Measuring Thermal Conductivity

There are several methods available to measure k, but no single one is appropriate for all ceramics because of their wide range of thermal conductivities. 

The measurements can be performed at room temperature or at a range of higher temperatures by enclosing the sample in a furnace. 

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Figures 7 and 8 show thermal conductivity data for CBCF after exposure to temperatures of 2673, 2873, 3073, and 3273 K, for 5.7 and 15 7 seconds, respectively. The symbols in the Figs. 7 and 8 represent measured thermal conductivity values, and the solid lines are the predicted behavior from Eqs. (5) through (8) The model clearly accounts for the effects of measurement temperature, exposure tune, and exposure temperature The fit to the data is good (typically within 10%). However, the fit to the as fabricated CBCF data (Fig 6) was less good (-20%), although the scatter in the data was larger because of the much lower heat treatment temperature (1873 K) in that case.

Table 1 provides states the temperature range over which the correlation constants are reported from the literature. Estimates from this expression using the constants in Table 1 are generally accurate and typically provide agreement to well within + 1% compared to experimentally measured thermal conductivities. 

The W-F law is fairly well verified at T 0D. At intermediate temperatures, the measured thermal conductivity is smaller than that calculated from the electrical conductivity by means of the W-F law. 

The diode laser is scanned up and down in frequency by a triangle wave, so that the scan should be linear in time and have the same rate in both directions. In the thermal accommodation coefficient experiments, the external beam heats the microsphere to a few K above room temperature and is then turned off. The diode laser is kept at fairly low power ( 7 pW) so that it does not appreciably heat the microsphere. Displacement of a WGM s throughput dip from one scan trace to the next is analyzed to find the relaxation time constant as the microsphere returns to room temperature. Results from the two scan directions are averaged to reduce error due to residual scan nonlinearity. This is done over a wide range of pressures (about four orders of magnitude). The time constant provides the measured thermal conductivity of the surrounding air, and fitting the thermal conductivity vs. pressure curve determines the thermal accommodation coefficient, as described in Sect. 5.5.2. 

The thermal conductivity of suspended graphene has been calculated by measuring the frequency shift of the G-band in the Raman spectrum with varying laser power. These measurements yielded a value for thermal conductivity of 4840 5300 W m 1 K 1 [23], better than that of SWCNTs, with the exception of crystalline ropes of nanotubes, which gave values up to 5800 W m 1 K 1 [24]. Even when deposited on a substrate, the measured thermal conductivity is 600 W m 1 K 1 [25], higher than in commonly used heat dissipation materials such as copper and silver. 

Schematic of the equipment used to measure thermal conductivity of thin materials. (Reprinted from M. Khandelwal and M. M. Mench. Journal of Power Sources 161 (2006) 1106-1115. With permission from Elsevier.)...

More detailed studies have been made where the thermal conductivity in the different crystal directions have been determined for SiC (see Table 1.1 [5]). As can be seen, there is a dependence on the purity of the crystal as well as on the crystal direction. At the time of this study, the material was not of the high quality we see today, and more sophisticated techniques have been developed to measure thermal conductivity. Thus, as higher-quality material has been grown, values close to the theoretical values have been measured using the laser flash technique [10]. 

Even more interesting and important than the foregoing unique method of measuring thermal conductivities of suspensions is the procedure used to calculate thermal conductivities theoretically. Orr and DallaValle noted that electrical and thermal fields are similar hence the usual equation for calculation of electrical conductivity of a suspension should also be applicable to thermal conductivities. Their extensive tabulated results support this contention to within 3 %. This equation is... 

On the application of Angstrom s method of measuring thermal conductivity (with C.H. Bosanquet) Br. J. Appl. Phys. 5,252-255 (1954). 

FIGURE 6.7 Schematic of the pressure vessel and needle probe system used to measure thermal conductivity. (Reproduced from Waite, W.F., deMartin, B.J., Kirby, S.H., Pinkston, J., Ruppel, C.D., Geophys. Res. Lett., 29, 2229 (2002). With permission from the American Geophysical Union.)... 

Thermal Conductivity Measures thermal conductivity of gas Universal 6 x 10- ° 104 10-5 gm of CH4 per vol. of detector effluent Good... 

Figure 9.3 Schematic of the calorimeter method of measuring thermal conductivity [2]. Specimen sizes are approximately three bricks of dimensions 23 x 11.4 x 6.4 cm3.

This monograph, I believe, is unique in that it covers the broader topic of pyrometry the latter chapters on infrared and optical temperature measurement, thermal conductivity, and glass viscosity are generally not treated in books on thermal analysis but are commercially and academically important. I have resisted the urge to elaborate on some topics by using ex-... 

Figure 18.11 Measured thermal conductivity of Ti02-added Fe203 against temperature. Standard means no addition of Ti02.

Achwal and Stepanek1 recently measured the holdup profile in a packed bubble-column by a method based on measuring thermal conductivity. They found that the gas holdup in a packed bed increased with height and related this increase to the change in pressure. Two separate correlations for the average gas holdup were derived. One, based on the homogeneous flow model, was expressed as... 

A careful test of Nernst s theory was reported by Isnardi243 in 1915. His work consisted of the measurement of the thermal conductivity of iodine (whose dissociation as a function of temperature and pressure was well known), comparison of the experimental results with those of Nernst s theory, and the use of the method to determine JD(H2) which was not then known. Isnardi measured thermal conductivities by the hot wire method, in which the rate of heat removal by conduction from the wire arranged concentrically in a cylinder containing the gas is given by... 

Thermal conductance. . (TCD) Measures thermal conductivity, change in carrier gas on elution. . of compounds Universal <400pg propane/mL. He ... 

Electronic conductivity It has been reported that glasses which contain significant concentrations of Fe ions behave in a similar manner to semi-conductors and hence thermal conduction via conduction electrons, holes, etc could be significant, according to Fine et al -I. Little is known of this mechanism in relation to the heat transfer in slags and consequently the contribution of k. to the measured thermal conductivities has been ignored in this review. 

B.J. Filla, A Steady-State High-Temperature Apparatus for Measuring Thermal Conductivity of Ceramics, submitted to Review of Scientific Instruments. 

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. 

Another method for measuring thermal diffusivity is the flash method developed by Parker et al. [48] and successfully used for the thermal diffusivity measurement of solid materials [49]. A high intensity short duration heat pulse is absorbed in the front surface of a thermally insulated sample of a few millimeters thick. The sample is coated with absorbing black paint if the sample is transparent to the heat pulse. The resulting temperature of the rear surface is measured by a thermocouple or infrared detector, as a function of time and is recorded either by an oscilloscope or a computer having a data acquisition system. The thermal diffusivity is calculated from this time-temperature curve and the thickness of the sample. This method is commercialized now, and there are ready made apparatus with sample holders for fluids. There is only one publication on nanofluids with this method. Shaikh et al. [50] measured thermal conductivity of carbon nanoparticle doped PAO oil. 

S. Lee, S.U.S. Choi, S. Li and J.A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles. Journal of Heat Transfer, 121, 280-289 (1999). 

Rossiter and Brown, 1990). The foamed cement was formulated as a calcium magnesium oxychloride silicate composition and was pumped into the cavity walls of the test house. The density of cement was 46.5 kg m-3 and had a measured thermal conductivity of 0.0430 W/m°C at 24°C, which is comparable to other commercially available insulation materials. 

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