Thermal conductivity of sample

Figure 3.8 Borchardt and Daniels DTA [3]. Stirring rods maintain temperature uniformity within the sample and reference containers. The sample consisted of both reactive and reference fluid. Mixing in this way allowed the heat capacities and thermal conductivities of sample and reference to closely approach.

Table I. Thermal diffusion coeflicienl and thermal conductivity of samples...

One purpose of using a diluent has already been discussed it permits the thermal conductivities of sample and reference to be matched. In addition, it may be used to maintain a constant sample-size while the amount of the reacting component is varied this will decrease the influence of many of the factors listed in Table 17.2. A diluent can also be used where the sample is so small that weighing it out directly is inconvenient. 

While we know that temperature differentials of order lOK do occur across the calorimeter cup under ordinary operating conditions, we cannot immediately conclude from this that similarly large drops occur across samples in the cup. Indeed if the ratio of the thermal conductivities of sample and of surrounding gas is large, so that the gas in effect provides thermal insulation, then the steady state temperature drop across the sample will indeed be small. Polystyrene and other good insulators, however, have thermal conductivities which differ from that of a gas only by a factor of about four, and samples of such material will be shown below to have in fact steady state gradients the same order of magnitude as those across the calorimeter cups. 

The strong dependencies of the sample gradient on sample thickness and on the heating rate are evident in Fig.2, in which are plotted the differences in indicated temperatures for melting of indiiim on the cup lid and bottom and on the top of four polystyrene samples of varying thickness. The sample gradients for the steady state (T = 0) are seen to vary from nearly zero for sample X to almost the total drop across the sample cup itself in the case of sample W. In our mathematical model these steady state gradients are independent of the sample specific heat but dependent on the ratio of thermal conductivities of sample and... 

The thermal conductivity of samples with composition (Cai.x,Mgx)Zr4(P04)6 where x= 0.2 and 0.5 was investigated using a laser flash thermal diffusivity apparatus and a differential scanning calorimeter (DSC) at. ..e HTML facility, Oak Ridge National Laboratory, Thermal conductivity was determined by the product of the thermal diffusivity, specific heat, and bulk density of each sample. Samples were made by sol-gel Process 1. 

Figure 2.28 Schematic diagram of sample film and the backing substrate a, thermal diffusitivity of sample and substrate, respectively /,/ , thermal conductivity of sample and substrate, respectively...

A key aim of the ceramic industry is to improve thermal insulation of ceramic products without impairing their mechanical properties. The thermal conductivity of the materials used plays a key role in avoiding heat loss and conserving energy. The bulk density and porosity are the major factors governing thermal conductivity [44, 52-55]. Figure 10 shows the thermal conductivity of samples. Thermal conductivity of extruded bricks is lower than... 

FIGURE 9.4 Thermal conductivity of samples from the KTB borehole. Samples are gneiss from a depth of 1793 m, amphibolite from a depth of 147 m. (a) Conductivity as a function of uniaxial pressure, measured at T= 54 °C. (b) Conductivity as a function of temperature, measured at p = 10 MPa. Data from Huenges et at. (1990). 

Thermal conductivity is used as an analytical tool in the deterrnination of hydrogen. Because the thermal conductivities of ortho- and i7n -hydrogen are different, thermal conductivity detectors are used to determine the ortho para ratio of a hydrogen sample (240,241). In one method (242), an analy2er is described which spHts a hydrogen sample of unknown ortho para ratio into two separate streams, one of which is converted to normal hydrogen with a catalyst. The measured difference in thermal conductivity between the two streams is proportional to the ortho para ratio of the sample. 

The temperature dependence of the thermal conductivity of CBCF has been examined by several workers [10,13,14]. Typically, models for the thermal conductivity behavior include a density term and two temperaUrre (7) terms, i.e., a T term representing conduction within the fibers, and a term to account for the radiation contribution due to conduction. The thermal conductivity of CBCF (measured perpendicular to the fibers) over the temperature range 600 to 2200 K for four samples is shown in Fig. 6 [14]. The specimen to specimen variability in the insulation, and typical experimental scatter observed in the thermal conductivity data is evident in Fig. 6. The thermal conductivity of CBCF increases with temperature due to the contribution from radiation and thermally induced improvements in fiber structure and conductivity above 1873 K. 

Recently, Dinwiddie et al. [14] reported the effects of short-time, high-temperatme exposures on the temperature dependence of the thermal conductivity of CBCF. Samples were exposed to temperatures ranging from 2673 to 3273 K, for periods of 10, 15, and 20 seconds, to examine the time dependent effects of graphitization on thermal conductivity measured over the temperature range from 673 to 2373 K. Typical experimental data are shown in Figs. 7 and 8 for exposure times of 10 and 20 seconds, respectively. The thermal conductivity was observed to increase with both heat treatment temperature and exposure time. 

In the laser flash method, the heat is put in by laser flash instead of electric current in the stepwise heating method mentioned above. Thus this method may be classified as a stepwise heating method. A two-layered laser flash method was developed by Tada et al. " The experimental method and the data analysis, including a case involving radiative heat flow, are described in detail in the review article by Waseda and Ohta. A thin metal plate is placed at the surface of a melt. A laser pulse is irradiated onto a metal plate of thickness / having high thermal conductivity. The sample liquid under the metal plate and the inert gas above the plate are designated as the third and first layers, respectively. The temperature of the second layer becomes uniform in a short time" and the response thereafter is expressed by... 

Here, Q is the heat energy input per area p and Cp are the density and specific heat capacity, respectively and indices g, d, and s refer to the gas, metal, and liquid sample layers, respectively. With Eq. (106), the thermal conductivity of the sample liquid is obtained from the measured temperature response of the metal without knowing the thermal conductivity of the metal disk and the thickness of the sample liquid. There is no constant characteristic of the apparatus used. Thus, absolute measurement of thermal conductivity is possible, and the thermal conductivities of molten sodium and potassium nitrates have been measured. ... 

Example Suppose one wants to measure the thermal conductivity of a solid (k). To do this, one needs to measure the heat flux (q), the thickness of the sample (d), and the temperature difference across the sample (AT). Each measurement has some error. The heat flux (q) may be the rate of electrical heat input (< ) divided by the area (A), and both quantities are measured to some tolerance. The thickness of the sample is measured with some accuracy, and the temperatures are probably measured with a thermocouple to some accuracy. These measurements are combined, however, to obtain the thermal conductivity, and it is desired to know the error in the thermal conductivity. The formula is... 

Fig. 3.20. Thermal conductivity of copper samples with residual resistivity ratio (RRR) ranging from 3000...

Among the shunt spurious contribution, the power exchanged through the residual gas in the vacuum chamber does not represent usually a problem. The shunt conductances are always to be compared with the thermal conductance of the sample. At temperatures above 77 K, the thermal contact drawback vanishes (see Section 4.4), but the problem of the radiative exchange (a T4) becomes very important. 

Only few measurements of the thermal conductivity of copper at very low temperatures have been published. Suomi et al. [21] reported about measurements carried out on Cu wires down to 20 mK more recently Gloos et al. [22] measured the thermal conductivity of rod and foil samples down to even lower temperatures. 

We have carried out the measurement of the thermal conductivity of six copper samples, whose characteristics are shown in Table 11.2. 

The thermal conductance of each glue spot below 150 mK was very low because of the two contact resistances Rc (Kapton-glue and glue-copper), and the power Ph delivered to the copper sample did not flow through the Kapton foil. To be sure of that, however, 1 mm large, 56 xm thick copper ribbon was internally glued around the upper end of the Kapton support. A heater Hk and a thermometer Tk (Fig. 11.6) were fixed on the ribbon and a power Pk was delivered to the Kapton support in such a way that T = Th. 

The measurement of the thermal conductivity of Torlon has been carried out on a sample whose shape and dimensions are shown in Fig. 11.12. 

The thermal resistance between the ends of the sample and the copper blocks must be negligible compared with the thermal resistance of the sample. This assumption must be verified especially for short samples at low temperature where the contact resistance is higher. For this reason, a second measurement of the thermal conductivity of Torlon in the 4.2-25 K range was carried out. The second sample had a different length (L = 24.51 mm) and the same section A. This additional measurement gave the same value of k within 2%. Moreover, we see from Fig. 11.15 that data of thermal conductivity at 4.2 K well join data at lower temperatures (within 3%) obtained on a sample of much smaller geometrical factor and with a different method (integrated thermal conductivity method) and a different apparatus [38], Finally, at room temperature, we find k = 0.26 W/mK, which is the data sheet value. 

Because of the possibility of focusing laser beams, thin films can be produced at precisely defined locations. Using a microscope train of lenses to focus a laser beam makes possible the production of microregions suitable for application in computer chip production. The photolytic process produces islands of product nuclei, which act as preferential nucleation sites for further deposition, and thus to some unevenness in the product film. This is because the substrate is relatively cool, and therefore the surface mobility of the deposited atoms is low. In pyrolytic decomposition, the region over which deposition occurs depends on the thermal conductivity of the substrate, being wider the lower the thermal conductivity. For example, the surface area of a deposit of silicon on silicon is narrower than the deposition of silicon on silica, or on a surface-oxidized silicon sample, using the same beam geometry. 

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