Thermal Conductivity and Diffusion

Actual temperatures in practical flames are lower than calculated values as a result of the heat losses by radiation, thermal conduction, and diffusion. At high temperatures, dissociation of products of combustion into species such as OH, O, and H reduces the theoretical flame temperature (7). Increasing the pressure tends to suppress dissociation of the products and thus generally raises the adiabatic flame temperature (4). 

The same data on physical properties of liquid refrigerants R-N (R-11, R-12, R-13, R-21, R-22, R-113) and their vapor are presented in Tables 7.3-7.8. The detailed data on thermophysical properties of different refrigerants (density, enthalpy, heat capacity, viscosity, thermal conductivity and diffusivity) are found in books by Platzer et al. (1990), Andersen (1959), and Danilova et al. (1976). 

Specific heat of each species is assumed to be the function of temperature by using JANAF [7]. Transport coefficients for the mixture gas such as viscosity, thermal conductivity, and diffusion coefficient are calculated by using the approximation formula based on the kinetic theory of gas [8]. As for the initial condition, a mixture is quiescent and its temperature and pressure are 300 K and 0.1 MPa, respectively. 

It is empirically known that a linear relation exists between a potential gradient or the force X and the conjugate flux J, and the laws of Ohm, Fourier, and Pick s first law for electrical conduction, thermal conduction, and diffusion, respectively, within a range of suitably small gradients ... 

Part AM This part lists permitted individual construction materials, applicable specifications, special requirements, design stress-intensity values, and other property information. Of particular importance are the ultrasonic-test and toughness requirements. Among the properties for which data are included are thermal conductivity and diffusivity, coefficient of thermal expansion, modulus of elasticity, and yield strength. The design stress-intensity values include a safety factor of 3 on ultimate strength at temperature or 1.5 on yield strength at temperature. 

The increased understanding of turbulence and the extension of the analysis of potential flow have made possible the consideration of many thermal and material transfer problems which formerly were not susceptible to analysis. However, at present the application of such methods is hampered by the absence of adequate information concerning the thermal conductivities and diffusion coefficients of the components of petroleum. The diffusion coefficient in particular is markedly influenced by the state of the phase. For this reason much experimental effort will be required to obtain the requisite experimental background to permit the quantitative application of the recent advances in fluid mechanics and potential theory to dynamic transfer problems of practical interest. 

Waves of chemical reaction may travel through a reaction medium, but the ideas of important stationary spatial patterns are due to Turing (1952). They were at first invoked to explain the slowly developing stripes that can be exhibited by reactions like the Belousov-Zhabotinskii reaction. This (rather mathematical) chapter sets out an analysis of the physically simplest circumstances but for a system (P - A - B + heat) with thermal feedback in which the internal transport of heat and matter are wholly controlled by molecular collision processes of thermal conductivity and diffusion. After a careful study the reader should be able to ... 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

This chapter gives an overview of the fundamental physical basis for the thermodynamic (enthalpy, entropy and heat capacity) properties of chemical species. Other chapters discuss chemical kinetics and transport properties (viscosity, thermal conductivity, and diffusion coefficients) in a similar spirit. 

It is clear that the viscosity, thermal conductivity, and diffusion coefficients transport coefficients are defined in analogous ways. They relate the gradient in velocity, temperature, or concentration to the flux of momentum, energy, or mass, respectively. Section 12.3 will present a kinetic gas theory that allows an approximate calculation of each of these coefficients, and more rigorous theories are given later in this chapter. 

The transport properties of gases arise from collisional interactions between molecules. The rigorous mathematical treatment of transport properties is very complex [35,60,103, 115,178], However, the underlying physical basis for the viscosity, thermal conductivity, and diffusion coefficient can be readily understood. This section gives a model to derive... 

Figure 17.2 shows SiFLj and SiH2 species profiles for three different surface temperatures. In all cases there is a boundary layer near the surface, which is about 0.75 cm thick. The boundary becomes a bit thicker at the higher temperatures, owing to the temperature-dependent increases in viscosity, thermal conductivity, and diffusion coefficients. The temperature and velocity boundary layers (not illustrated) are approximately the same thickness as the species boundary layers. 

S. Chapman. The Kinetic Theory of Simple and Composite Monatomic Gases Viscosity, Thermal Conductivity, and Diffusion. Proc. R. Soc. A, 98 1-20,1916. 

The role of hydroperoxy at the second limit leads directly to an explanation for the occurrence of a third limit (13, 36). The hydroperoxy radical, which is predominantly destroyed at the vessel wall at the second limit, will, at higher pressures, undergo an increasing number of collisions in the gas phase before reaching the wall. Thus, Reaction 45 may predominate in the gas phase over Reaction 44. This will result in a pressure-dependent increase in the number of chain carriers and lead to the formation of another limit, as shown in Figure 3. It is experimentally difficult to distinguish between such a third limit and a thermal explosion limit. It would be necessary to distinguish between thermal conduction and diffusion effects. 

The term thermal properties is open to more than one interpretation. Specific heat, thermal conductivity and diffusivity clearly come under this heading but the term can be taken to also include heat ageing, low temperature tests and fire resistance. However, these are more properly dealt with, as in this volume, under Effect of Temperature. Thermal analysis is a group of techniques in which a property of a sample is monitored against temperature, or time at a temperature, and, therefore, is also generally concerned with measuring the effect of temperature. Nevertheless, for convenience, a brief overview of thermal analysis is given here. 

Compared to MC, the MD technique is used more often, perhaps because it can calculate time-dependent phenomena and transport properties such as viscosity, thermal conductivity, and diffusivity, in addition to thermodynamic properties. However, Haile, (1992, p. 17) states a criterion for calculation of time-dependent... 

Steady-state periodic heating and unsteady-state methods can be applied to measure the thermal conductivity and diffusivity of coal. Methods such as the compound bar method and calorimetry have been replaced by transient hot-wire/line heat source, and transient hot plate methods that allow very rapid and independent measurements of a and X. In fact, such methods offer the additional advantage of measuring these properties not only for monolithic samples but also for coal aggregates and powders under conditions similar to those encountered in coal utilization systems. 

Comprehensive data on viscosity, thermal conductivity, and diffusion coefficients of gases and liquids are presented in convenient tabular format. 

Here, Ds and Dd are the coefficients representing the Soret and Dufour effects, respectively, Du is the self-diffusion coefficient, and Dik is the diffusion coefficient between components / and k. Equations (7.149) and (7.150) may be nonlinear because of, for example, reference frame differences, an anisotropic medium for heat and mass transfer, and temperature- and concentration-dependent thermal conductivity and diffusion coefficients. 

Example 9.2 Maximum temperature difference in the hydrogenation of benzene Consider the hydrogenation of benzene, which is exothermic with a heat of reaction 50 kcal/mol. For the catalyst pellet containing 58% Ni on Kieselguhr Harshaw (Ni-0104P), the effective thermal conductivity and diffusivity are 3.6 X 10 4cal/(cmsK) and 0.052 cm2/s, respectively. For a benzene surface concentration of 4.718 X 10-6 mol/cm3, and a surface temperature of 340 K, fromEqs. (9.18) and (9.19),... 

We shall consider in detail the predictions of the hard-sphere model for the viscosity, thermal conductivity, and diffusion of gases indeed, the kinetic theory treatment of these three transport properties is very similar. But first let us consider the simpler problem of molecular effusion. 

The thermal conductivity and diffusion coefficient of the inert gas in the arc-discharge method have profound effects on the diameter of SWNTs. It was shown that an argon atmosphere produces smaller diameter SWNTs compared to helium and the average diameter of the tubes decreases 0.2nm per 10% increase of argon in the argon-helium ratio. In situ observation of HRTEM of the growth process... 

Considep two-dimensional transient heat transfer in an L-shaped solid body that is initially at a uniform temperalure of 90°C and whose cross section is given in Fig. 5-51. The thermal conductivity and diffusivity of the body are k = 15 W/m C and a - 3.2 x 10 rriVs, respectively, and heat is generated in Ihe body at a rate of e = 2 x 10 W/m. The left sutface of the body is insulated, and the bottom surface is maintained at a uniform temperalure of 90°C at all times. A1 time f = 0, the entire top surface is subjected to convection to ambient air at = 25°C with a convection coefficient of h = 80 W/m C, and the right surface is subjected to heat flux at a uniform rate of r/p -5000 W/m. The nodal network of the problem consists of 15 equally spaced nodes vrith Ax = Ay = 1.2 cm, as shown in the figure, Five of the nodes are at the bottom surface, and thus their temperatures are known. Using the explicit method, determine the temperature at the top corner (node 3) of the body after 1,3, 5, 10, and 60 min. 

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