Density and thermal conductivity

In design considerations for Thermonized process lines, temperatures may be determined by the Stagnation Method. The calculations involved in this method are based on static conditions where process fluid flow is not present, and are independent of the viscosity, density and thermal conductivity of the process fluid. The process temperature may be calculated from the following relationship ... 

The incorporation of nanocarbons in hierarchical composites can also result in large improvements in their electrical conductivity, and to a lesser extent in their thermal conductivity. For ceramic fibers both in-plane and out-of-plane electrical conductivities are increased by several orders of magnitude [41], whereas for CF the improvement is significant only perpendicular to the fiber direction due to the already high conductivity of the fiber itself [46]. The out-of-plane electrical conductivity of CNT/CF/epoxy composites is approaching the requirements for lightning strike protection in aerospace composites, thought to be around 1 10 S/m. Yet further improvements are required, as well as the evaluation of other composite properties relevant for this application, such as maximum current density and thermal conductivity. 

The energy equation for the filling stage is for constant density and thermal conductivity as follows ... 

If one assumes that the resin has a constant density and thermal conductivity, an energy equation for the IP process can be obtained by simplifying Equation 5.41. First by using the mass balance equation (i.e., V (Ur) — 0) one of the convective heat transfer terms in the resin phase can be neglected. Another term can be neglected by setting V (Uf ) = 0. This assumption is justified since in the IP process der/dt = 0. 

Friazinov (F4) deals with a generalized Stefan problem involving finite depth of the two-phase layer, densities and thermal conductivities which are functions of position, and arbitrary initial and boundary conditions, by an approximate expansion in terms of appropriate Sturm-Liouville eigenfunctions. 

In the second edition of this volume, special attention has been paid lo improving the accuracy of the estimation techniques used for liquid heat capacity, vapor and liquid viscosity. and vapor thermal conductivity. Improved methods of extending data on liquid density and thermal conductivity have been used m this edition New experimental data has also been included. Particular attention has been paid to include new data on aqueous solution and pressure effects on physical properties... 

In a numerical solution, we can include temperature dependent density and thermal conductivity. The temperature dependent density can be modeled interpolating throughout a pvT diagram. The temperature dependence of the thermal conductivity is not always available, as is the case for many properties used in modeling. Chapter 2 presents the Tait equation, which can be used to model the pvT behavior of a polymer. 

We should note that the Navier-Stokes equation holds only for Newtonian fluids and incompressible flows. Yet this equation, together with the equation of continuity and with proper initial and boundary conditions, provides all the equations needed to solve (analytically or numerically) any laminar, isothermal flow problem. Solution of these equations yields the pressure and velocity fields that, in turn, give the stress and rate of strain fields and the flow rate. If the flow is nonisothermal, then simultaneously with the foregoing equations, we must solve the thermal energy equation, which is discussed later in this chapter. In this case, if the temperature differences are significant, we must also account for the temperature dependence of the viscosity, density, and thermal conductivity. 

Example 3 One-Dimensional, Unsteady Conduction Calculation As an example of the use of Eq. (5-21), Taole 5-1, and Table 5-2, consider the cooking time required to raise the center of a spherical, 8-cm-diameter dumpling from 20 to 80°C. The initial temperature is uniform. The dumpling is heated with saturated steam at 95°C. The heat capacity, density, and thermal conductivity are estimated to be c = 3500 J/(kg K), p = 1000 kg/m3, and k = 0.5 W/(m K), respectively. 

Two test rigs have been built for investigation of the combustion processes in a bed of solid fuels and particularly the influence of primary airflow and of particle properties (size, density and thermal conductivity) on the rate and temperature of the ignition front. Also the gas composition downstream of the bed has been investigated. The following conclusions can be drawn from the results ... 

Figures 20 and 21 show the effect of foam density on thermal conductivity. Water-blown (carbon dioxide blown) foam (Figure 20) shows a linear relationship between foam density and thermal conductivity (212). In contrast, CFC-ll-blown foam (Figure 21) shows a minimum value of thermal conductivity at a density of about 2 Ib/ft (212).

Figure 1. Initially added PSS concentration dependence of sample density and thermal conductivity. The right side ordinate (closed cirele) indicates thermal conductivity measured at room temperature. The left side ordinate (open circle) indicates sample density and packing density.

The properties of a system are those quantities such as the pressure, volume, temperature, and its composition, which are in principle measurable and capable of assuming definite values. There are of course many properties other than those mentioned above the density and thermal conductivity are two examples. However, the pressure, volume, and temperature have special significance because they determine the values of all the other properties they are therefore known asstate properties because if their values are known then the system is in a definite State. 

Following [208, 276], we assume that the heat release does not affect the physical properties of the fluid (i.e., viscosity, density, and thermal conductivity coefficient are temperature independent). In this case, the velocity profile can be found independently of the heat problem (for laminar flow, see Subsection 1.5-2). 

The density and thermal conductivity of liquids vary so little with temperature that they may be assumed constant at the following values ... 

TABLE 2.34 Density and Thermal Conductivity of Alloys (Continued)... 

System variables. Viscosity, density and thermal conductivity of the liquid, interfacial tension, diffusion coefficients, chemical reaction rate constants Operating variables. Impeller speed, gas flow rate, liquid volume, pressure Equipment variables. Impeller type and diameter, geometry of the equipment. 

The validity of (4) is further tested by the data of the present investigation using both hot and cold CO2. The agreement between the hot and cold data is considered good, since a variation in the density and thermal conductivity of the cryodeposit, or the surface temperature required for condensation, would cause differences between the experimentally determined values for the hot and cold gas. 

Question by N. G. Wilson, University of Colorado Have you been able to measure the density and thermal conductivity of the cryopumped materials ... 

---