Thermal diffusivity constant

Here U = T — T )Cp/L is the appropriately rescaled temperature field T measured from the imposed temperature of the undercooled melt far away from the interface. The indices L and 5 refer to the liquid and solid, respectively, and the specific heat Cp and the thermal diffusion constant D are considered to be the same in both phases. L is the latent heat, and n is the normal to the interface. In terms of these parameters,... 

From Eq. (11), an obviously desirable characteristic for thermoelectric materials is to have low thermal conductivity k. The thermal diffusivity constant, Dt, of ErB44Si2 has been found to have small values of Dt < 1.1 x 10 2 cm 2/s (Mori, 2006c). These values are significantly smaller than what has been observed for boron carbide samples (Wood et ah, 1985). Although no data exists for the sound velocities of ErB44Si2, the velocities are probably high since borides are typically hard materials. Therefore, the small values of Dt indicate extremely short phonon... 

Measurement of steady-state compositions y and y after thermal diffusion equilibrium has been established between temperatures T and T" is the most accurate way of determining the thermal diffusion constant. The next-to-the-last column of Table 14.26 pves values of the measured thermal diffusion constant for several binary isotopic mixtures. In all these cases, 7 is positive, which means that the light isotope concentrates at the higher temperature under the experimental conditions listed. 

Values of the thermal diffusion constant can be calculated by the kinetic theory of gases if the intermolecular potential energy is known. Because the calculation is quite sensitive to the detailed intermolecular interaction, calculated values of the thermal diffusion constant are in less satisfactory agreement with experiment than other transport properties. 

Ifitschfelder et al. [H9] gives a generalized relation for the variation of the thermal diffusion constant with temperature for gases whose molecules interact with the so-called Lennard-Jones potential function, the difference between a repulsion energy inversely... 

Table 14.26. Thermal diffusion constants for isotopic mixtures...

Isotopes Log mean reciprocal temperature, K Thermal diffusion constant, 7 Reference... 

Figure 14.39, based on this theory, may be used to predict the magnitude and temperature dependence of the thermal diffusion constant for 15 isotopic mixtures. The quantity plotted, kj-, is the ratio of the calculated thermal diffusion constant to the thermal diffusion constant... 

Figure 14,39 The function fcf for calculating thermal diffusion constants of isotopic mixtures from Lennard-Jones 6-12 potential function.

Figure 14.40 shows the most accurate measurements of the thermal diffusion effect in UF vapor at low pressure, by Kirch and Schutte [K2]. Results are plotted both as k, for comparison with other gases in Fig. 14.39, and as the thermal diffusion constant y. The very low values, under 0.00005, explain Nier s [N3] inability to detect a thermal diffusion effect in UF5 vapor. The thermal diffusion coefficient 7 is so much smaller than the analogous parameter in gaseous diffusion, Qq 1 = 0.0043, that vapor-phase thermal diffusion caimot compete economically with gaseous diffusion for uranium enrichment. 

Figure 14.40 Thermal diffusion constant of UF vapor at subatmospheric pressure. (From Kirch and Schutte [K2JJ...

Thermal diffusion constant 7, 0.0074 What is the percent CH4 at the bottom of the column at steady state ... 

The physical interpretation of (15) is quite simple. If the neutrons did not diffuse while in the thermal region but all the diffusion took place in the fast neutron region evidently Uf would be continuous and likewise the product of the derivative of n/ with the diffusion constant. On the other hand, if all the neutron diffusion took place while the neutrons are thermal, rtt would be continuous and so would the thermal diffusion constant times the derivative of rtf. If the diffusion takes place for both thermal and fast neutrons one must expect that a linear combination of the above quantities will be continuous with coefficients which are proportional to the amount of diffusion in the corresponding regions. This is exactly what the above equations show. 

For transient wave mixings, the detailed calculations for the three-dimensional thermal grating buildup and temperature distribution and dissipation are obviously very complex, and are further complicated by the anisotropic thermal diffusion constants of the liquid crystals, as well as the enclosing glass slides. In the simplest case where the thermal grating is reducible to a one-dimensional problem [14] (e.g., the case of very small grating constant A compared to the cell thickness /), the thermal decay time constants for heat dissipation along and per-... 

Often, kr is expressed as -fc j.Xi(l-Xi), where fc j. is a thermal diffusion constant this leads to... 

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