Thermal conductivity mixtures

Effect of Addition of Inert Diluents. The addition of inert gases to an explosive mixture will have two major effects. It will increase the heat capacity of the mixture, and depending upon the nature of the added gas, it will change the mixture thermal conductivity. Equation 26 shows that an increase in the heat capacity of the mixture will tend to increase the induction period. The addition of a high thermal conductivity gas such as helium will increase the limiting pressure. Rearranging Equation 18 shows that for a given vessel diameter, reactant concentration, and furnace temperature, the ratio... 

Equilibrium constant for an ideal mixture Thermal conductivity Thermal conductivity of a mixture Latent heat of vaporisation Latent heat at normal boiling point Molecular mass (weight)... 

In an early work by Kottke and Niiler (1988), a cellular model was used to simulate the combustion wave initiation and propagation for the TH-C model system. The interactions between neighboring cells were described by the electrical circuit analogy to heat conduction. At the reaction initiation temperature (i.e., melting point of titanium), the cell is instantly converted to the product, TiC, at the adiabatic combustion temperature. The cell size was chosen to be twice as large as the Ti particles (44 /xm). Experimentally determined values for the green mixture thermal conductivity as a function of density were used in the simulations. As a result, the effects of thermal conductivity of the reactant mixture on combustion wave velocity were determined (see Fig. 21). Advani et al. (1991) used the same model, and also computed the effects of adding TiC as a diluent on the combustion velocity. 

Description The mixture thermal conductivity is calculated from the pure-component values using... 

Heat of reaction evaluated for the temperature range of interest Heat capacity (C ) of the reaction mixture Thermal conductivity of the reaction mixture... 

The third column uses Mason and Saxena method(26) for mixture thermal conductivity estimations. The fourth column gives the results for the simplified reaction model and thermal physical properties of the mixture. In this run, the first two reactions are considered in the five reaction model of Sundaram and Froment (22), Thus, the following two reaction model, given below, give reasonably accurate results. 

Table 12.4. Sample results for dense fluid mixture thermal conductivity. ...

The methods used to estimate gas mixture thermal conductivity are as follows ... 

The methods used to estimate gas mixture thermal conductivity are less accurate as compared to empirical data than those used to estimate gas mixture viscosity. Thermal conductivity is more susceptible to variations in the size of the molecules, variations in mass, concentration dependence, and temperature dependence (Singh, Dham, and Gupta, 1992). Additionally, the kinetic theory assumes a single average of the mean molecular velocities deviations from actual thermal conductivity may be accounted for in the wide spectrum of molecular velocities in a mixture (Poling, Prausnitz, and O Connell, 2001). Therefore, there is a greater expected error in HeXe gas mixture thermal conductivities than in gas mixture viscosities. 

The empirical data obtained by INL for HeXe gas mixture thermal conductivity are provided at five temperatures for several mole fractions. The temperatures are 291.2 K, 302.2 K, 311.2 K, 793.2 K, and 1500 K. The experimental data were obtained from several different researchers. As a result, the mole fractions of the various empirical data at different temperatures do not match. Therefore, it is not possible to compare the theoretical results to empirical data as a function of temperature for one mole fraction, as was done with viscosity. Because of this, Table 1 is provided to compare the various mixture methods to INL empirical data at only the mole fractions of interest (0.1 to 0.4 xenon) to Project Prometheus for the available temperatures. To show the divergence of methods at higher temperatures, Figure 6 was included for the baseline Prometheus xenon mole fraction (0.216 xenon). This graph does not benchmark against any empirical data, but is used to show divergence of methods as temperature increases. The methods used for the comparison in Figure 6 and labeled as such are as follows ... 

TABLE 1. HeXe Mixture Thermal Conductivity Comparison Results... 

HeXe gas mixture thermal conductivity estimates are not as consistent as the mixture viscosity estimates and do not compare as well to empirical data. TTie Wassiljewa formnlation and the method of Chnng were veiy inaccurate. The Chapman (DIPPR) method stayed within 5.7% of INL provided empirical data, while the Mason (DIPPR) method was less accurate. 

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