Thermal conductivity predicting

Figure 7 (a). In-plane silicon thermal conductivity predicted by molecular dynamics at 376K ( ), predicted from BTE for pure (dashed lines) and natural (solid lines) silicon, and available experimental data ( ) [53] and (A) [80] at300K. 

Zamel et al. presented a study on the estimation of effective thermal conductivity of carbon paper GDL stmctures based on the aforementioned DNS formalism (Eq. 9.12). The 3D carbon paper GDL microstractures were reconstracted using the stochastic method by Schulz et al. They investigated the influence of fiber orientation, anisotropy, compression and binder fraction. Figure 9.27 shows the representative effective thermal conductivity prediction along with experimental data available in the literatirre." " ... 

The thermal conductivity of a multicomponent mixture of monatomic species therefore requires a knowledge of the diermal conductivity of the pure components and of three quantities characteristic of the unlike interaction. The final three quantities may be obtained by direct calculation from intermolecular potentials, whereas the interaction thermal conductivity, Xgg, can also be obtained by means of an analysis of viscosity and/or diffusion measurements through equations (4.112) and (4.125) or by the application of equation (4.122) to an analysis of the thermal conductivity data for all possible binary mixtures, or by a combination of both. If experimental data are used in the prediction it may be necessary to estimate both and This is readily done using a realistic model potential or the correlations of the extended law of corresponding states (Maitland et al. 1987). Generally, either of these procedures can be expected to yield thermal conductivity predictions with an accuracy of a few percent for monatomic systems. Naturally, all of the methods of evaluating the properties of the pure components and the quantities characteristic of binary interactions that were discussed in the case of viscosity are available for use here too. 

Notwithstanding the further modification of the Enskog theory required to achieve this result, the procedure yields thermal conductivity predictions for a dense polyatomic gas which are little worse than for monatomic systems. 

Wu K-J, Chen Q-L, He C-H (2014) Speed of sound of ionic liquids database, estimation, and its application for thermal conductivity prediction. AIChE J 60 1120-1131... 

The effective thermal conductivity of a Hquid—soHd suspension has been reported to be (46) larger than that of a pure Hquid. The phenomenon was attributed to the microconvection around soHd particles, resulting in an increased convective heat-transfer coefficient. For example, a 30-fold increase in the effective thermal conductivity and a 10-fold increase in the heat-transfer coefficient were predicted for a 30% suspension of 1-mm particles in a 10-mm diameter pipe at an average velocity of 10 m/s (45). 

The third characteristic of interest grows directly from the first, ie, the high thermal conductance of the heat pipe can make possible the physical separation of the heat source and the heat consumer (heat sink). Heat pipes >100 m in length have been constmcted and shown to behave predictably (3). Separation of source and sink is especially important in those appHcations in which chemical incompatibilities exist. For example, it may be necessary to inject heat into a reaction vessel. The lowest cost source of heat may be combustion of hydrocarbon fuels. However, contact with an open flame or with the combustion products might jeopardize the desired reaction process. In such a case it might be feasible to carry heat from the flame through the wall of the reaction vessel by use of a heat pipe. 

Vacuum gauges may be broadly classified as either direct or indirect (10). Direct gauges measure pressure as force pet unit area. Indirect gauges measure a physical property, such as thermal conductivity or ionisation potential, known to change in a predictable manner with the molecular density of the gas. 

External coils spaced away from the tank wall exhibit a coefficient of around 5.7 W/(m -°C) [1 Btu/(h-ft of coil surface-°F)j. Direct contact with the tank wall produces higher coefficients, but these are difficult to predict since they are strongly dependent upon the degree of contact. The use of beat-transfer cements does improve performance. These puttylike materials of high thermal conductivity are troweled or camked into the space between the coil and the tank or pipe surface. 

Adequate prediction of the thermal conductivity for pure metals can be made by means of the Wiedeman-Franz law which states that the ratio of the thermal conductivity to the product of the electrical conductivity and the absolute temperature is a constant. This ratio for... 

All ciyogenic hquids except hydrogen and helium have thermal conductivities that increase as the temperature is decreased. For these two exceptions, the thermal conductivity decreases with a decrease in temperature. The kinetic theory of gases correc tly predicts the decrease in thermal conductivity or all gases when the temperature is lowered. 

Fig. 7. Thermal conductivity data for CBCF specimens heat treated for 10 seconds (5.7 seconds at temperature) at four different temperatures. Solid lines are predicted curves from Eqs. (5) through (8). Reprinted from [14], copyright 1996 Technomic Publishing Company, Inc., with permission.

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.

An algorithm has been developed to predict the thermal conductivity degradation for a high thermal conductivity composite ( 555 W/m-K at room temperature) as a function of radiation dose and temperature [33]. The absence of irradiation data on CFCs of this type required the use of data from intermediate thermal conductivity materials as well as pyrolitic graphite to derive an empirical radiation damage term [14, 17, 19, 25, 26]. 

The data of ONB in trapezoidal micro-channels of results reported by Lee et al. (2004) and prediction of Eq. (6.10) with various different values of r x- the experimental data points in Fig. 6.5, the saturation temperature is corresponding to the local pressure at each of the ONB locations. The local pressure is estimated by assuming a linear pressure distribution in the channel between the inlet and exit ones. The system pressure may vary from case to case. For Fig. 6.5 an average system pressure of 161.7 kPa over various different cases of this study was employed. As for the wall temperature, it is assumed that the channel wall temperature is uniform as the channel is relatively short and the wall material, silicon, has relatively good thermal conductivity. The figure indi-... 

The Keyes figure of merit, based on thermal conductivity as an additional factor, (see following section) predicts the suitability of a semiconductor for dense logic circuit applications. Again, diamond is far superior to other materials. 

As was discussed in the previous part, the temperature elevation in the solutions can be ascribed to the absorption of the NIR light by the solvents. In order to quantitatively explain the temperature elevation coefficient, AT/AP, for other solvents, we proposed a simple model that can parametrize the temperature elevation. As easily predicted, the AT/AP value is closely related to the extinction coefficient of light absorption, a, and the thermal conductivity, X. Heat generated at the focal point ofthe NIR beam is proportional to the extinction coefficient, a, and the incident laser power, P, as represented by Eq. (8.5). 

The free-electron gas was first applied to a metal by A. Sommerfeld (1928) and this application is also known as the Sommerfeld model. Although the model does not give results that are in quantitative agreement with experiments, it does predict the qualitative behavior of the electronic contribution to the heat capacity, electrical and thermal conductivity, and thermionic emission. The reason for the success of this model is that the quantum effects due to the antisymmetric character of the electronic wave function are very large and dominate the effects of the Coulombic interactions. 

Figure 9. Simulated thermal conductivity X/(t) for a Lennard-Jones fluid. The density in the center of the system is p = 0.8 and the zeroth temperature is To = 2. (a) A fluid confined between walls, with the numbers referring to the width of the fluid phase. (From Ref. 6.) (b) The case I, — 11.2 compared to the Markov (dashed) and the Onsager-Machlup (dotted) prediction.

An approximate relationship that is sometimes useful in predicting effective thermal conductivities is the geometric average value discussed by Woodside and Messmer (53). 

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