (psi urfaces) Modulus of Elasticity (MPa /psi) 1 2 T ec) Volume Resistivity, ohm-cm Thennal Conductivity (W/m K) Ionic Impurities (ppm)... 

As shown in Tables 12.3 and 12.4, the thennal conductivities of dry layers of foods and pharmaceuticals are extremely low compared with the conductivities of insulators, such as cork and styrofoam. As a consequence, the temperatnre drop across the dry layer is large, and with surface tanperatures often limited to values below 65°C because of danger of discoloration and in some cases to values below 38°C because of the danger of denaturation, the resultant ice temperature is usually weU below -18°C. Except for materials with very low melting points, it is the surface temperature that limits the drying rate. 

FIGURE 18. Thennal Conductivity (In-Plane and Thru-Plane) of SiOC Nextel 312 BN 2-D Composites... 

F1GURE21.8 Schematic drawing of a thennal conductivity meter. The electrical elements are configured in a typical Wheatstone bridge circuit The variable resistors are usually thermistors. 

TABLE 74 Thennal Conductivities and TCD Response Valnes for Selected Compounds [20] ... 

S.2.5.2 Thermal Conductivity. Thennal conductivity can be increased to shorten molding cycles and to avoid overheating of electrical equipment. Silver, copper, and aluminum have conductivities 1000 times that of unfilled plastics loading them into plastics can increase conductivity considerably, in proportion to their volume fraction (Table 5.22). Beryllium oxide, boron nitride, aluminum oxide, aluminum nitride, and graphite are also quite effective. 

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