Coaxial-cylinder thermal conductivity

The traditional way to measure thermal conductivity is with steady-state instruments, in which a measured heat flux is compared to a temperature difference between surfaces. Most often the geometry is coaxial cylinders, a thin wire inside a cylinder, or parallel plates. In such instruments, eliminating convection currents is crucial many old data taken with steady-state instruments are unreliable because of convection. Multiple experiments at different heat fluxes are often performed to verify the absence of convection. With good design and operation, such instruments may achieve accuracy in the 1% to 3% range. 

Fig. 3, Error in thermal conductivity due to axial displacement of the two coaxial cylinders is 4 in. and Yg is 4f in.

In Table 5.1 all available experimental thermal conductivity data sources at high temperatures (above 200 °C) and high pressures are presented. As one can see from this table, all data were derived by the parallel-plate and the coaxial-cylinder techniques, except only two datasets for LiBr by Bleazard et al. (1994) and DiGuilio and Teja (1992) which were obtained by the transient hot-wire technique. We further note that almost all investigators quote an uncertainty of better than 2%. In this section a brief analyses of these methods is presented. The theoretical bases of the methods, and the working equations employed is presented, together with a brief description of the experimental apparatus and the measurements procedure of each technique. For a more thorough discussion of the various techniques employed, the reader is referred to relevant literature (Kestin and Wakeham, 1987 Wakeham et al., 1991 Assael et al, 1991, and Wakeham and Assael, in press). 

To reduce the values of the Rayleigh number, Ra, a small gap distance between cylinders d = (0.97 0.03) x 10 m was used. This way the risk of convection was minimized. Convection could develop when the Ra exceeds a certain critical value Ra, which for vertical coaxial cylinders is about 1000 (Gershuni, 1952). The absence of convection can be verified experimentally by measuring the thermal conductivity with different temperature differences AT across the measuring gap and different power Q transferred from inner to outer cylinder. Since heat transfer by radiation is proportional to 4r AT, we would expect radiation losses to substantially increase as a function of the cell temperature. This kind of correction is included in the calibration procedure. The emissivity of the walls was small and Qrad, estimated by Equation (5.7) is negligible 0.164 W) by comparison with the heat transfer (13.06 W) by conduction in the temperature range up to 600 K. 

Figure 5.6 Thermal conductivity apparatus and coaxial-cylinder cell, developed by Yata et al (1979a). (a) 1 high pressure vessel 2 fluid separator 3 heater 4 heat insulator 5 support table for bath 6 heat transfer fluid (water or glycerin) 7 screw propeller 8 standard resistance thermometer 9 thermocouples and heaters, (b) 1 inner cylinder 2 outer cylinder 3 upper guard cylinder 4 lower guard cylinder 5 inner heater 6 thermocouples 7 upper alumina insulator 8 lower alumina insulator 9 mica spacer 10 alumina piece 11 brass screw 12 alumina pin 13 brass screw 14 compensative heater 15 top closure of high pressure vessel.

Carbon Nanotubes (CNTs), the third allotrope of carbon next to diamond and graphite, were discovered in 1991. Since then, their exceptional properties, such as extremely high tensile strengths (150-180 GPa) and modulus (640 GPa to 1 TPa), "ballistic thermal conduction (>3000 W/mK for individual tubes) and exceptional electrical conductivity, have been unveiled. These properties are directly attributed to their unique structure. CNTs are long cylinders of covalently bonded carbon atoms, which look somewhat like graphene sheets that have been rolled-up into seamless tubes. The tube ends may be capped by hemi-fullerenes. Single-walled carbon nanotubes (SWCNTs) comprise only one such cylinder, while multi-walled carbon nanotubes (MWCNTs) contain a set of coaxial cylinders, see Figure 1.3. 

The overall sample geometry is governed by unidirectional heat flow. The only two practical geometries are either a slab-shaped solid with two parallel faces and heat flow perpendicular to these faces (Fig. 2a), most commonly used for polymers, or a right circular cylinder with heat flow in the radial direction and perpendicular to the axis (Fig. 2b), which is little used for pol3rmers. Because of the low thermal conductivity of polymers, the slab (or radius of the cylinder) is usually thin, so that heat losses in directions perpendicular to the desired heat-flow direction are minimized and the temperature drop AT is not excessive. Therefore, the preferred specimen shape is usually a thin disk with parallel faces and less commonly a long, thin rod or coaxial cylinder. 

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